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The School of Mathematical and Physical Sciences<\/a>,The University of Reading<\/a><\/td>\n<\/tr>\n<!—<\/p>\n\n\n\nHome<\/a><\/td>\nGlossary<\/a><\/td>\nFeedback<\/a><\/td>\nNews<\/a><\/td>\nHelp<\/a><\/td>\n<\/tr>\n<\/table>\n<\/td>\n—><!–<\/p>\n<\/td>\n–><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/p>\n<\/p>\nAll three courses<\/h2>\n\nMaths<\/h4>\n\nAlgebra<\/a>: manipulation of fractions, equations and powers<\/li>\nLogarithms and exponentials<\/a><\/li>\nAngles: trigonometric functions<\/a><\/li>\nSpherical geometry: radius<\/a>, circumference<\/a>, arclength<\/a><\/li>\nForces and velocity and acceleration<\/a> (section 2)<\/li>\nForce diagrams<\/a><\/li>\nGradients: definition and discrete estimates<\/li>\nTangent and normal (perpendicular) vectors<\/a><\/li>\nDerivatives and integrals<\/a><\/li>\nDifferentiation <\/a>(including the product and quotient rules and chain rule) and integration<\/li>\nPartial differentiation<\/a>.<\/li>\n<\/ul>\n <\/p>\nPhysics<\/h4>\n\nBasic thermal physics: Boyle’s law <\/a>, the ideal gas law<\/a>, <a” href=”https:\/\/www.bbc.co.uk\/bitesize\/guides\/zc9q7ty\/revision\/8″ target=”_blank”>diffusion and heat transfer \u2013 conduction, convection and radiation<\/a><\/li>\nBasic mechanics: Newton’s laws of motion<\/a>, kinetic energy<\/a> and potential energy<\/a><\/li>\nTechnical problem solving: significant figures<\/a>, estimation<\/a>, orders of magnitude<\/a><\/li>\nProblem solving skills: know how to translate a physical situation into a solvable problem. Have a look at these 10 steps and this video<\/a><\/li>\nLinear approximations using Taylor series<\/a>.<\/li>\n<\/ul>\nMSc Atmosphere, Ocean and Climate only<\/h2>\n\nMaths<\/h4>\n\nVector calculus: gradient<\/a>, divergence and curl<\/a>, Green’s theorem<\/a>, Stokes’ theorem<\/a>, divergence theorem<\/a> and <ahref=”http:\/\/tutorial.math.lamar.edu\/Classes\/CalcIII\/SurfaceIntegrals.aspx” target=”_blank”>surface integrals<\/li>\nSimple harmonic motion<\/a> (sections 1 and 2 only)<\/li>\nTaylor expansions<\/a><\/li>\nDifferentiation: separation of variables<\/a>.<\/li>\n<\/ul>\n <\/p>\nMaths worksheet<\/h4>\nThis maths worksheet<\/a>\u00a0covers some extra topics, such as complex numbers, and will need to be handed in near the beginning of the autumn term. It contains revision notes and exercises to be attempted so lecturers know where more help will be needed. It is available now so you can have a look at it before starting the course.<\/p>\nPhysics<\/h4>\n\nInertial<\/a> and non-inertial <\/a>frames of reference<\/li>\nFirst law of thermodynamics<\/a><\/li>\nSecond law of thermodynamics and entropy<\/a>.<\/li>\n<\/ul>\n <\/p>\n\n<\/div>\n\nIntroduction<\/h2>\nWelcome to PPLATO<\/b>, a set of resources for Physics students and educators.<\/p>\nPhysics is the branch of science concerned with the nature and properties of matter and energy, and therefore underpins many other areas of science, both theoretical and applied, and also technical subjects such as Engineering.<\/p>\nBecause Physics draws heavily on concepts and tools provided by its sister subject, Mathematics, PPLATO also includes a section devoted to relevant Mathematics topics.<\/p>\nPPLATO Resources<\/h2>\nThe PPLATO resources are listed in the table on the right, and are arranged by topic. There are two types of resource: in the left column are the Open University’s FLAP (Flexible Learning Approach to Physics) modules, whilst on the right are supplementary self-assessment modules produced by the Universities of Plymouth and Salford.<\/p>\nClick on individual topic names to reveal or hide their associated modules.<\/p>\nTo view a module click on its name.<\/p>\nFurther Information<\/h2>\nThe source material for PPLATO were originally distributed in PDF format and are still available HERE<\/b>. Please note that the Maths for Science handbook<\/b><\/a> is only available in PDF format.<\/p>\nAccess the Glossary<\/b> (which defines many of the terms used in PPLATO and contains many links between FLAP modules), and the Feedback<\/a><\/b>, News<\/a><\/b> and Help<\/a><\/b> pages. Note that these pages open in a new window.<\/p>\n <\/p>\nThe PPLATO web site is maintained by Dr Gary J Robinson at the University of Reading.<\/i><\/p>\n <\/p>\n<\/div>\n<\/p>\n<\/div>\n<\/p>\n\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/a><\/p>\n<\/p>\n\n\n<\/a>PHYSICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nPHYS 1: Measurement<\/th>\n<\/tr>\n\nPHYS 1.1 Introducing\u00a0measurement<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.2: Errors\u00a0and\u00a0uncertainty<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.3: Graphs\u00a0and\u00a0measurements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2: Mechanics<\/th>\n<\/tr>\n\nPHYS 2.1: Introducing\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.2: Projectile\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.3: Forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.4: Work\u00a0and\u00a0energy<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.5: Momentum\u00a0and\u00a0collisions<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.6: Circular motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.7: Rotational\u00a0mechanics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.8: Angular\u00a0momentum<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3: Fields<\/th>\n<\/tr>\n\nPHYS 3.1: Introducing\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.2: Gravitation\u00a0and\u00a0orbits<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.3: Electric charge,\u00a0field and\u00a0potential<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4: Electricity and Magnetism<\/th>\n<\/tr>\n\nPHYS 4.1: DC\u00a0circuits\u00a0and\u00a0currents<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.2: Introducing\u00a0magnetism<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.3: Electromagnetic\u00a0forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.4: Electromagnetic induction<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.5: Energy\u00a0in\u00a0electric and magnetic\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5: Vibrations and Waves<\/th>\n<\/tr>\n\nPHYS 5.1: Simple\u00a0harmonic\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.2: Energy,\u00a0damping and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.3: Forced\u00a0vibrations and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.4: AC circuits and electrical oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.5: The\u00a0mathematics\u00a0of\u00a0oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.6: Introducing\u00a0waves<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.7: Sound\u00a0–\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6: Light and Optics<\/th>\n<\/tr>\n\nPHYS 6.1: Light\u00a0\u00e2\u20ac\u201c\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.2: Rays and geometrical\u00a0optics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.3: Optical\u00a0elements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.4: Optical\u00a0instruments<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7: Heat and Properties of Matter<\/th>\n<\/tr>\n\nPHYS 7.1: The atomic basis of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.2: Temperature, pressure and the ideal gas law<\/span><\/a><\/td>\n\nPressure<\/span><\/td>\n<\/tr>\n\nPHYS 7.3: Internal energy, heat and energy transfer<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.4: Specific heat, latent heat and entropy<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.5: Kinetic theory<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.6: Mechanical properties of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8: Atoms and Molecules<\/th>\n<\/tr>\n\nPHYS 8.1: Introducing atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.2: Atomic spectra and hydrogen<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.3: Multi-electron atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.4: The periodic table and chemical bonding<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9: Nuclei, Particles and Relativity<\/th>\n<\/tr>\n\nPHYS 