This module is not currently running in 2024 to 2025.
This module builds on MAST4014 Calculus and Differential Equations. We will cover advanced methods for solving ordinary differential equations and introduce, and learn to solve, partial differential equations. We will explore the properties of these differential equations and discuss the physical interpretation of certain equations and their solutions.
Introduction to ODEs: review of ordinary differentiation; what is an ODE; qualitative methods for ODEs; stationary points and stability.
Series methods for ODEs: solution methods for Cauchy-Euler equations; properties of power series; the Frobenius method.
Introduction to linear PDEs: review of partial differentiation; first and second order linear and partial differential equations; simple models that lead to the heat equation, Laplace's equation and the wave equation; the principle of superposition; initial and boundary conditions.
Fourier series: properties of Fourier series, derivation of coefficients, orthogonality of the Fourier basis.
Separable PDEs: The method of separation of variables; simple separable solutions of the heat equation and Laplace’s equation; examples and interpretation of solutions.
Total contact hours: 42
Private study hours: 108
Total study hours: 150
Assessment 1: (10-15 hrs) 20%
Assessment 2: (10-15 hrs) 20%
Examination: (2 hours) 60%
Reassessment methods
Like-for-like
T. Myint-U, L. Debnath, Linear Partial Differential Equations for Scientists and Engineers, Birkhäuser 2007 (online)
L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, 3rd edition, Birkhäuser 2012 (online)
E. Kreyszig, Advanced Engineering Mathematics, Wiley 2011
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes.
On successfully completing the module students will be able to:
1 demonstrate knowledge and critical understanding of the well-established principles within linear partial differential equations (PDEs);
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the
following areas: separation of variables, Fourier series, the method of characteristics;
3 apply the concepts and principles in basic linear PDE methods in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate
critically the appropriateness of different tools and techniques.
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