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linear algebra

The Secrets of Mathematics

Oxford Mathematics 1st Year Student Lecture - Linear Algebra II

Our latest student lecture features the first lecture in the second term introductory course on Linear Algebra from leading Oxford Mathematician James Maynard.
Scientific Computing for DPhil Students
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PDEs (5.8)

In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms?
Scientific Computing for DPhil Students
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PDEs (5.7)

In this lecture, Professor Trefethen discusses Chebyshev spectral discretization.
Scientific Computing for DPhil Students
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PDEs (5.6)

In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants
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PDEs (5.5)

In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT.
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PDEs (5.4)

In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions.
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PDEs (5.3)

In this lecture, Professor Trefethen discusses order of accuracy and reaction-diffusion equations and other stiff PDEs.
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PDEs (5.2)

In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences.
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PDEs (5.1)

In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences.
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ODEs and Nonlinear Dynamics (4.4)

In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun.
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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.
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ODEs and Nonlinear Dynamics (4.2)

In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes.
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ODEs 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.
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Optimization (3.3)

In this lecture, Professor Trefethen discusses NEOS and COIN-OR, constraints and linear programming, and quadratic programming and linear constraints.
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Optimization (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.
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Optimization (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.
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Dense Linear Algebra (2.5)

In this lecture, Professor Trefethen provides a demonstration of Chebfun.
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Dense Linear Algebra (2.4)

In this lecture, Professor Trefethen discusses matrix factorizations and SVD.
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Dense Linear Algebra (2.3)

In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis.
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Dense Linear Algebra (2.2)

In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear least-squares.

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