9.1: Introducing atomic nuclei<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.2: Radioactive decay<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.3: Fission, fusion and radiation hazards<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 10: Principles of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 10.1: A particle model for light<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.2: A wave model for matter<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.3: Wavefunctions<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.4: The Schrodinger equation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11: Applications of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 11.1: Reflection and transmission at steps and barriers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.2: The quantum harmonic oscillator<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.3: The Schrodinger model of the hydrogen atom<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.4: Quantum physics of solids<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n\n<\/a>MATHEMATICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nMATH 1: Algebra, Functions and Equations<\/th>\n<\/tr>\n\n[Algebra: manipulation of fractions, equations and powers:]<\/strong> MATH 1.1: Arithmetic and algebra<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> | Brackets<\/span><\/a> | Fractions<\/span><\/a> | Factorising<\/span><\/a> | Algebraic\u00a0fractions<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.2: Numbers, units and physical quantities<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/a> |\nFractions<\/span><\/a> |\nUnits<\/span><\/a> |\nDimensional\u00a0analysis<\/span><\/a> |\nConverting\u00a0units<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.3: Functions and graphs<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nFunctions<\/span> | Straight\u00a0line\u00a0graphs<\/span> |\nQuadratic\u00a0function\u00a0graphs<\/span> |\nLog-log\u00a0plots<\/span><\/td>\n<\/tr>\n\nMATH 1.4: Solving equations<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nSimple\u00a0equations<\/span> | Inequalities<\/span> | Simultaneous\u00a0equations<\/span> |\nQuadratic\u00a0equations<\/span><\/td>\n<\/tr>\n\n[Logarithms and exponentials:]<\/strong>MATH 1.5: Exponential and logarithmic functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nPowers<\/span> | Logarithms<\/span><\/td>\n<\/tr>\n\nMATH 1.6: Trigonometric functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/td>\n<\/tr>\n\nMATH 1.7: Series expansions and approximations <\/span><\/a><\/td>\nPower\u00a0series\u00a0representation<\/span> | Fourier Series<\/span><\/td>\n<\/tr>\n\nMATH 2: Vectors and Geometry<\/th>\n<\/tr>\n\nMATH 2.1: Introducing geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.2: Introducing coordinate geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.3: Conic sections<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.4: Introducing scalars and vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.5: Working with vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.6: Scalar\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n<\/p>\nScalar product<\/span><\/span><\/td>\n<\/tr>\n\nMATH 2.7: Vector\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n\nVector product<\/span><\/td>\n<\/tr>\n\nMATH 2.8: Matrices\u00a0and\u00a0determinants<\/span><\/td>\n\nMatrix multiplication<\/span><\/td>\n<\/tr>\n\nMATH 3: Complex Numbers<\/th>\n<\/tr>\n\nMATH 3.1: Introducing\u00a0complex\u00a0numbers<\/span><\/a><\/td>\nComplex\u00a0numbers<\/span><\/td>\n<\/tr>\n\nMATH 3.2: Polar\u00a0representation\u00a0of\u00a0complex\u00a0numbers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 3.3: Complex\u00a0algebra and Demoivre’s\u00a0theorem<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4: Differentiation<\/th>\n<\/tr>\n\nMATH 4.1: Introducing differentiation<\/span><\/a><\/td>\nIntroductory\u00a0Differentiation<\/span><\/td>\n<\/tr>\n\nMATH 4.2: Basic differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.3: Further differentiation<\/span><\/a><\/td>\nProduct\u00a0and\u00a0Quotient\u00a0Rules<\/span> | Chain\u00a0rule<\/span><\/td>\n<\/tr>\n\nMATH 4.4: Stationary\u00a0points and graph\u00a0sketching<\/span><\/a><\/td>\nMaxima\u00a0and\u00a0minima<\/span><\/td>\n<\/tr>\n\nMATH 4.5: Taylor\u00a0expansions and polynomial\u00a0approximations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.6: Hyperbolic\u00a0functions and differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.7: Differentiation\u00a0of\u00a0vectors<\/span><\/td>\nGradients and Directional\u00a0Derivatives<\/span> | Div\u00a0and\u00a0Curl<\/span><\/td>\n<\/tr>\n\nMATH 5: Integration<\/th>\n<\/tr>\n\nMATH 5.1: Introducing\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.2: Basic\u00a0integration<\/span><\/a><\/td>\nDefinite\u00a0integration<\/span> | Indefinite\u00a0integration<\/span><\/td>\n<\/tr>\n\nMATH 5.3: Techniques\u00a0of\u00a0integration<\/span><\/a><\/td>\nIntegration\u00a0by\u00a0parts : <\/span><\/p>\nIntegration\u00a0by\u00a0substitution(1)<\/span> | Integration\u00a0by\u00a0substitution(2)<\/span> | Integration\u00a0by\u00a0substitution(3)<\/span><\/td>\n<\/tr>\n\nMATH 5.4: Applications\u00a0of\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.5: Further\u00a0integration<\/span><\/a><\/td>\n\nIntegration of algebraic fractions<\/span> | Integration\u00a0of\u00a0trigonometric\u00a0functions<\/span><\/td>\n<\/tr>\n\nMATH 5.6: Integration of Vectors<\/span><\/td>\n<\/td>\n<\/tr>\n\nMATH 6: Differential\u00a0Equations<\/th>\n<\/tr>\n\nMATH 6.1: Introducing\u00a0differential\u00a0equations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 6.2: Solving\u00a0first-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nDirect\u00a0Integration<\/span> | Separation\u00a0of\u00a0variables<\/span> | Homogeneous\u00a0functions<\/span> | Integration\u00a0factor\u00a0method<\/span><\/td>\n<\/tr>\n\nMATH 6.3: Solving\u00a0second-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nSecond Order homogeneous differential equations<\/span><\/a> [PDF]<\/span> |<\/p>\nSecond Order Inhomogeneous differential equations<\/span>\n[PDF]<\/span><\/td>\n<\/tr>\n\nMATH 6.4: Waves and partial\u00a0differential\u00a0equations<\/span><\/td>\n\nWaves<\/span><\/a> |\nBernoulli\u00a0 Equations<\/span> |\nExact\u00a0Equations<\/span><\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/p>\n<\/p>\n
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This maths worksheet<\/a>\u00a0covers some extra topics, such as complex numbers, and will need to be handed in near the beginning of the autumn term. It contains revision notes and exercises to be attempted so lecturers know where more help will be needed. It is available now so you can have a look at it before starting the course.<\/p>\nPhysics<\/h4>\n\nInertial<\/a> and non-inertial <\/a>frames of reference<\/li>\nFirst law of thermodynamics<\/a><\/li>\nSecond law of thermodynamics and entropy<\/a>.<\/li>\n<\/ul>\n <\/p>\n\n<\/div>\n\nIntroduction<\/h2>\nWelcome to PPLATO<\/b>, a set of resources for Physics students and educators.<\/p>\nPhysics is the branch of science concerned with the nature and properties of matter and energy, and therefore underpins many other areas of science, both theoretical and applied, and also technical subjects such as Engineering.<\/p>\nBecause Physics draws heavily on concepts and tools provided by its sister subject, Mathematics, PPLATO also includes a section devoted to relevant Mathematics topics.<\/p>\nPPLATO Resources<\/h2>\nThe PPLATO resources are listed in the table on the right, and are arranged by topic. There are two types of resource: in the left column are the Open University’s FLAP (Flexible Learning Approach to Physics) modules, whilst on the right are supplementary self-assessment modules produced by the Universities of Plymouth and Salford.<\/p>\nClick on individual topic names to reveal or hide their associated modules.<\/p>\nTo view a module click on its name.<\/p>\nFurther Information<\/h2>\nThe source material for PPLATO were originally distributed in PDF format and are still available HERE<\/b>. Please note that the Maths for Science handbook<\/b><\/a> is only available in PDF format.