Computational Projects in Applied Mathematics

Lecturer: Sheehan Olver
Time: Tuesday and Thursday, 2pm
Location: Carlsaw AGR



Lecture notes

Lecture 1: Introduction to Julia
Lecture 2: Approximating functions
Lecture 3: Decay of Fourier coefficients
Lecture 4: Convergence of Fourier series
Lecture 5: Discrete Fourier coefficients
Lecture 6: The discrete Fourier transform
Lecture 7: The fast Fourier transform
Lecture 8: The discrete Cosine transform
Lecture 9: Discrete Chebyshev series
Lecture 10: Root finding and Fourier differentiation
Lecture 11: Chebyshev differentiation
Lecture 12: Solving ODEs with Chebyshev series
Lecture 13: Second order ODEs, general orthogonal polynomials
Lecture 14: Orthogonal polynomials and Jacobi operators
Lecture 15: Variable coefficients and nonlinear ODEs
Lecture 16: Homotopy method for nonlinear ODEs
Lecture 17: Operator norms and the operator exponential
Lecture 19: Operator exponential for unbounded operators
Lecture 20: Operator exponential with boundary conditions
Lecture 22: The SVD and low rank approximation of functions
Lecture 23: Solving PDEs in squares
Lecture 24: Time evolution PDEs in squares

Lecture slides

Lecture 1: Approximating functions
Lecture 2: Quadrature
Lecture 3: Approximating Fourier series
Lecture 4: The discrete Fourier transform
Lecture 5: The fast Fourier transform
Lecture 6: Approximating Taylor series
Lecture 7: Chebyshev series
Lecture 9: Signal denoising and root finding
Lecture 10: Differentiation and integration
Lecture 11: Spectral methods
Lecture 12: Ultraspherical spectral methods
Lecture 18: Least squares
Lecture 19: QR Decomposition
Lecture 20: Singular value decomposition
Lecture 21: Computation of eigenvalues
Lecture 22: QR algorithm
Lecture 23: Linear partial differential equations

Further reading