# Mathematics

## Calculus

Module code: G5086
Level 4
15 credits in autumn teaching
Teaching method: Lecture, Workshop
Assessment modes: Unseen examination, Coursework

Topics covered on this module include:

1. Functions of one real variable: graphical representation, inverse functions, composition of functions, polynomial, trigonometric, exponential and hyperbolic functions.
2. Limits, continuity and differentiation: one-sided limits, infinite limits, algebra of limits, continuity and the intermediate value theorem, differentiation from first principles, product rule and chain rule, Rolle's Theorem, the mean value theorem and Taylor's theorem, stationary points of a function.
3. Integration: indefinite and definite integrals, fundamental theorem of calculus, integration by parts and integration by substitution.
4. Solutions to first order ODEs.
5. Solutions to second order ODEs.

### Module learning outcomes

• Compute limits.
• Differentiate functions from first principles.
• Compute integrals using integrations by parts and substitution.
• Solve second order ordinary differential equations