<\/p>\nAccess the Glossary<\/b> (which defines many of the terms used in PPLATO and contains many links between FLAP modules), and the Feedback<\/a><\/b>, News<\/a><\/b> and Help<\/a><\/b> pages. Note that these pages open in a new window.<\/p>\n <\/p>\nThe PPLATO web site is maintained by Dr Gary J Robinson at the University of Reading.<\/i><\/p>\n <\/p>\n<\/div>\n<\/p>\n<\/div>\n<\/p>\n\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/a><\/p>\n<\/p>\n\n\n<\/a>PHYSICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nPHYS 1: Measurement<\/th>\n<\/tr>\n\nPHYS 1.1 Introducing\u00a0measurement<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.2: Errors\u00a0and\u00a0uncertainty<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.3: Graphs\u00a0and\u00a0measurements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2: Mechanics<\/th>\n<\/tr>\n\nPHYS 2.1: Introducing\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.2: Projectile\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.3: Forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.4: Work\u00a0and\u00a0energy<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.5: Momentum\u00a0and\u00a0collisions<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.6: Circular motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.7: Rotational\u00a0mechanics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.8: Angular\u00a0momentum<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3: Fields<\/th>\n<\/tr>\n\nPHYS 3.1: Introducing\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.2: Gravitation\u00a0and\u00a0orbits<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.3: Electric charge,\u00a0field and\u00a0potential<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4: Electricity and Magnetism<\/th>\n<\/tr>\n\nPHYS 4.1: DC\u00a0circuits\u00a0and\u00a0currents<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.2: Introducing\u00a0magnetism<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.3: Electromagnetic\u00a0forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.4: Electromagnetic induction<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.5: Energy\u00a0in\u00a0electric and magnetic\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5: Vibrations and Waves<\/th>\n<\/tr>\n\nPHYS 5.1: Simple\u00a0harmonic\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.2: Energy,\u00a0damping and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.3: Forced\u00a0vibrations and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.4: AC circuits and electrical oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.5: The\u00a0mathematics\u00a0of\u00a0oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.6: Introducing\u00a0waves<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.7: Sound\u00a0–\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6: Light and Optics<\/th>\n<\/tr>\n\nPHYS 6.1: Light\u00a0\u00e2\u20ac\u201c\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.2: Rays and geometrical\u00a0optics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.3: Optical\u00a0elements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.4: Optical\u00a0instruments<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7: Heat and Properties of Matter<\/th>\n<\/tr>\n\nPHYS 7.1: The atomic basis of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.2: Temperature, pressure and the ideal gas law<\/span><\/a><\/td>\n\nPressure<\/span><\/td>\n<\/tr>\n\nPHYS 7.3: Internal energy, heat and energy transfer<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.4: Specific heat, latent heat and entropy<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.5: Kinetic theory<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.6: Mechanical properties of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8: Atoms and Molecules<\/th>\n<\/tr>\n\nPHYS 8.1: Introducing atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.2: Atomic spectra and hydrogen<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.3: Multi-electron atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.4: The periodic table and chemical bonding<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9: Nuclei, Particles and Relativity<\/th>\n<\/tr>\n\nPHYS 9.1: Introducing atomic nuclei<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.2: Radioactive decay<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.3: Fission, fusion and radiation hazards<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 10: Principles of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 10.1: A particle model for light<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.2: A wave model for matter<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.3: Wavefunctions<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.4: The Schrodinger equation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11: Applications of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 11.1: Reflection and transmission at steps and barriers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.2: The quantum harmonic oscillator<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.3: The Schrodinger model of the hydrogen atom<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.4: Quantum physics of solids<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n\n<\/a>MATHEMATICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nMATH 1: Algebra, Functions and Equations<\/th>\n<\/tr>\n\n[Algebra: manipulation of fractions, equations and powers:]<\/strong> MATH 1.1: Arithmetic and algebra<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> | Brackets<\/span><\/a> | Fractions<\/span><\/a> | Factorising<\/span><\/a> | Algebraic\u00a0fractions<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.2: Numbers, units and physical quantities<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/a> |\nFractions<\/span><\/a> |\nUnits<\/span><\/a> |\nDimensional\u00a0analysis<\/span><\/a> |\nConverting\u00a0units<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.3: Functions and graphs<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nFunctions<\/span> | Straight\u00a0line\u00a0graphs<\/span> |\nQuadratic\u00a0function\u00a0graphs<\/span> |\nLog-log\u00a0plots<\/span><\/td>\n<\/tr>\n\nMATH 1.4: Solving equations<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nSimple\u00a0equations<\/span> | Inequalities<\/span> | Simultaneous\u00a0equations<\/span> |\nQuadratic\u00a0equations<\/span><\/td>\n<\/tr>\n\n[Logarithms and exponentials:]<\/strong>MATH 1.5: Exponential and logarithmic functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nPowers<\/span> | Logarithms<\/span><\/td>\n<\/tr>\n\nMATH 1.6: Trigonometric functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/td>\n<\/tr>\n\nMATH 1.7: Series expansions and approximations <\/span><\/a><\/td>\nPower\u00a0series\u00a0representation<\/span> | Fourier Series<\/span><\/td>\n<\/tr>\n\nMATH 2: Vectors and Geometry<\/th>\n<\/tr>\n\nMATH 2.1: Introducing geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.2: Introducing coordinate geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.3: Conic sections<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.4: Introducing scalars and vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.5: Working with vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.6: Scalar\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n<\/p>\nScalar product<\/span><\/span><\/td>\n<\/tr>\n\nMATH 2.7: Vector\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n\nVector product<\/span><\/td>\n<\/tr>\n\nMATH 2.8: Matrices\u00a0and\u00a0determinants<\/span><\/td>\n\nMatrix multiplication<\/span><\/td>\n<\/tr>\n\nMATH 3: Complex Numbers<\/th>\n<\/tr>\n\nMATH 3.1: Introducing\u00a0complex\u00a0numbers<\/span><\/a><\/td>\nComplex\u00a0numbers<\/span><\/td>\n<\/tr>\n\nMATH 3.2: Polar\u00a0representation\u00a0of\u00a0complex\u00a0numbers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 3.3: Complex\u00a0algebra and Demoivre’s\u00a0theorem<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4: Differentiation<\/th>\n<\/tr>\n\nMATH 