INTRODUCTION TO APPLIED MATHEMATICS Gilbert Strang
Wellesley-Cambridge Press

TABLE OF CONTENTS       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 Theory      2. 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 Filter      3. 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 Variations      4. 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 Integration      5. 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 Transform      6. 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 Laws      7. Network Flows and Combinatorics7.1  Spanning Trees and Shortest Paths7.2  The Marriage Problem7.3  Matching Algorithms7.4  Maximal Flow in a Network      8. 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