Physics and astronomy

Mathematical Methods for Physics 1

Module code: F3201
Level 4
15 credits in autumn teaching
Teaching method: Class, Practical, Lecture
Assessment modes: Coursework, Unseen examination

Topics covered include:

  1. Introduction to functions: functions and graphs;
  2. Classical functions: trigonometry, exponential and logarithmic functions, hyperbolic functions;
  3. Differentiation: standard derivatives, differentiation of composite functions;
  4. Curves and functions: stationary points, local/global minima/maxima; graph sketching;
  5. Integration: standard integrals, integration by parts and substitution, areas, volumes, averages, special integration techniques;
  6. Power series expansions: Taylor expansions, approximations, hyperbolic and trigonometric functions;
  7. Convergence of series: absolute convergence; integral test; ratio test
  8. Complex numbers: complex conjugates, complex plane, polar representation, complex algebra, exponential function, DeMoivre's Theorem;
  9. Vectors: working with vectors, scalar product of vectors, vector product of vectors;
  10. 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.