Physics and astronomy
Mathematical Methods for Physics 1
Module code: F3201
15 credits in autumn semester
Teaching method: Class, Practical, Lecture
Assessment modes: Unseen examination, Coursework
Topics covered include:
- Introduction to functions: functions and graphs.
- Classical functions: trigonometry, exponential and logarithmic functions and hyperbolic functions.
- Differentiation: standard derivatives and the differentiation of composite functions.
- Curves and functions: stationary points, local/global minima/maxima and graph sketching.
- Integration: standard integrals, integration by parts and substitution, areas, volumes, averages and special integration techniques.
- Power series expansions: Taylor expansions, approximations, hyperbolic and trigonometric functions.
- Convergence of series: absolute convergence, integral test and ratio test.
- Complex numbers: complex conjugates, complex plane, polar representation, complex algebra, exponential function and DeMoivre's Theorem.
- Vectors: working with vectors, scalar product of vectors and vector product of vectors.
- Determinants and matrices: definition and properties, matrices and matrix algebra and solutions of systems of linear equations.
The computer lab component of the course will introduce the 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.