# Physics and astronomy

## Mathematical Methods for Physics 1

Module code: F3201
Level 4
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.