PDEs (5.8) 
In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms? 
Nick Trefethen 
17 October, 2016 

PDEs (5.7) 
In this lecture, Professor Trefethen discusses Chebyshev spectral discretization. 
Nick Trefethen 
17 October, 2016 

PDEs (5.6) 
In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants 
Nick Trefethen 
17 October, 2016 

PDEs (5.5) 
In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT. 
Nick Trefethen 
17 October, 2016 

PDEs (5.4) 
In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions. 
Nick Trefethen 
17 October, 2016 

PDEs (5.3) 
In this lecture, Professor Trefethen discusses order of accuracy and reactiondiffusion equations and other stiff PDEs. 
Nick Trefethen 
17 October, 2016 

PDEs (5.2) 
In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences. 
Nick Trefethen 
17 October, 2016 

PDEs (5.1) 
In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences. 
Nick Trefethen 
17 October, 2016 

ODEs and Nonlinear Dynamics (4.4) 
In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun. 
Nick Trefethen 
17 October, 2016 

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 100digit challenge. 
Nick Trefethen 
17 October, 2016 

ODEs and Nonlinear Dynamics (4.2) 
In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes. 
Nick Trefethen 
17 October, 2016 

ODEs and Nonlinear Dynamics (4.1) 
In this lecture, Professor Trefethen discusses ODEs and IVPs, RungeKutta and multistep formulas, IVP codes in MATLAB and Simulink, and in the end reviews IVP solutions in Chebfun. 
Nick Trefethen 
17 October, 2016 

Optimization (3.3) 
In this lecture, Professor Trefethen discusses NEOS and COINOR, constraints and linear programming, and quadratic programming and linear constraints. 
Nick Trefethen 
3 October, 2016 

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. 
Nick Trefethen 
3 October, 2016 

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. 
Nick Trefethen 
3 October, 2016 

Dense Linear Algebra (2.5) 
In this lecture, Professor Trefethen provides a demonstration of Chebfun. 
Nick Trefethen 
3 October, 2016 

Dense Linear Algebra (2.4) 
In this lecture, Professor Trefethen discusses matrix factorizations and SVD. 
Nick Trefethen 
3 October, 2016 

Dense Linear Algebra (2.3) 
In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis. 
Nick Trefethen 
3 October, 2016 

Dense Linear Algebra (2.2) 
In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear leastsquares. 
Nick Trefethen 
3 October, 2016 

Dense Linear Algebra (2.1) 
In this lecture, Professor Trefethen discusses matrices, vectors and expansions, including orthogonal vectors and matrices. 
Nick Trefethen 
3 October, 2016 

Sparse 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. 
Nick Trefethen 
3 October, 2016 

Sparse Matrices and Iterative Methods (1.3) 
In this lecture, Professor Trefethen discusses preconditioned CG and also provides examples of preconditioners 
Nick Trefethen 
3 October, 2016 

Sparse Matrices and Iterative Methods (1.2) 
In this lecture, Professor Trefethen discusses the topic of conjugate gradients and the convergence of CG. 
Nick Trefethen 
3 October, 2016 

Sparse 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 
Nick Trefethen 
3 October, 2016 
