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Computational Science and Engineering  Gilbert Strang
1   Applied Linear Algebra

1.1 Four Special Matrices1.2 Differences, Derivatives, and Boundary Conditions1.3 Elimination Leads to K = LDL^T1.4 Inverses and Delta Functions1.5 Eigenvalues and Eigenvectors1.6 Positive Definite Matrices1.7 Numerical Linear Algebra: LU, QR, SVD1.8 Best Basis from the SVD

2   A Framework for Applied Mathematics

2.1 Equilibrium and the Stiffness Matrix2.2 Oscillation by Newton's Law2.3 Least Squares for Rectangular Matrices2.4 Graph Models and Kirchhoff's Laws2.5 Networks and Transfer Functions2.6 Nonlinear Problems2.7 Structures in Equilibrium2.8 Covariances and Recursive Least Squares*2.9 Graph Cuts and Gene Clustering

3   Boundary Value Problems

3.1 Differential Equations of Equilibrium3.2 Cubic Splines and Fourth Order Equations3.3 Gradient and Divergence3.4 Laplace's Equation3.5 Finite Differences and Fast Poisson Solvers3.6 The Finite Element Method3.7 Elasticity and Solid Mechanics

4   Fourier Series and Integrals

4.1 Fourier Series for Periodic Functions4.2 Chebyshev, Legendre, and Bessel4.3 The Discrete Fourier Transform and the FFT4.4 Convolution and Signal Processing4.5 Fourier Integrals4.6 Deconvolution and Integral Equations4.7 Wavelets and Signal Processing

5   Analytic Functions

5.1 Taylor Series and Complex Integration5.2 Famous Functions and Great Theorems5.3 The Laplace Transform and z-Transform5.4 Spectral Methods of Exponential Accuracy

6   Initial Value Problems

6.1 Introduction6.2 Finite Difference Methods for ODE's6.3 Accuracy and Stability for u_t = c u_x6.4 The Wave Equation and Staggered Leapfrog6.5 Diffusion, Convection, and Finance6.6 Nonlinear Flow and Conservation Laws6.7 Fluid Mechanics and Navier-Stokes6.8 Level Sets and Fast Marching

7   Solving Large Systems

7.1 Elimination with Reordering7.2 Iterative Methods7.3 Multigrid Methods7.4 Conjugate Gradients and Krylov Subspaces

8   Optimization and Minimum Principles

8.1 Two Fundamental Examples8.2 Regularized Least Squares8.3 Calculus of Variations8.4 Errors in Projections and Eigenvalues8.5 The Saddle Point Stokes Problem8.6 Linear Programming and Duality8.7 Adjoint Methods in Design

Appendix   Linear Algebra in a Nutshell