F19AB - Applied Mathematics B

Course leader(s):

Richard Davison (Edinburgh, January)

Aims

The objective of the module is to introduce some fundamental ideas and techniques in Applied Mathematics.

Syllabus

1. Fourier Analysis (1.1 Fourier Series)

2. Partial differential equations (2.1 Introduction to PDEs, 2.2 The heat equation, 2.3 The wave equation, 2.4 Laplace's equation)

3. Calculus of variations (3.1 The Euler Lagrange equation, 3.2 Simplifications and generalisations of the Euler-Lagrange equation, 3.3 Calculus of variations with constraints)

4. Mechanics (4.1 The Lagrangian formulation of mechanics, 4.2 Conservation laws in Lagrangian mechanics, 4.3 The Hamiltonian formulation of mechanics, 4.4 Conservation laws in Hamiltonian mechanics)

Learning outcomes

By the end of the course, students should be able to do the following:

Compute Fourier series representations of functions defined on the intervals [-L,L] and [0,L].
Solve initial and boundary value problems for PDEs using the method of separation of variables.
Use the Euler-Lagrange equations to extremise integrals.
Determine the evolution of a classical mechanical system using Hamilton’s principle of least action.
Determine the evolution of a classical mechanical system using Hamilton’s equations.
Demonstrate an understanding of the relation between conservation laws and symmetries in mechanics.

Further details

Curriculum explorer: Click here

SCQF Level: 9

Credits: 15