Computational Science and Engineering

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  • Format: Hardcover
  • Copyright: 2007-10-01
  • Publisher: Wellesley Cambridge Pr
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Encompasses the full range of computational 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.

Table of Contents

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

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