Physics and astronomy
Mathematical Methods for Physics 1
Module code: F3201
15 credits in autumn teaching
Teaching method: Class, Practical, Lecture
Assessment modes: Coursework, Unseen examination
Topics covered include:
- Introduction to functions: functions and graphs;
- Classical functions: trigonometry, exponential and logarithmic functions, hyperbolic functions;
- Differentiation: standard derivatives, differentiation of composite functions;
- Curves and functions: stationary points, local/global minima/maxima; graph sketching;
- Integration: standard integrals, integration by parts and substitution, areas, volumes, averages, special integration techniques;
- Power series expansions: Taylor expansions, approximations, hyperbolic and trigonometric functions;
- Convergence of series: absolute convergence; integral test; ratio test
- Complex numbers: complex conjugates, complex plane, polar representation, complex algebra, exponential function, DeMoivre's Theorem;
- Vectors: working with vectors, scalar product of vectors, vector product of vectors;
- Determinants and matrices: definition and properties, matrices and matrix algebra, solutions of systems of linear equations.
The computer lab component of the module will introduce you to Maple.
Module learning outcomes
- A successful student should be able to: perform basic algebraic manipulations involving trigonometric, exponential, hyperbolic or logarithmic functions.
- Differentiate and integrate standard functions and products and ratios of them, sketch curves of functions, and derive the series expansions.
- Use and manipulate complex numbers and vectors, perform elementary operations with determinants and matrices.
- Use Maple to solve simple mathematical problems.