#### Maths

- Algebra: manipulation of fractions, equations and powers
- Logarithms and exponentials
- Angles: trigonometric functions
- Spherical geometry: radius, circumference, arclength
- Forces and velocity and acceleration (section 2)
- Force diagrams
- Gradients: definition and discrete estimates
- Tangent and normal (perpendicular) vectors
- Derivatives and integrals
- Differentiation (including the product and quotient rules and chain rule) and integration
- Partial differentiation.

#### Physics

- Basic thermal physics: Boyle’s law , the ideal gas law, <a” href=”https://www.bbc.co.uk/bitesize/guides/zc9q7ty/revision/8″ target=”_blank”>diffusion and heat transfer – conduction, convection and radiation
- Basic mechanics: Newton’s laws of motion, kinetic energy and potential energy
- Technical problem solving: significant figures, estimation, orders of magnitude
- Problem solving skills: know how to translate a physical situation into a solvable problem. Have a look at these 10 steps and this video
- Linear approximations using Taylor series.

## MSc Atmosphere, Ocean and Climate only

#### Maths

- Vector calculus: gradient, divergence and curl, Green’s theorem, Stokes’ theorem, divergence theorem and <ahref=”http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceIntegrals.aspx” target=”_blank”>surface integrals
- Simple harmonic motion (sections 1 and 2 only)
- Taylor expansions
- Differentiation: separation of variables.

#### 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

- Inertial and non-inertial frames of reference
- First law of thermodynamics
- Second law of thermodynamics and entropy.