4.1: Introducing differentiation<\/span><\/a><\/td>\nIntroductory\u00a0Differentiation<\/span><\/td>\n<\/tr>\n\nMATH 4.2: Basic differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.3: Further differentiation<\/span><\/a><\/td>\nProduct\u00a0and\u00a0Quotient\u00a0Rules<\/span> | Chain\u00a0rule<\/span><\/td>\n<\/tr>\n\nMATH 4.4: Stationary\u00a0points and graph\u00a0sketching<\/span><\/a><\/td>\nMaxima\u00a0and\u00a0minima<\/span><\/td>\n<\/tr>\n\nMATH 4.5: Taylor\u00a0expansions and polynomial\u00a0approximations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.6: Hyperbolic\u00a0functions and differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.7: Differentiation\u00a0of\u00a0vectors<\/span><\/td>\nGradients and Directional\u00a0Derivatives<\/span> | Div\u00a0and\u00a0Curl<\/span><\/td>\n<\/tr>\n\nMATH 5: Integration<\/th>\n<\/tr>\n\nMATH 5.1: Introducing\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.2: Basic\u00a0integration<\/span><\/a><\/td>\nDefinite\u00a0integration<\/span> | Indefinite\u00a0integration<\/span><\/td>\n<\/tr>\n\nMATH 5.3: Techniques\u00a0of\u00a0integration<\/span><\/a><\/td>\nIntegration\u00a0by\u00a0parts : <\/span><\/p>\nIntegration\u00a0by\u00a0substitution(1)<\/span> | Integration\u00a0by\u00a0substitution(2)<\/span> | Integration\u00a0by\u00a0substitution(3)<\/span><\/td>\n<\/tr>\n\nMATH 5.4: Applications\u00a0of\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.5: Further\u00a0integration<\/span><\/a><\/td>\n\nIntegration of algebraic fractions<\/span> | Integration\u00a0of\u00a0trigonometric\u00a0functions<\/span><\/td>\n<\/tr>\n\nMATH 5.6: Integration of Vectors<\/span><\/td>\n<\/td>\n<\/tr>\n\nMATH 6: Differential\u00a0Equations<\/th>\n<\/tr>\n\nMATH 6.1: Introducing\u00a0differential\u00a0equations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 6.2: Solving\u00a0first-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nDirect\u00a0Integration<\/span> | Separation\u00a0of\u00a0variables<\/span> | Homogeneous\u00a0functions<\/span> | Integration\u00a0factor\u00a0method<\/span><\/td>\n<\/tr>\n\nMATH 6.3: Solving\u00a0second-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nSecond Order homogeneous differential equations<\/span><\/a> [PDF]<\/span> |<\/p>\nSecond Order Inhomogeneous differential equations<\/span>\n[PDF]<\/span><\/td>\n<\/tr>\n\nMATH 6.4: Waves and partial\u00a0differential\u00a0equations<\/span><\/td>\n\nWaves<\/span><\/a> |\nBernoulli\u00a0 Equations<\/span> |\nExact\u00a0Equations<\/span><\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/p>\n<\/p>\n
Welcome to PPLATO<\/b>, a set of resources for Physics students and educators.<\/p>\n
Physics is the branch of science concerned with the nature and properties of matter and energy, and therefore underpins many other areas of science, both theoretical and applied, and also technical subjects such as Engineering.<\/p>\n
Because Physics draws heavily on concepts and tools provided by its sister subject, Mathematics, PPLATO also includes a section devoted to relevant Mathematics topics.<\/p>\n
The PPLATO resources are listed in the table on the right, and are arranged by topic. There are two types of resource: in the left column are the Open University’s FLAP (Flexible Learning Approach to Physics) modules, whilst on the right are supplementary self-assessment modules produced by the Universities of Plymouth and Salford.<\/p>\n
Click on individual topic names to reveal or hide their associated modules.<\/p>\n
To view a module click on its name.<\/p>\n
The source material for PPLATO were originally distributed in PDF format and are still available HERE<\/b>. Please note that the Maths for Science handbook<\/b><\/a> is only available in PDF format.<\/p>\nAccess the Glossary<\/b> (which defines many of the terms used in PPLATO and contains many links between FLAP modules), and the Feedback<\/a><\/b>, News<\/a><\/b> and Help<\/a><\/b> pages. Note that these pages open in a new window.<\/p>\n <\/p>\nThe PPLATO web site is maintained by Dr Gary J Robinson at the University of Reading.<\/i><\/p>\n <\/p>\n<\/div>\n<\/p>\n<\/div>\n<\/p>\n\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/a><\/p>\n<\/p>\n\n\n<\/a>PHYSICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nPHYS 1: Measurement<\/th>\n<\/tr>\n\nPHYS 1.1 Introducing\u00a0measurement<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.2: Errors\u00a0and\u00a0uncertainty<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.3: Graphs\u00a0and\u00a0measurements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2: Mechanics<\/th>\n<\/tr>\n\nPHYS 2.1: Introducing\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.2: Projectile\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.3: Forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.4: Work\u00a0and\u00a0energy<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.5: Momentum\u00a0and\u00a0collisions<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.6: Circular motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.7: Rotational\u00a0mechanics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.8: Angular\u00a0momentum<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3: Fields<\/th>\n<\/tr>\n\nPHYS 3.1: Introducing\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.2: Gravitation\u00a0and\u00a0orbits<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.3: Electric charge,\u00a0field and\u00a0potential<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4: Electricity and Magnetism<\/th>\n<\/tr>\n\nPHYS 4.1: DC\u00a0circuits\u00a0and\u00a0currents<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.2: Introducing\u00a0magnetism<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.3: Electromagnetic\u00a0forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.4: Electromagnetic induction<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.5: Energy\u00a0in\u00a0electric and magnetic\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5: Vibrations and Waves<\/th>\n<\/tr>\n\nPHYS 5.1: Simple\u00a0harmonic\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.2: Energy,\u00a0damping and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.3: Forced\u00a0vibrations and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.4: AC circuits and electrical oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.5: The\u00a0mathematics\u00a0of\u00a0oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.6: Introducing\u00a0waves<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.7: Sound\u00a0–\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6: Light and Optics<\/th>\n<\/tr>\n\nPHYS 6.1: Light\u00a0\u00e2\u20ac\u201c\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.2: Rays and geometrical\u00a0optics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.3: Optical\u00a0elements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.4: Optical\u00a0instruments<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7: Heat and Properties of Matter<\/th>\n<\/tr>\n\nPHYS 7.1: The atomic basis of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.2: Temperature, pressure and the ideal gas law<\/span><\/a><\/td>\n\nPressure<\/span><\/td>\n<\/tr>\n\nPHYS 7.3: Internal energy, heat and energy transfer<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.4: Specific heat, latent heat and entropy<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.5: Kinetic theory<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.6: Mechanical properties of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8: Atoms and Molecules<\/th>\n<\/tr>\n\nPHYS 8.1: Introducing atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.2: Atomic spectra and hydrogen<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.3: Multi-electron atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.4: The periodic table and chemical bonding<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9: Nuclei, Particles and Relativity<\/th>\n<\/tr>\n\nPHYS 9.1: Introducing atomic nuclei<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.2: Radioactive decay<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.3: Fission, fusion and radiation hazards<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 