Scientific Computing for DPhil Students
By Oxford University
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Description
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.
| Name | Description | Released | Price | ||
|---|---|---|---|---|---|
| 1 | CleanVideoSparse Matrices and Iterative Methods (1.1) | 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 | 3 10 2016 | Free | View in iTunes |
| 2 | CleanVideoSparse Matrices and Iterative Methods (1.2) | In this lecture, Professor Trefethen discusses the topic of conjugate gradients and the convergence of CG. | 3 10 2016 | Free | View in iTunes |
| 3 | CleanVideoSparse Matrices and Iterative Methods (1.3) | In this lecture, Professor Trefethen discusses preconditioned CG and also provides examples of preconditioners | 3 10 2016 | Free | View in iTunes |
| 4 | CleanVideoSparse Matrices and Iterative Methods (1.4) | 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. | 3 10 2016 | Free | View in iTunes |
| 5 | CleanVideoDense Linear Algebra (2.1) | In this lecture, Professor Trefethen discusses matrices, vectors and expansions, including orthogonal vectors and matrices. | 3 10 2016 | Free | View in iTunes |
| 6 | CleanVideoDense Linear Algebra (2.2) | In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear least-squares. | 3 10 2016 | Free | View in iTunes |
| 7 | CleanVideoDense Linear Algebra (2.3) | In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis. | 3 10 2016 | Free | View in iTunes |
| 8 | CleanVideoDense Linear Algebra (2.4) | In this lecture, Professor Trefethen discusses matrix factorizations and SVD. | 3 10 2016 | Free | View in iTunes |
| 9 | CleanVideoDense Linear Algebra (2.5) | In this lecture, Professor Trefethen provides a demonstration of Chebfun. | 3 10 2016 | Free | View in iTunes |
| 10 | CleanVideoOptimization (3.1) | 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. | 3 10 2016 | Free | View in iTunes |
| 11 | CleanVideoOptimization (3.2) | 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. | 3 10 2016 | Free | View in iTunes |
| 12 | CleanVideoOptimization (3.3) | In this lecture, Professor Trefethen discusses NEOS and COIN-OR, constraints and linear programming, and quadratic programming and linear constraints. | 3 10 2016 | Free | View in iTunes |
| 13 | CleanVideoODEs and Nonlinear Dynamics (4.1) | 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. | 17 10 2016 | Free | View in iTunes |
| 14 | CleanVideoODEs and Nonlinear Dynamics (4.2) | In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes. | 17 10 2016 | Free | View in iTunes |
| 15 | CleanVideoODEs 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 10 2016 | Free | View in iTunes |
| 16 | CleanVideoODEs and Nonlinear Dynamics (4.4) | In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun. | 17 10 2016 | Free | View in iTunes |
| 17 | CleanVideoPDEs (5.1) | In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences. | 17 10 2016 | Free | View in iTunes |
| 18 | CleanVideoPDEs (5.2) | In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences. | 17 10 2016 | Free | View in iTunes |
| 19 | CleanVideoPDEs (5.3) | In this lecture, Professor Trefethen discusses order of accuracy and reaction-diffusion equations and other stiff PDEs. | 17 10 2016 | Free | View in iTunes |
| 20 | CleanVideoPDEs (5.4) | In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions. | 17 10 2016 | Free | View in iTunes |
| 21 | CleanVideoPDEs (5.5) | In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT. | 17 10 2016 | Free | View in iTunes |
| 22 | CleanVideoPDEs (5.6) | In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants | 17 10 2016 | Free | View in iTunes |
| 23 | CleanVideoPDEs (5.7) | In this lecture, Professor Trefethen discusses Chebyshev spectral discretization. | 17 10 2016 | Free | View in iTunes |
| 24 | CleanVideoPDEs (5.8) | In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms? | 17 10 2016 | Free | View in iTunes |
| 24 Items |
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