Applied Mathematical Methods
- Bhaskar Dasgupta
Contents
- List of Figures
- List of Tables
- Preface
- Acknowledgements
- Preliminary Background
- Matrices and Linear Transformations
- Operational Fundamentals of Linear Algebra
- Systems of Linear Equations
- Gauss Elimination Family of Methods
- Special Systems and Special Methods
- Numerical Aspects in Linear Systems
- Eigenvalues and Eigenvectors
- Diagonalization and Similarity Transformations
- Jacobi and Givens Rotation Methods
- Householder Transformation and Tridiagonal Matrices
- QR Decomposition Method
- Eigenvalue Problem of General Matrices
- Singular Value Decomposition
- Vector Spaces: Fundamental Concepts*
- Topics in Multivariate Calculus
- Vector Analysis: Curves and Surfaces
- Scalar and Vector Fields
- Polynomial Equations
- Solution of Nonlinear Equations and Systems
- Optimization: Introduction
- Multivariate Optimization
- Methods of Nonlinear Optimization*
- Constrained Optimization
- Linear and Quadratic Programming Problems*
- Interpolation and Approximation
- Basic Methods of Numerical Integration
- Advanced Topics in Numerical Integration*
- Numerical Solution of Ordinary Differential Equations
- ODE Solutions: Advanced Issues
- Existence and Uniqueness Theory
- First Order Ordinary Differential Equations
- Second Order Linear Homogeneous ODE's
- Second Order Linear Non-Homogeneous ODE's
- Higher Order Linear ODE's
- Laplace Transforms
- ODE Systems
- Stability of Dynamic Systems
- Series Solutions and Special Functions
- Sturm-Liouville Theory
- Fourier Series and Integrals
- Fourier Transforms
- Minimax Approximation*
- Partial Differential Equations
- Analytic Functions
- Integrals in the Complex Plane
- Singularities of Complex Functions
- Variational Calculus*
- Epilogue
- Bibliography
- Appendix A: Answers, Solution Outlines and Comments to Exercises
- Appendix B: Basic Formulae and Results
- Index