﻿ PDE 2018 Lectures

# Partial Differential Equations 2018

### Mathematica and Matlab files

• Mathematica:

• Week 1:
Lecture 1: Appendix A, Three simple ODEs
Lecture 2: Chapter 1, Example of solving the heat equation
Lecture 3: Chapter 1, Parity
Lecture 3: Chapter 2, Introducing the Fourier series

Week 2:
Lecture 4: Chapter 1, "Closeness" of two function (the inner product)
Lecture 4: Chapter 1, Approximations: Using non-orthogonal basis functions
Lecture 5: Chapter 1, Approximations: Using orthogonal basis functions
Lecture 5: Chapter 2, Fourier series examples

Week 3:
Lecture 7: Chapter 2, Complex Fourier series example
Lecture 8: Chapter 4, The heat equation (Half range series)
Lecture 9: Chapter 4, The heat equation - insulated ends (Half range series)

Week 4:
Lecture 10: Chapter 4, The wave equation
Lecture 11: Chapter 4, The heat equation (Quarter range series)

Week 5:
Lecture 13: Chapter 4, Laplace's equation (Rectangular domain)
Lecture 14: Chapter 4, Laplacian derivation (Cylindrical coordinates)
Lecture 15: Chapter 4, Laplace's equation (On a disc)

Week 11:
Lecture 29: Chapter 6, Lagrange (Checking PDE)

Week 12:
Lecture 30: Chapter 9, Lagrange Polynomial Example

• Matlab:

• Week 5:
Lecture 15: Chapter 4, Laplace's equation on a disc: source code for Fig. 4.10 in the notes

Week 7:
Lecture 19: Chapter 3, Numerical Integration

Week 12:
Lecture 31: Chapter 9, The truncation error: First derivative, Second derivative
Matlab-functions you also need to save in the same folder: Our random function, First derivative (analytical), Second derivative (analytical)
Lecture 32: Chapter 9, Laplace: Rectangular domain, Semi-circular domain

• Powerpoint:

• Week 9:
Lecture 25: Chapter 6, The chain rule

Week 12:
Lecture 32: Chapter 9, Example of Laplace on a semi-circular domain

Week 13:
Lecture 33: Chapter 9, Time stepping