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Applied Linear Algebra | |
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Four special matrices | |
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Differences, derivatives, and boundary conditions | |
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Elimination leads to K = LDL^T | |
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Inverses and delta functions | |
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Eigenvalues and eigenvectors | |
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Positive definite matrices | |
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Numerical linear algebra: LU, QR, SVD | |
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Best basis from the SVD | |
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A Framework for Applied Mathematics | |
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Equilibrium and the stiffness matrix | |
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Oscillation by Newton's law | |
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Least squares for rectangular matrices | |
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Graph models and Kirchhoff's laws | |
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Networks and transfer functions | |
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Nonlinear problems | |
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Structures in equilibrium | |
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Covariances and recursive least squares | |
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Graph cuts and gene clustering | |
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Boundary Value Problems | |
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Differential equations of equilibrium | |
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Cubic splines and fourth order equations | |
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Gradient and divergence | |
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Laplace's equation | |
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Finite differences and fast Poisson solvers | |
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The finite element method | |
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Elasticity and solid mechanics | |
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Fourier Series and Integrals | |
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Fourier series for periodic functions | |
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Chebyshev, Legendre, and Bessel | |
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The discrete Fourier transform and the FFT | |
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Convolution and signal processing | |
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Fourier integrals | |
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Deconvolution and integral equations | |
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Wavelets and signal processing | |
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Analytic Functions | |
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Taylor series and complex integration | |
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Famous functions and great theorems | |
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The Laplace transform and z-transform | |
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Spectral methods of exponential accuracy | |
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Initial Value Problems | |
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Introduction | |
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Finite difference methods for ODEs | |
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Accuracy and stability for u_t = c u_x | |
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The wave equation and staggered leapfrog | |
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Diffusion, convection, and finance | |
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Nonlinear flow and conservation laws | |
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Fluid mechanics and Navier-Stokes | |
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Level sets and fast marching | |
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Solving Large Systems | |
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Elimination with reordering | |
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Iterative methods | |
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Multigrid methods | |
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Conjugate gradients and Krylov subspaces | |
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Optimization and Minimum Principles | |
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Two fundamental examples | |
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Regularized least squares | |
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Calculus of variations | |
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Errors in projections and eigenvalues | |
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The Saddle Point Stokes problem | |
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Linear programming and duality | |
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Adjoint methods in design | |