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# pplato

## MSc Atmosphere, Ocean and Climate only

#### Maths worksheet

This maths worksheet covers 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.

#### Physics

PHYS 1: Measurement PHYS 2: Mechanics PHYSICS FLAP Topic and Modules Supporting PPLATO Resource(s) PHYS 1.1 Introducing measurement PHYS 1.2: Errors and uncertainty PHYS 1.3: Graphs and measurements PHYS 2.1: Introducing motion PHYS 2.2: Projectile motion PHYS 2.3: Forces PHYS 2.4: Work and energy PHYS 2.5: Momentum and collisions PHYS 2.6: Circular motion PHYS 2.7: Rotational mechanics PHYS 2.8: Angular momentum PHYS 3.1: Introducing fields PHYS 3.2: Gravitation and orbits PHYS 3.3: Electric charge, field and potential PHYS 4.1: DC circuits and currents PHYS 4.2: Introducing magnetism PHYS 4.3: Electromagnetic forces PHYS 4.4: Electromagnetic induction PHYS 4.5: Energy in electric and magnetic fields PHYS 5.1: Simple harmonic motion PHYS 5.2: Energy, damping and resonance PHYS 5.3: Forced vibrations and resonance PHYS 5.4: AC circuits and electrical oscillations PHYS 5.5: The mathematics of oscillations PHYS 5.6: Introducing waves PHYS 5.7: Sound – a wave phenomenon PHYS 6.1: Light â€“ a wave phenomenon PHYS 6.2: Rays and geometrical optics PHYS 6.3: Optical elements PHYS 6.4: Optical instruments PHYS 7.1: The atomic basis of matter PHYS 7.2: Temperature, pressure and the ideal gas law PHYS 7.3: Internal energy, heat and energy transfer PHYS 7.4: Specific heat, latent heat and entropy Chemistry PHYS 7.5: Kinetic theory Chemistry PHYS 7.6: Mechanical properties of matter PHYS 8.1: Introducing atoms PHYS 8.2: Atomic spectra and hydrogen PHYS 8.3: Multi-electron atoms PHYS 8.4: The periodic table and chemical bonding PHYS 9.1: Introducing atomic nuclei PHYS 9.2: Radioactive decay PHYS 9.3: Fission, fusion and radiation hazards PHYS 10.1: A particle model for light Quantum Theory PHYS 10.2: A wave model for matter Quantum Theory PHYS 10.3: Wavefunctions Quantum Theory PHYS 10.4: The Schrodinger equation PHYS 11.1: Reflection and transmission at steps and barriers PHYS 11.2: The quantum harmonic oscillator PHYS 11.3: The Schrodinger model of the hydrogen atom PHYS 11.4: Quantum physics of solids MATHEMATICS FLAP Topic and Modules Supporting PPLATO Resource(s) [Algebra: manipulation of fractions, equations and powers:] MATH 1.1: Arithmetic and algebra Maths for Science | Brackets | Fractions | Factorising | Algebraic fractions MATH 1.2: Numbers, units and physical quantities Maths for Science | Fractions | Units | Dimensional analysis | Converting units MATH 1.3: Functions and graphs Maths for Science | Functions | Straight line graphs | Quadratic function graphs | Log-log plots MATH 1.4: Solving equations Maths for Science | Simple equations | Inequalities | Simultaneous equations | Quadratic equations [Logarithms and exponentials:]MATH 1.5: Exponential and logarithmic functions Maths for Science | Powers | Logarithms MATH 1.6: Trigonometric functions Maths for Science MATH 1.7: Series expansions and approximations Power series representation | Fourier Series MATH 2.1: Introducing geometry MATH 2.2: Introducing coordinate geometry MATH 2.3: Conic sections MATH 2.4: Introducing scalars and vectors MATH 2.5: Working with vectors MATH 2.6: Scalar product of vectors MATH 2.7: Vector product of vectors Vector product MATH 2.8: Matrices and determinants Matrix multiplication MATH 3.1: Introducing complex numbers Complex numbers MATH 3.2: Polar representation of complex numbers MATH 3.3: Complex algebra and Demoivre’s theorem MATH 4.1: Introducing differentiation Introductory Differentiation MATH 4.2: Basic differentiation MATH 4.3: Further differentiation Product and Quotient Rules | Chain rule MATH 4.4: Stationary points and graph sketching Maxima and minima MATH 4.5: Taylor expansions and polynomial approximations MATH 4.6: Hyperbolic functions and differentiation MATH 4.7: Differentiation of vectors Gradients and Directional Derivatives | Div and Curl MATH 5.1: Introducing integration MATH 5.2: Basic integration Definite integration | Indefinite integration MATH 5.3: Techniques of integration Integration by parts : MATH 5.4: Applications of integration MATH 5.5: Further integration Integration of algebraic fractions | Integration of trigonometric functions MATH 5.6: Integration of Vectors MATH 6.1: Introducing differential equations MATH 6.2: Solving first-order differential equations Direct Integration | Separation of variables | Homogeneous functions | Integration factor method MATH 6.3: Solving second-order differential equations MATH 6.4: Waves and partial differential equations Waves | Bernoulli  Equations | Exact Equations

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