Introduction to applied mathematics / Gilbert Strang.
Editor: Wellesley, Mass. : Wellesley-Cambridge Press, c1986Descripción: ix, 758 p. : il. ; 25 cmISBN: 0961408804Otra clasificación: 00A69 Recursos en línea: Table of contents1. SYMMETRIC LINEAR SYSTEMS 1.1 Introduction [1] 1.2 Gaussian Elimination [4] 1.3 Positive Definite Matrices and A = LDLT [15] 1.4 Minimum Principles [32] 1.5 Eigenvalues and Dynamical Systems [47] 1.6 A Review of Matrix Theory [68] 2. EQUILIBRIUM EQUATIONS 2.1 A Framework for the Applications [87] 2.2 Constraints and Lagrange Multipliers [96] 2.3 Electrical Networks [110] 2.4 Structures in Equilibrium [123] 2.5 Least Squares Estimation and the Kalman Filter [137] 3. EQUILIBRIUM IN THE CONTINUOUS CASE 3.1 Introduction: One-dimensional Problems [155] 3.2 Differential Equations of Equilibrium [166] 3.3 Laplace’s Equation and Potential Flow [182] 3.4 Vector Calculus in Three Dimensions [199] 3.5 Equilibrium of Fluids and Solids [220] 3.6 Calculus of Variations [242] 4. ANALYTICAL METHODS 4.1 Fourier Series and Orthogonal Expansions [263] 4.2 Discrete Fourier Series and Convolution [290] 43 Fourier Integrals [309] 4.4 Complex Variables and Conformal Mapping [330] 45 Complex Integration [352] 5. NUMERICAL METHODS 5.1 Linear and Nonlinear Equations [367] 5.2 Orthogonalization and Eigenvalue Problems [382] 5.3 Semi-direct and Iterative Methods [403] 5.4 The Finite Element Method [428] 5.5 The Fast Fourier Transform [448] 6. INITIAL-VALUE PROBLEMS 6.1 Ordinary Differential Equations [471] 6.2 Stability and the Phase Plane and Chaos [492] 6.3 The Laplace Transform and the z-Transform [513] 6.4 The Heat Equation vs. the Wave Equation 53$ 6.5 Difference Methods for Initial-Value Problems [562] 6.6 Nonlinear Conservation Laws [587] 7. NETWORK FLOWS AND COMBINATORICS 7.1 Spanning Trees and Shortest Paths [607] 7.2 The Marriage Problem [620] 7.3 Matching Algorithms [629] 7.4 Maximal Flow in a Network [640] 7.5 The Transportation Problem [651] 8. OPTIMIZATION 8.1 Introduction to Linear Programming [665] 8.2 The Simplex Method and Karmarkar’s Method [673] 8.3 Duality in Linear Programming [692] 8.4 Saddle Points (Minimax) and Game Theory [704] 8.5 Nonlinear Optimization [718] Appendix: Software for Scientific Computing [735] References and Acknowledgements [738] Solutions to Selected Exercises [741] Index [751]
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A69 St897 (Browse shelf) | Available | A-6793 | ||||
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Bibliografía: p. [738]-739.
1. SYMMETRIC LINEAR SYSTEMS --
1.1 Introduction [1] --
1.2 Gaussian Elimination [4] --
1.3 Positive Definite Matrices and A = LDLT [15] --
1.4 Minimum Principles [32] --
1.5 Eigenvalues and Dynamical Systems [47] --
1.6 A Review of Matrix Theory [68] --
2. EQUILIBRIUM EQUATIONS --
2.1 A Framework for the Applications [87] --
2.2 Constraints and Lagrange Multipliers [96] --
2.3 Electrical Networks [110] --
2.4 Structures in Equilibrium [123] --
2.5 Least Squares Estimation and the Kalman Filter [137] --
3. EQUILIBRIUM IN THE CONTINUOUS CASE --
3.1 Introduction: One-dimensional Problems [155] --
3.2 Differential Equations of Equilibrium [166] --
3.3 Laplace’s Equation and Potential Flow [182] --
3.4 Vector Calculus in Three Dimensions [199] --
3.5 Equilibrium of Fluids and Solids [220] --
3.6 Calculus of Variations [242] --
4. ANALYTICAL METHODS --
4.1 Fourier Series and Orthogonal Expansions [263] --
4.2 Discrete Fourier Series and Convolution [290] --
43 Fourier Integrals [309] --
4.4 Complex Variables and Conformal Mapping [330] --
45 Complex Integration [352] --
5. NUMERICAL METHODS --
5.1 Linear and Nonlinear Equations [367] --
5.2 Orthogonalization and Eigenvalue Problems [382] --
5.3 Semi-direct and Iterative Methods [403] --
5.4 The Finite Element Method [428] --
5.5 The Fast Fourier Transform [448] --
6. INITIAL-VALUE PROBLEMS --
6.1 Ordinary Differential Equations [471] --
6.2 Stability and the Phase Plane and Chaos [492] --
6.3 The Laplace Transform and the z-Transform [513] --
6.4 The Heat Equation vs. the Wave Equation 53$ --
6.5 Difference Methods for Initial-Value Problems [562] --
6.6 Nonlinear Conservation Laws [587] --
7. NETWORK FLOWS AND COMBINATORICS --
7.1 Spanning Trees and Shortest Paths [607] --
7.2 The Marriage Problem [620] --
7.3 Matching Algorithms [629] --
7.4 Maximal Flow in a Network [640] --
7.5 The Transportation Problem [651] --
8. OPTIMIZATION --
8.1 Introduction to Linear Programming [665] --
8.2 The Simplex Method and Karmarkar’s Method [673] --
8.3 Duality in Linear Programming [692] --
8.4 Saddle Points (Minimax) and Game Theory [704] --
8.5 Nonlinear Optimization [718] --
Appendix: Software for Scientific Computing [735] --
References and Acknowledgements [738] --
Solutions to Selected Exercises [741] --
Index [751] --
MR, 88a:00006
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