Introduction to Applied Mathematics

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Gilbert StrangWellesley-Cambridge Press, 1/1/1986EAN 9780961408800, ISBN10: 0961408804Hardcover, 760 pages, 23.1 x 16.5 x 4 cmLanguage: EnglishRenowned applied mathematician Gilber t Strang teaches applied mathematics with the clear explanations, examples and insights of an experienced teacher. This book progresses steadily through a range of topics from symmetric linear systems to differential equations to least squares and Kalman filtering and optimization. It clearly demonstrates the power of matrix algebra in engineering problem solving. This is an ideal book (beloved by many readers) for a first course on applied mathematics and a reference for more advanced applied mathematicians. The only prerequisite is a basic course in linear algebra.1. Symmetric Linear Systems1.1 Introduction1.2 Gaussian elimination1.3 Positive definite matrices1.4 Minimum principles1.5 Eigenvalues and dynamical systems1.6 A review of matrix theory2. Equilibrium Equations2.1 A framework for the applications2.2 Constraints and Lagrange multipliers2.3 Electrical networks2.4 Structures in equilibrium2.5 Least squares estimation and the Kalman filter3. Equilibrium in the Continuous Case3.1 One-dimensional problems3.2 Differential equations of equilibrium3.3 Laplace's equation and potential flow3.4 Vector calculus in three dimensions3.5 Equilibrium of fluids and solids3.6 Calculus of variations4. Analytical Methods4.1 Fourier series and orthogonal expansions4.2 Discrete Fourier series and convolution4.3 Fourier integrals4.4 Complex variables and conformal mapping4.5 Complex integration5. Numerical Methods5.1 Linear and nonlinear equations5.2 Orthogonalization and eigenvalue problems5.3 Semi-direct and iterative methods5.4 The finite element method5.5 The fast Fourier transform6. Initial-Value Problems6.1 Ordinary differential equations6.2 Stability and the phase plane and chaos6.3 The Laplace transform and the z-transform6.4 The heat equation vs. the wave equation6.5 Difference methods for initial-value problems6.6 Nonlinear conservation laws7. Network Flows and Combinatorics7.1 Spanning trees and shortest paths7.2 The marriage problem7.3 Matching algorithms7.4 Maximal flow in a network8. Optimization8.1 Introduction to linear programming8.2 The simplex method and Karmarkar's method8.3 Duality in linear programming8.4 Saddle points (minimax) and game theory8.5 Nonlinear optimizationSoftware for scientific computingReferences and acknowledgementsSolutions to selected exercisesIndex. Show more