Applied Mathematics
MP554: Advanced Applied Mathematics for Engineers 2 (5 ECTS)
This is a follow-up on the course Advanced Applied Mathematics for Engineers 1 (new code). Topics covered include:
(i) The 1-dimensional heat equation. Introduction to Initial Value Boundary Value Problems. Solution for various boundary conditions and initial conditions.
(ii) Sturm-Liouville Systems. General properties and application to simple systems.
(iii) The 2-dimensional Laplace equation. Solution for various boundary conditions on a rectangular or rotationally symmetric region;
(iv) The Fourier Transform. Properties, the inverse transform. Application to solving the 1- dimensional heat equation on an infinite region.
(v) Finite difference methods. Application to numerically solving the 1-dimensional heat equation. Stability of numerical method
Taught in Semester(s) II. Examined in Semester(s) II.
Workload: 35 hours (24 Lecture hours, 11 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Solve the 1-dimensional heat equation subject to different boundary conditions and initial conditions.
- Prove orthogonality of eigensolutions and reality of eigenvalues of a Sturm-Liouville system.
- Apply Sturm-Liouville method to obtain the solution in simple examples.
- Solve the 2-dimensional Laplace equation subject to different boundary conditions in a rectangular or rotionally symmetric region.
- Solve the 1-dimensional heat equation on an infinite region by use of the Fourier transform.
- Solve the 1-d heat equation numerically by use of the finite difference method
Indicative Content
Partial Differential Equations; Heat Equation; Laplace Equation; Fourier Transforms; Finite Differences.
Module Resources
Advanced engineering mathematics, Erwin Kreizig (Willey)
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