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Department of Meteorology – University of Reading

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All three courses




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.



PHYS 1: Measurement
PHYS 1.1 Introducing measurement
PHYS 1.2: Errors and uncertainty
PHYS 1.3: Graphs and measurements
PHYS 2: Mechanics
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: Fields
PHYS 3.1: Introducing fields
PHYS 3.2: Gravitation and orbits
PHYS 3.3: Electric charge, field and potential
PHYS 4: Electricity and Magnetism
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: Vibrations and Waves
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: Light and Optics
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: Heat and Properties of Matter
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: Atoms and Molecules
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: Nuclei, Particles and Relativity
PHYS 9.1: Introducing atomic nuclei
PHYS 9.2: Radioactive decay
PHYS 9.3: Fission, fusion and radiation hazards
PHYS 10: Principles of Quantum Physics
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: Applications of Quantum Physics
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
MATH 1: Algebra, Functions and Equations
[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: Vectors and Geometry
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

Scalar product
MATH 2.7: Vector product of vectors
Vector product
MATH 2.8: Matrices and determinants
Matrix multiplication
MATH 3: Complex Numbers
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: Differentiation
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: Integration
MATH 5.1: Introducing integration
MATH 5.2: Basic integration Definite integration | Indefinite integration
MATH 5.3: Techniques of integration Integration by parts :

Integration by substitution(1) | Integration by substitution(2) | Integration by substitution(3)

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: Differential Equations
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
Bernoulli  Equations
Exact Equations

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