Scientific Computing for DPhil Students: Recent Episodes
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.
In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms?
In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants
In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT.
In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions.
In this lecture, Professor Trefethen discusses order of accuracy and reaction-diffusion equations and other stiff PDEs.
In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences.
In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences.
In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun.
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.
In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes.
In this lecture, Professor Trefethen discusses ODEs and IVPs, Runge-Kutta and multistep formulas, IVP codes in MATLAB and Simulink, and in the end reviews IVP solutions in Chebfun.
In this lecture, Professor Trefethen discusses NEOS and COIN-OR, constraints and linear programming, and quadratic programming and linear constraints.
In this lecture, Professor Trefethen discusses Newton's methods for minimizing a function of several variables. He then moves on from Newton's method to practical optimization.
In this lecture, Professor Trefethen discusses Newton's methods for 1) a single equation, 2) a system of equations, and 3) minimizing a function of 1 variable.
In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis.
In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear least-squares.
In this lecture, Professor Trefethen discusses matrices, vectors and expansions, including orthogonal vectors and matrices.
In this lecture, Professor Trefethon provides a definition of numerical analysis and provides an overview of matrix iterations, including a discussion on the Lanczos iteration. He also reviews various numerical software tools and information sources.
In this lecture, Professor Trefethen discusses preconditioned CG and also provides examples of preconditioners
In this lecture, Professor Trefethen discusses the topic of conjugate gradients and the convergence of CG.
In this lecture, Professor Trefethen first provides an overview of the field of linear algebra and optimization. Secondly, he discusses the question of how fast we can solve Ax=3Db? Thirdly, he discusses sparse matrices