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