Computational science and engineering

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Computational science and engineering / Gilbert Strang

資料種別:: 図書
出版情報:: Wellesley, Mass. : Wellesley-Cambridge Press, c2007
形態:: xi, 716 p. ; 27 cm
著者名:: Strang, Gilbert, 1934- <DA00732202>
ISBN:: 9780961408817 [0961408812]
書誌ID:: BA88002092

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注記:

Some copies have different pagination: xi, 713 p
Some copies have different pagination: xi, 735 p. (2nd printing, 2012)
Some copies have no content of "Sampling and Aliasing"
Includes bibliographical references (p. 698-703) and index

主題:

Engineering mathematics; Numerical analysis; Science--Mathematics

言語:

英語

目次情報:

Applied Linear Algebra / 1：

Four special matrices / 1.1：

Differences, derivatives, and boundary conditions / 1.2：

Elimination leads to K = LDL^T / 1.3：

Inverses and delta functions / 1.4：

Eigenvalues and eigenvectors / 1.5：

Positive definite matrices / 1.6：

Numerical linear algebra: LU, QR, SVD / 1.7：

Best basis from the SVD / 1.8：

A Framework for Applied Mathematics / 2：

Equilibrium and the stiffness matrix / 2.1：

Oscillation by Newton's law / 2.2：

Least squares for rectangular matrices / 2.3：

Graph models and Kirchhoff's laws / 2.4：

Networks and transfer functions / 2.5：

Nonlinear problems / 2.6：

Structures in equilibrium / 2.7：

Covariances and recursive least squares / 2.8：

Graph cuts and gene clustering / 2.9：

Boundary Value Problems / 3：

Differential equations of equilibrium / 3.1：

Cubic splines and fourth order equations / 3.2：

Gradient and divergence / 3.3：

Laplace's equation / 3.4：

Finite differences and fast Poisson solvers / 3.5：

The finite element method / 3.6：

Elasticity and solid mechanics / 3.7：

Fourier Series and Integrals / 4：

Fourier series for periodic functions / 4.1：

Chebyshev, Legendre, and Bessel / 4.2：

The discrete Fourier transform and the FFT / 4.3：

Convolution and signal processing / 4.4：

Fourier integrals / 4.5：

Deconvolution and integral equations / 4.6：

Wavelets and signal processing / 4.7：

Analytic Functions / 5：

Taylor series and complex integration / 5.1：

Famous functions and great theorems / 5.2：

The Laplace transform and z-transform / 5.3：

Spectral methods of exponential accuracy / 5.4：

Initial Value Problems / 6：

Introduction / 6.1：

Finite difference methods for ODEs / 6.2：

Accuracy and stability for u_t = c u_x / 6.3：

The wave equation and staggered leapfrog / 6.4：

Diffusion, convection, and finance / 6.5：

Nonlinear flow and conservation laws / 6.6：

Fluid mechanics and Navier-Stokes / 6.7：

Level sets and fast marching / 6.8：

Solving Large Systems / 7：

Elimination with reordering / 7.1：

Iterative methods / 7.2：

Multigrid methods / 7.3：

Conjugate gradients and Krylov subspaces / 7.4：

Optimization and Minimum Principles / 8：

Two fundamental examples / 8.1：

Regularized least squares / 8.2：

Calculus of variations / 8.3：

Errors in projections and eigenvalues / 8.4：

The Saddle Point Stokes problem / 8.5：

Linear programming and duality / 8.6：

Adjoint methods in design / 8.7：

Applied Linear Algebra / 1：

Four special matrices / 1.1：

Differences, derivatives, and boundary conditions / 1.2：

Elimination leads to K = LDL^T / 1.3：

Inverses and delta functions / 1.4：

Eigenvalues and eigenvectors / 1.5：

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