10: Principles of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 10.1: A particle model for light<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.2: A wave model for matter<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.3: Wavefunctions<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.4: The Schrodinger equation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11: Applications of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 11.1: Reflection and transmission at steps and barriers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.2: The quantum harmonic oscillator<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.3: The Schrodinger model of the hydrogen atom<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.4: Quantum physics of solids<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n\n<\/a>MATHEMATICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nMATH 1: Algebra, Functions and Equations<\/th>\n<\/tr>\n\n[Algebra: manipulation of fractions, equations and powers:]<\/strong> MATH 1.1: Arithmetic and algebra<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> | Brackets<\/span><\/a> | Fractions<\/span><\/a> | Factorising<\/span><\/a> | Algebraic\u00a0fractions<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.2: Numbers, units and physical quantities<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/a> |\nFractions<\/span><\/a> |\nUnits<\/span><\/a> |\nDimensional\u00a0analysis<\/span><\/a> |\nConverting\u00a0units<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.3: Functions and graphs<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nFunctions<\/span> | Straight\u00a0line\u00a0graphs<\/span> |\nQuadratic\u00a0function\u00a0graphs<\/span> |\nLog-log\u00a0plots<\/span><\/td>\n<\/tr>\n\nMATH 1.4: Solving equations<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nSimple\u00a0equations<\/span> | Inequalities<\/span> | Simultaneous\u00a0equations<\/span> |\nQuadratic\u00a0equations<\/span><\/td>\n<\/tr>\n\n[Logarithms and exponentials:]<\/strong>MATH 1.5: Exponential and logarithmic functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nPowers<\/span> | Logarithms<\/span><\/td>\n<\/tr>\n\nMATH 1.6: Trigonometric functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/td>\n<\/tr>\n\nMATH 1.7: Series expansions and approximations <\/span><\/a><\/td>\nPower\u00a0series\u00a0representation<\/span> | Fourier Series<\/span><\/td>\n<\/tr>\n\nMATH 2: Vectors and Geometry<\/th>\n<\/tr>\n\nMATH 2.1: Introducing geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.2: Introducing coordinate geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.3: Conic sections<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.4: Introducing scalars and vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.5: Working with vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.6: Scalar\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n<\/p>\nScalar product<\/span><\/span><\/td>\n<\/tr>\n\nMATH 2.7: Vector\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n\nVector product<\/span><\/td>\n<\/tr>\n\nMATH 2.8: Matrices\u00a0and\u00a0determinants<\/span><\/td>\n\nMatrix multiplication<\/span><\/td>\n<\/tr>\n\nMATH 3: Complex Numbers<\/th>\n<\/tr>\n\nMATH 3.1: Introducing\u00a0complex\u00a0numbers<\/span><\/a><\/td>\nComplex\u00a0numbers<\/span><\/td>\n<\/tr>\n\nMATH 3.2: Polar\u00a0representation\u00a0of\u00a0complex\u00a0numbers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 3.3: Complex\u00a0algebra and Demoivre’s\u00a0theorem<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4: Differentiation<\/th>\n<\/tr>\n\nMATH 4.1: Introducing differentiation<\/span><\/a><\/td>\nIntroductory\u00a0Differentiation<\/span><\/td>\n<\/tr>\n\nMATH 4.2: Basic differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.3: Further differentiation<\/span><\/a><\/td>\nProduct\u00a0and\u00a0Quotient\u00a0Rules<\/span> | Chain\u00a0rule<\/span><\/td>\n<\/tr>\n\nMATH 4.4: Stationary\u00a0points and graph\u00a0sketching<\/span><\/a><\/td>\nMaxima\u00a0and\u00a0minima<\/span><\/td>\n<\/tr>\n\nMATH 4.5: Taylor\u00a0expansions and polynomial\u00a0approximations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.6: Hyperbolic\u00a0functions and differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.7: Differentiation\u00a0of\u00a0vectors<\/span><\/td>\nGradients and Directional\u00a0Derivatives<\/span> | Div\u00a0and\u00a0Curl<\/span><\/td>\n<\/tr>\n\nMATH 5: Integration<\/th>\n<\/tr>\n\nMATH 5.1: Introducing\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.2: Basic\u00a0integration<\/span><\/a><\/td>\nDefinite\u00a0integration<\/span> | Indefinite\u00a0integration<\/span><\/td>\n<\/tr>\n\nMATH 5.3: Techniques\u00a0of\u00a0integration<\/span><\/a><\/td>\nIntegration\u00a0by\u00a0parts : <\/span><\/p>\nIntegration\u00a0by\u00a0substitution(1)<\/span> | Integration\u00a0by\u00a0substitution(2)<\/span> | Integration\u00a0by\u00a0substitution(3)<\/span><\/td>\n<\/tr>\n\nMATH 5.4: Applications\u00a0of\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.5: Further\u00a0integration<\/span><\/a><\/td>\n\nIntegration of algebraic fractions<\/span> | Integration\u00a0of\u00a0trigonometric\u00a0functions<\/span><\/td>\n<\/tr>\n\nMATH 5.6: Integration of Vectors<\/span><\/td>\n<\/td>\n<\/tr>\n\nMATH 6: Differential\u00a0Equations<\/th>\n<\/tr>\n\nMATH 6.1: Introducing\u00a0differential\u00a0equations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 6.2: Solving\u00a0first-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nDirect\u00a0Integration<\/span> | Separation\u00a0of\u00a0variables<\/span> | Homogeneous\u00a0functions<\/span> | Integration\u00a0factor\u00a0method<\/span><\/td>\n<\/tr>\n\nMATH 6.3: Solving\u00a0second-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nSecond Order homogeneous differential equations<\/span><\/a> [PDF]<\/span> |<\/p>\nSecond Order Inhomogeneous differential equations<\/span>\n[PDF]<\/span><\/td>\n<\/tr>\n\nMATH 6.4: Waves and partial\u00a0differential\u00a0equations<\/span><\/td>\n\nWaves<\/span><\/a> |\nBernoulli\u00a0 Equations<\/span> |\nExact\u00a0Equations<\/span><\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/p>\n<\/p>\n
Access the Glossary<\/b> (which defines many of the terms used in PPLATO and contains many links between FLAP modules), and the Feedback<\/a><\/b>, News<\/a><\/b> and Help<\/a><\/b> pages. Note that these pages open in a new window.<\/p>\n <\/p>\nThe PPLATO web site is maintained by Dr Gary J Robinson at the University of Reading.<\/i><\/p>\n <\/p>\n<\/div>\n<\/p>\n<\/div>\n<\/p>\n\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/a><\/p>\n<\/p>\n\n\n<\/a>PHYSICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nPHYS 1: Measurement<\/th>\n<\/tr>\n\nPHYS 1.1 Introducing\u00a0measurement<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.2: Errors\u00a0and\u00a0uncertainty<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.3: Graphs\u00a0and\u00a0measurements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2: Mechanics<\/th>\n<\/tr>\n\nPHYS 2.1: Introducing\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.2: Projectile\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.3: Forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.4: Work\u00a0and\u00a0energy<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.5: Momentum\u00a0and\u00a0collisions<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.6: Circular motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.7: Rotational\u00a0mechanics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.8: Angular\u00a0momentum<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3: Fields<\/th>\n<\/tr>\n\nPHYS 3.1: Introducing\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.2: Gravitation\u00a0and\u00a0orbits<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.3: Electric charge,\u00a0field and\u00a0potential<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4: Electricity and Magnetism<\/th>\n<\/tr>\n\nPHYS 4.1: DC\u00a0circuits\u00a0and\u00a0currents<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.2: Introducing\u00a0magnetism<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.3: