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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 | |