Applied Mathematical Methods
- Bhaskar Dasgupta

Contents


  • List of Figures

  • List of Tables

  • Preface

  • Acknowledgements


  1. Preliminary Background

  2. Matrices and Linear Transformations

  3. Operational Fundamentals of Linear Algebra

  4. Systems of Linear Equations

  5. Gauss Elimination Family of Methods

  6. Special Systems and Special Methods

  7. Numerical Aspects in Linear Systems

  8. Eigenvalues and Eigenvectors

  9. Diagonalization and Similarity Transformations

  10. Jacobi and Givens Rotation Methods

  11. Householder Transformation and Tridiagonal Matrices

  12. QR Decomposition Method

  13. Eigenvalue Problem of General Matrices

  14. Singular Value Decomposition

  15. Vector Spaces: Fundamental Concepts*

  16. Topics in Multivariate Calculus

  17. Vector Analysis: Curves and Surfaces

  18. Scalar and Vector Fields

  19. Polynomial Equations

  20. Solution of Nonlinear Equations and Systems

  21. Optimization: Introduction

  22. Multivariate Optimization

  23. Methods of Nonlinear Optimization*

  24. Constrained Optimization

  25. Linear and Quadratic Programming Problems*

  26. Interpolation and Approximation

  27. Basic Methods of Numerical Integration

  28. Advanced Topics in Numerical Integration*

  29. Numerical Solution of Ordinary Differential Equations

  30. ODE Solutions: Advanced Issues

  31. Existence and Uniqueness Theory

  32. First Order Ordinary Differential Equations

  33. Second Order Linear Homogeneous ODE's

  34. Second Order Linear Non-Homogeneous ODE's

  35. Higher Order Linear ODE's

  36. Laplace Transforms

  37. ODE Systems

  38. Stability of Dynamic Systems

  39. Series Solutions and Special Functions

  40. Sturm-Liouville Theory

  41. Fourier Series and Integrals

  42. Fourier Transforms

  43. Minimax Approximation*

  44. Partial Differential Equations

  45. Analytic Functions

  46. Integrals in the Complex Plane

  47. Singularities of Complex Functions

  48. Variational Calculus*

  • Epilogue

  • Bibliography

  • Appendix A: Answers, Solution Outlines and Comments to Exercises

  • Appendix B: Basic Formulae and Results

  • Index