Electromagnetic\u00a0forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.4: Electromagnetic induction<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.5: Energy\u00a0in\u00a0electric and magnetic\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5: Vibrations and Waves<\/th>\n<\/tr>\n\nPHYS 5.1: Simple\u00a0harmonic\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.2: Energy,\u00a0damping and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.3: Forced\u00a0vibrations and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.4: AC circuits and electrical oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.5: The\u00a0mathematics\u00a0of\u00a0oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.6: Introducing\u00a0waves<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.7: Sound\u00a0–\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6: Light and Optics<\/th>\n<\/tr>\n\nPHYS 6.1: Light\u00a0\u00e2\u20ac\u201c\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.2: Rays and geometrical\u00a0optics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.3: Optical\u00a0elements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.4: Optical\u00a0instruments<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7: Heat and Properties of Matter<\/th>\n<\/tr>\n\nPHYS 7.1: The atomic basis of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.2: Temperature, pressure and the ideal gas law<\/span><\/a><\/td>\n\nPressure<\/span><\/td>\n<\/tr>\n\nPHYS 7.3: Internal energy, heat and energy transfer<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.4: Specific heat, latent heat and entropy<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.5: Kinetic theory<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.6: Mechanical properties of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8: Atoms and Molecules<\/th>\n<\/tr>\n\nPHYS 8.1: Introducing atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.2: Atomic spectra and hydrogen<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.3: Multi-electron atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.4: The periodic table and chemical bonding<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9: Nuclei, Particles and Relativity<\/th>\n<\/tr>\n\nPHYS 9.1: Introducing atomic nuclei<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.2: Radioactive decay<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.3: Fission, fusion and radiation hazards<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 10: Principles of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 10.1: A particle model for light<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.2: A wave model for matter<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.3: Wavefunctions<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.4: The Schrodinger equation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11: Applications of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 11.1: Reflection and transmission at steps and barriers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.2: The quantum harmonic oscillator<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.3: The Schrodinger model of the hydrogen atom<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.4: Quantum physics of solids<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n\n<\/a>MATHEMATICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nMATH 1: Algebra, Functions and Equations<\/th>\n<\/tr>\n\n[Algebra: manipulation of fractions, equations and powers:]<\/strong> MATH 1.1: Arithmetic and algebra<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> | Brackets<\/span><\/a> | Fractions<\/span><\/a> | Factorising<\/span><\/a> | Algebraic\u00a0fractions<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.2: Numbers, units and physical quantities<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/a> |\nFractions<\/span><\/a> |\nUnits<\/span><\/a> |\nDimensional\u00a0analysis<\/span><\/a> |\nConverting\u00a0units<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.3: Functions and graphs<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nFunctions<\/span> | Straight\u00a0line\u00a0graphs<\/span> |\nQuadratic\u00a0function\u00a0graphs<\/span> |\nLog-log\u00a0plots<\/span><\/td>\n<\/tr>\n\nMATH 1.4: Solving equations<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nSimple\u00a0equations<\/span> | Inequalities<\/span> | Simultaneous\u00a0equations<\/span> |\nQuadratic\u00a0equations<\/span><\/td>\n<\/tr>\n\n[Logarithms and exponentials:]<\/strong>MATH 1.5: Exponential and logarithmic functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nPowers<\/span> | Logarithms<\/span><\/td>\n<\/tr>\n\nMATH 1.6: Trigonometric functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/td>\n<\/tr>\n\nMATH 1.7: Series expansions and approximations <\/span><\/a><\/td>\nPower\u00a0series\u00a0representation<\/span> | Fourier Series<\/span><\/td>\n<\/tr>\n\nMATH 2: Vectors and Geometry<\/th>\n<\/tr>\n\nMATH 2.1: Introducing geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.2: Introducing coordinate geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.3: Conic sections<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.4: Introducing scalars and vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.5: Working with vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.6: Scalar\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n<\/p>\nScalar product<\/span><\/span><\/td>\n<\/tr>\n\nMATH 2.7: Vector\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n\nVector product<\/span><\/td>\n<\/tr>\n\nMATH 2.8: Matrices\u00a0and\u00a0determinants<\/span><\/td>\n\nMatrix multiplication<\/span><\/td>\n<\/tr>\n\nMATH 3: Complex Numbers<\/th>\n<\/tr>\n\nMATH 3.1: Introducing\u00a0complex\u00a0numbers<\/span><\/a><\/td>\nComplex\u00a0numbers<\/span><\/td>\n<\/tr>\n\nMATH 3.2: Polar\u00a0representation\u00a0of\u00a0complex\u00a0numbers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 3.3: Complex\u00a0algebra and Demoivre’s\u00a0theorem<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4: Differentiation<\/th>\n<\/tr>\n\nMATH 4.1: Introducing differentiation<\/span><\/a><\/td>\nIntroductory\u00a0Differentiation<\/span><\/td>\n<\/tr>\n\nMATH 4.2: Basic differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.3: Further differentiation<\/span><\/a><\/td>\nProduct\u00a0and\u00a0Quotient\u00a0Rules<\/span> | Chain\u00a0rule<\/span><\/td>\n<\/tr>\n\nMATH 4.4: Stationary\u00a0points and graph\u00a0sketching<\/span><\/a><\/td>\nMaxima\u00a0and\u00a0minima<\/span><\/td>\n<\/tr>\n\nMATH 4.5: Taylor\u00a0expansions and polynomial\u00a0approximations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.6: Hyperbolic\u00a0functions and differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.7: Differentiation\u00a0of\u00a0vectors<\/span><\/td>\nGradients and Directional\u00a0Derivatives<\/span> | Div\u00a0and\u00a0Curl<\/span><\/td>\n<\/tr>\n\nMATH 5: Integration<\/th>\n<\/tr>\n\nMATH 5.1: Introducing\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.2: Basic\u00a0integration<\/span><\/a><\/td>\nDefinite\u00a0integration<\/span> | Indefinite\u00a0integration<\/span><\/td>\n<\/tr>\n\nMATH 5.3: Techniques\u00a0of\u00a0integration<\/span><\/a><\/td>\nIntegration\u00a0by\u00a0parts : <\/span><\/p>\nIntegration\u00a0by\u00a0substitution(1)<\/span> | Integration\u00a0by\u00a0substitution(2)<\/span> | Integration\u00a0by\u00a0substitution(3)<\/span><\/td>\n<\/tr>\n\nMATH 5.4: Applications\u00a0of\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.5: Further\u00a0integration<\/span><\/a><\/td>\n\nIntegration of algebraic fractions<\/span> | Integration\u00a0of\u00a0trigonometric\u00a0functions<\/span><\/td>\n<\/tr>\n\nMATH 5.6: Integration of Vectors<\/span><\/td>\n<\/td>\n<\/tr>\n\nMATH 6: Differential\u00a0Equations<\/th>\n<\/tr>\n\nMATH 6.1: Introducing\u00a0differential\u00a0equations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 6.2: Solving\u00a0first-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nDirect\u00a0Integration<\/span> | Separation\u00a0of\u00a0variables<\/span> | Homogeneous\u00a0functions<\/span> | Integration\u00a0factor\u00a0method<\/span><\/td>\n<\/tr>\n\nMATH 6.3: Solving\u00a0second-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nSecond Order homogeneous differential equations<\/span><\/a> [PDF]<\/span> |<\/p>\nSecond Order Inhomogeneous differential equations<\/span>\n[PDF]<\/span><\/td>\n<\/tr>\n\nMATH 6.4: Waves and partial\u00a0differential\u00a0equations<\/span><\/td>\n\nWaves<\/span><\/a> |\nBernoulli\u00a0 Equations<\/span> |\nExact\u00a0Equations<\/span><\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/p>\n<\/p>\n
