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| Symmetric Linear Systems | |
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| Introduction | |
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| Gaussian elimination | |
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| Positive definite matrices | |
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| Minimum principles | |
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| Eigenvalues and dynamical systems | |
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| A review of matrix theory | |
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| Equilibrium Equations | |
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| A framework for the applications | |
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| Constraints and Lagrange multipliers | |
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| Electrical networks | |
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| Structures in equilibrium | |
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| Least squares estimation and the Kalman filter | |
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| Equilibrium in the Continuous Case | |
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| One-dimensional problems | |
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| Differential equations of equilibrium | |
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| Laplace's equation and potential flow | |
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| Vector calculus in three dimensions | |
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| Equilibrium of fluids and solids | |
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| Calculus of variations | |
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| Analytical Methods | |
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| Fourier series and orthogonal expansions | |
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| Discrete Fourier series and convolution | |
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| Fourier integrals | |
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| Complex variables and conformal mapping | |
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| Complex integration | |
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| Numerical Methods | |
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| Linear and nonlinear equations | |
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| Orthogonalization and eigenvalue problems | |
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| Semi-direct and iterative methods | |
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| The finite element method | |
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| The fast Fourier transform | |
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| Initial-Value Problems | |
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| Ordinary differential equations | |
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| Stability and the phase plane and chaos | |
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| The Laplace transform and the z-transform | |
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| The heat equation vs. the wave equation | |
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| Difference methods for initial-value problems | |
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| Nonlinear conservation laws | |
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| Network Flows and Combinatorics | |
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| Spanning trees and shortest paths | |
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| The marriage problem | |
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| Matching algorithms | |
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| Maximal flow in a network | |
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| Optimization | |
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| Introduction to linear programming | |
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| The simplex method and Karmarkar's method | |
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| Duality in linear programming | |
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| Saddle points (minimax) and game theory | |
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| Nonlinear optimization | |
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| Software for scientific computing | |
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| References and acknowledgements | |
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| Solutions to selected exercises | |
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| Index | |