Computational Science and Engineering

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Gilbert StrangWellesley-Cambridge Press, 11/1/2007EAN 9780961408817, ISBN10: 0961408812Hardcover, 750 pages, 25.3 x 17.7 x 3.8 cmLanguage: EnglishEncompasses the full range of comp utational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6). His experience is seen in his clear explanations, wide range of examples, and teaching method. The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provided at math.mit.edu/cse.1. Applied Linear Algebra1.1 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 algebraLU, QR, SVD1.8 Best basis from the SVD2. A Framework for Applied Mathematics2.1 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 squares2.9 Graph cuts and gene clustering3. Boundary Value Problems3.1 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 mechanics4. Fourier Series and Integrals4.1 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 processing5. Analytic Functions5.1 Taylor series and complex integration5.2 Famous functions and great theorems5.3 The Laplace transform and z-transform5.4 Spectral methods of exponential accuracy6. Initial Value Problems6.1 Introduction6.2 Finite difference methods for ODEs6.3 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 marching7. Solving Large Systems7.1 Elimination with reordering7.2 Iterative methods7.3 Multigrid methods7.4 Conjugate gradients and Krylov subspaces8. Optimization and Minimum Principles8.1 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.'Gil Strang has given the discipline of computational science and engineering its first testament in this new and comprehensive book. It surely extends Gil's long tradition of practical, wide-ranging, and insightful books that are invaluable for students, teachers, and researchers alike. If you could have only one book on a desert island, this might be it.' William Briggs, Professor of Mathematics at University of Colorado at Denver, and SIAM Vice-President for Education Show more