The PPLATO web site is maintained by Dr Gary J Robinson at the University of Reading.<\/i><\/p>\n
<\/p>\n<\/div>\n
Click on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/a><\/p>\n<\/p>\n\n\n<\/a>PHYSICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nPHYS 1: Measurement<\/th>\n<\/tr>\n\nPHYS 1.1 Introducing\u00a0measurement<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.2: Errors\u00a0and\u00a0uncertainty<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 1.3: Graphs\u00a0and\u00a0measurements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2: Mechanics<\/th>\n<\/tr>\n\nPHYS 2.1: Introducing\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.2: Projectile\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.3: Forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.4: Work\u00a0and\u00a0energy<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.5: Momentum\u00a0and\u00a0collisions<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.6: Circular motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.7: Rotational\u00a0mechanics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 2.8: Angular\u00a0momentum<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3: Fields<\/th>\n<\/tr>\n\nPHYS 3.1: Introducing\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.2: Gravitation\u00a0and\u00a0orbits<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 3.3: Electric charge,\u00a0field and\u00a0potential<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4: Electricity and Magnetism<\/th>\n<\/tr>\n\nPHYS 4.1: DC\u00a0circuits\u00a0and\u00a0currents<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.2: Introducing\u00a0magnetism<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.3: Electromagnetic\u00a0forces<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.4: Electromagnetic induction<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 4.5: Energy\u00a0in\u00a0electric and magnetic\u00a0fields<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5: Vibrations and Waves<\/th>\n<\/tr>\n\nPHYS 5.1: Simple\u00a0harmonic\u00a0motion<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.2: Energy,\u00a0damping and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.3: Forced\u00a0vibrations and resonance<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.4: AC circuits and electrical oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.5: The\u00a0mathematics\u00a0of\u00a0oscillations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.6: Introducing\u00a0waves<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 5.7: Sound\u00a0–\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6: Light and Optics<\/th>\n<\/tr>\n\nPHYS 6.1: Light\u00a0\u00e2\u20ac\u201c\u00a0a\u00a0wave\u00a0phenomenon<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.2: Rays and geometrical\u00a0optics<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.3: Optical\u00a0elements<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 6.4: Optical\u00a0instruments<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7: Heat and Properties of Matter<\/th>\n<\/tr>\n\nPHYS 7.1: The atomic basis of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.2: Temperature, pressure and the ideal gas law<\/span><\/a><\/td>\n\nPressure<\/span><\/td>\n<\/tr>\n\nPHYS 7.3: Internal energy, heat and energy transfer<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 7.4: Specific heat, latent heat and entropy<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.5: Kinetic theory<\/span><\/a><\/td>\nChemistry<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 7.6: Mechanical properties of matter<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8: Atoms and Molecules<\/th>\n<\/tr>\n\nPHYS 8.1: Introducing atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.2: Atomic spectra and hydrogen<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.3: Multi-electron atoms<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 8.4: The periodic table and chemical bonding<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9: Nuclei, Particles and Relativity<\/th>\n<\/tr>\n\nPHYS 9.1: Introducing atomic nuclei<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.2: Radioactive decay<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 9.3: Fission, fusion and radiation hazards<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 10: Principles of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 10.1: A particle model for light<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.2: A wave model for matter<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.3: Wavefunctions<\/span><\/a><\/td>\nQuantum\u00a0Theory<\/span><\/a><\/td>\n<\/tr>\n\nPHYS 10.4: The Schrodinger equation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11: Applications of Quantum Physics<\/th>\n<\/tr>\n\nPHYS 11.1: Reflection and transmission at steps and barriers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.2: The quantum harmonic oscillator<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.3: The Schrodinger model of the hydrogen atom<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nPHYS 11.4: Quantum physics of solids<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n\n<\/a>MATHEMATICS<\/td>\n<\/tr>\n\nFLAP Topic and Modules<\/td>\nSupporting PPLATO Resource(s)<\/td>\n<\/tr>\n\nMATH 1: Algebra, Functions and Equations<\/th>\n<\/tr>\n\n[Algebra: manipulation of fractions, equations and powers:]<\/strong> MATH 1.1: Arithmetic and algebra<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> | Brackets<\/span><\/a> | Fractions<\/span><\/a> | Factorising<\/span><\/a> | Algebraic\u00a0fractions<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.2: Numbers, units and physical quantities<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/a> |\nFractions<\/span><\/a> |\nUnits<\/span><\/a> |\nDimensional\u00a0analysis<\/span><\/a> |\nConverting\u00a0units<\/span><\/a><\/td>\n<\/tr>\n\nMATH 1.3: Functions and graphs<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nFunctions<\/span> | Straight\u00a0line\u00a0graphs<\/span> |\nQuadratic\u00a0function\u00a0graphs<\/span> |\nLog-log\u00a0plots<\/span><\/td>\n<\/tr>\n\nMATH 1.4: Solving equations<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nSimple\u00a0equations<\/span> | Inequalities<\/span> | Simultaneous\u00a0equations<\/span> |\nQuadratic\u00a0equations<\/span><\/td>\n<\/tr>\n\n[Logarithms and exponentials:]<\/strong>MATH 1.5: Exponential and logarithmic functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span> |\nPowers<\/span> | Logarithms<\/span><\/td>\n<\/tr>\n\nMATH 1.6: Trigonometric functions<\/span><\/a><\/td>\nMaths\u00a0for\u00a0Science<\/span><\/td>\n<\/tr>\n\nMATH 1.7: Series expansions and approximations <\/span><\/a><\/td>\nPower\u00a0series\u00a0representation<\/span> | Fourier Series<\/span><\/td>\n<\/tr>\n\nMATH 2: Vectors and Geometry<\/th>\n<\/tr>\n\nMATH 2.1: Introducing geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.2: Introducing coordinate geometry<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.3: Conic sections<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.4: Introducing scalars and vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.5: Working with vectors<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 2.6: Scalar\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n<\/p>\nScalar product<\/span><\/span><\/td>\n<\/tr>\n\nMATH 2.7: Vector\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n\nVector product<\/span><\/td>\n<\/tr>\n\nMATH 2.8: Matrices\u00a0and\u00a0determinants<\/span><\/td>\n\nMatrix multiplication<\/span><\/td>\n<\/tr>\n\nMATH 