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Scientific Computing for DPhil Students

Oxford University

Nick Trefethen FRS, Professor of Numerical Analysis at Oxford University, teaches a course for DPhil (PhD) students across all the science departments at the university. The course is distinctive for its exceptionally strong conceptual basis, focussing on fundamental ideas of numerical algorithms and the world of science and engineering they sustain. Historical and philosophical notes on many subjects make these lectures unusual, offering deeper understanding and new perspectives for anyone involved with numerical analysis or scientific computing.

  • 53 minutes 32 seconds
    PDEs (5.8)
    In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms?
    17 October 2016, 11:54 am
  • 50 minutes 50 seconds
    PDEs (5.7)
    In this lecture, Professor Trefethen discusses Chebyshev spectral discretization.
    17 October 2016, 11:53 am
  • 50 minutes 50 seconds
    PDEs (5.6)
    In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants
    17 October 2016, 11:52 am
  • 50 minutes 2 seconds
    PDEs (5.5)
    In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT.
    17 October 2016, 11:50 am
  • 51 minutes 10 seconds
    PDEs (5.4)
    In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions.
    17 October 2016, 11:49 am
  • 52 minutes 8 seconds
    PDEs (5.3)
    In this lecture, Professor Trefethen discusses order of accuracy and reaction-diffusion equations and other stiff PDEs.
    17 October 2016, 11:48 am
  • 49 minutes 19 seconds
    PDEs (5.2)
    In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences.
    17 October 2016, 11:47 am
  • 51 minutes 18 seconds
    PDEs (5.1)
    In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences.
    17 October 2016, 11:46 am
  • 50 minutes 50 seconds
    ODEs and Nonlinear Dynamics (4.4)
    In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun.
    17 October 2016, 11:44 am
  • 50 minutes 45 seconds
    ODEs and Nonlinear Dynamics (4.3)
    In this lecture, Professor Trefethen discusses planetary motions, chaos and Lyapunov exponents, the Lorenz equations, and lastly Sinai billiards and the SIAM 100-digit challenge.
    17 October 2016, 11:43 am
  • 49 minutes 41 seconds
    ODEs and Nonlinear Dynamics (4.2)
    In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes.
    17 October 2016, 11:41 am
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