3: Complex Numbers<\/th>\n<\/tr>\n\nMATH 3.1: Introducing\u00a0complex\u00a0numbers<\/span><\/a><\/td>\nComplex\u00a0numbers<\/span><\/td>\n<\/tr>\n\nMATH 3.2: Polar\u00a0representation\u00a0of\u00a0complex\u00a0numbers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 3.3: Complex\u00a0algebra and Demoivre’s\u00a0theorem<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4: Differentiation<\/th>\n<\/tr>\n\nMATH 4.1: Introducing differentiation<\/span><\/a><\/td>\nIntroductory\u00a0Differentiation<\/span><\/td>\n<\/tr>\n\nMATH 4.2: Basic differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.3: Further differentiation<\/span><\/a><\/td>\nProduct\u00a0and\u00a0Quotient\u00a0Rules<\/span> | Chain\u00a0rule<\/span><\/td>\n<\/tr>\n\nMATH 4.4: Stationary\u00a0points and graph\u00a0sketching<\/span><\/a><\/td>\nMaxima\u00a0and\u00a0minima<\/span><\/td>\n<\/tr>\n\nMATH 4.5: Taylor\u00a0expansions and polynomial\u00a0approximations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.6: Hyperbolic\u00a0functions and differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.7: Differentiation\u00a0of\u00a0vectors<\/span><\/td>\nGradients and Directional\u00a0Derivatives<\/span> | Div\u00a0and\u00a0Curl<\/span><\/td>\n<\/tr>\n\nMATH 5: Integration<\/th>\n<\/tr>\n\nMATH 5.1: Introducing\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.2: Basic\u00a0integration<\/span><\/a><\/td>\nDefinite\u00a0integration<\/span> | Indefinite\u00a0integration<\/span><\/td>\n<\/tr>\n\nMATH 5.3: Techniques\u00a0of\u00a0integration<\/span><\/a><\/td>\nIntegration\u00a0by\u00a0parts : <\/span><\/p>\nIntegration\u00a0by\u00a0substitution(1)<\/span> | Integration\u00a0by\u00a0substitution(2)<\/span> | Integration\u00a0by\u00a0substitution(3)<\/span><\/td>\n<\/tr>\n\nMATH 5.4: Applications\u00a0of\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.5: Further\u00a0integration<\/span><\/a><\/td>\n\nIntegration of algebraic fractions<\/span> | Integration\u00a0of\u00a0trigonometric\u00a0functions<\/span><\/td>\n<\/tr>\n\nMATH 5.6: Integration of Vectors<\/span><\/td>\n<\/td>\n<\/tr>\n\nMATH 6: Differential\u00a0Equations<\/th>\n<\/tr>\n\nMATH 6.1: Introducing\u00a0differential\u00a0equations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 6.2: Solving\u00a0first-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nDirect\u00a0Integration<\/span> | Separation\u00a0of\u00a0variables<\/span> | Homogeneous\u00a0functions<\/span> | Integration\u00a0factor\u00a0method<\/span><\/td>\n<\/tr>\n\nMATH 6.3: Solving\u00a0second-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nSecond Order homogeneous differential equations<\/span><\/a> [PDF]<\/span> |<\/p>\nSecond Order Inhomogeneous differential equations<\/span>\n[PDF]<\/span><\/td>\n<\/tr>\n\nMATH 6.4: Waves and partial\u00a0differential\u00a0equations<\/span><\/td>\n\nWaves<\/span><\/a> |\nBernoulli\u00a0 Equations<\/span> |\nExact\u00a0Equations<\/span><\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/p>\n<\/p>\n
<\/a><\/p>\n
Scalar product<\/span><\/span><\/td>\n<\/tr>\n\nMATH 2.7: Vector\u00a0product\u00a0of\u00a0vectors<\/span><\/a><\/td>\n\nVector product<\/span><\/td>\n<\/tr>\n\nMATH 2.8: Matrices\u00a0and\u00a0determinants<\/span><\/td>\n\nMatrix multiplication<\/span><\/td>\n<\/tr>\n\nMATH 3: Complex Numbers<\/th>\n<\/tr>\n\nMATH 3.1: Introducing\u00a0complex\u00a0numbers<\/span><\/a><\/td>\nComplex\u00a0numbers<\/span><\/td>\n<\/tr>\n\nMATH 3.2: Polar\u00a0representation\u00a0of\u00a0complex\u00a0numbers<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 3.3: Complex\u00a0algebra and Demoivre’s\u00a0theorem<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4: Differentiation<\/th>\n<\/tr>\n\nMATH 4.1: Introducing differentiation<\/span><\/a><\/td>\nIntroductory\u00a0Differentiation<\/span><\/td>\n<\/tr>\n\nMATH 4.2: Basic differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.3: Further differentiation<\/span><\/a><\/td>\nProduct\u00a0and\u00a0Quotient\u00a0Rules<\/span> | Chain\u00a0rule<\/span><\/td>\n<\/tr>\n\nMATH 4.4: Stationary\u00a0points and graph\u00a0sketching<\/span><\/a><\/td>\nMaxima\u00a0and\u00a0minima<\/span><\/td>\n<\/tr>\n\nMATH 4.5: Taylor\u00a0expansions and polynomial\u00a0approximations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.6: Hyperbolic\u00a0functions and differentiation<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 4.7: Differentiation\u00a0of\u00a0vectors<\/span><\/td>\nGradients and Directional\u00a0Derivatives<\/span> | Div\u00a0and\u00a0Curl<\/span><\/td>\n<\/tr>\n\nMATH 5: Integration<\/th>\n<\/tr>\n\nMATH 5.1: Introducing\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.2: Basic\u00a0integration<\/span><\/a><\/td>\nDefinite\u00a0integration<\/span> | Indefinite\u00a0integration<\/span><\/td>\n<\/tr>\n\nMATH 5.3: Techniques\u00a0of\u00a0integration<\/span><\/a><\/td>\nIntegration\u00a0by\u00a0parts : <\/span><\/p>\nIntegration\u00a0by\u00a0substitution(1)<\/span> | Integration\u00a0by\u00a0substitution(2)<\/span> | Integration\u00a0by\u00a0substitution(3)<\/span><\/td>\n<\/tr>\n\nMATH 5.4: Applications\u00a0of\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.5: Further\u00a0integration<\/span><\/a><\/td>\n\nIntegration of algebraic fractions<\/span> | Integration\u00a0of\u00a0trigonometric\u00a0functions<\/span><\/td>\n<\/tr>\n\nMATH 5.6: Integration of Vectors<\/span><\/td>\n<\/td>\n<\/tr>\n\nMATH 6: Differential\u00a0Equations<\/th>\n<\/tr>\n\nMATH 6.1: Introducing\u00a0differential\u00a0equations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 6.2: Solving\u00a0first-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nDirect\u00a0Integration<\/span> | Separation\u00a0of\u00a0variables<\/span> | Homogeneous\u00a0functions<\/span> | Integration\u00a0factor\u00a0method<\/span><\/td>\n<\/tr>\n\nMATH 6.3: Solving\u00a0second-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nSecond Order homogeneous differential equations<\/span><\/a> [PDF]<\/span> |<\/p>\nSecond Order Inhomogeneous differential equations<\/span>\n[PDF]<\/span><\/td>\n<\/tr>\n\nMATH 6.4: Waves and partial\u00a0differential\u00a0equations<\/span><\/td>\n\nWaves<\/span><\/a> |\nBernoulli\u00a0 Equations<\/span> |\nExact\u00a0Equations<\/span><\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/p>\n<\/p>\n
Integration\u00a0by\u00a0substitution(1)<\/span> | Integration\u00a0by\u00a0substitution(2)<\/span> | Integration\u00a0by\u00a0substitution(3)<\/span><\/td>\n<\/tr>\n\nMATH 5.4: Applications\u00a0of\u00a0integration<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 5.5: Further\u00a0integration<\/span><\/a><\/td>\n\nIntegration of algebraic fractions<\/span> | Integration\u00a0of\u00a0trigonometric\u00a0functions<\/span><\/td>\n<\/tr>\n\nMATH 5.6: Integration of Vectors<\/span><\/td>\n<\/td>\n<\/tr>\n\nMATH 6: Differential\u00a0Equations<\/th>\n<\/tr>\n\nMATH 6.1: Introducing\u00a0differential\u00a0equations<\/span><\/a><\/td>\n<\/td>\n<\/tr>\n\nMATH 6.2: Solving\u00a0first-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nDirect\u00a0Integration<\/span> | Separation\u00a0of\u00a0variables<\/span> | Homogeneous\u00a0functions<\/span> | Integration\u00a0factor\u00a0method<\/span><\/td>\n<\/tr>\n\nMATH 6.3: Solving\u00a0second-order\u00a0differential\u00a0equations<\/span><\/a><\/td>\nSecond Order homogeneous differential equations<\/span><\/a> [PDF]<\/span> |<\/p>\nSecond Order Inhomogeneous differential equations<\/span>\n[PDF]<\/span><\/td>\n<\/tr>\n\nMATH 6.4: Waves and partial\u00a0differential\u00a0equations<\/span><\/td>\n\nWaves<\/span><\/a> |\nBernoulli\u00a0 Equations<\/span> |\nExact\u00a0Equations<\/span><\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/p>\n<\/p>\n
Second Order Inhomogeneous differential equations<\/span>\n[PDF]<\/span><\/td>\n<\/tr>\n\nMATH 6.4: Waves and partial\u00a0differential\u00a0equations<\/span><\/td>\n\nWaves<\/span><\/a> |\nBernoulli\u00a0 Equations<\/span> |\nExact\u00a0Equations<\/span><\/td>\n<\/tr>\n\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nClick on a topic name to reveal or hide its modules<\/span>\nCollapse All Topics<\/span>\nExpand All Topics<\/span><\/p>\n<\/div>\n<\/p>\n<\/p>\n
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