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## Book Description

Applied Mathematical Methods covers the material vital for research in today's world and can be covered in a regular semester course. It is the consolidation of the efforts of teaching the compulsory first semester post-graduate applied mathematics course at the Department of Mechanical Engineering at IIT Kanpur for two successive years.

1. Cover
2. Title page
3. Contents
4. List of Figures
5. List of Tables
6. Preface
7. Chapter 1. Preliminary Background
8. Chapter 2. Matrices and Linear Transformations
9. Chapter 3. Operational Fundamentals of Linear Algebra
10. Chapter 4. Systems of Linear Equations
11. Chapter 5. Gauss Elimination Family of Methods
12. Chapter 6. Special Systems and Special Methods
13. Chapter 7. Numerical Aspects in Linear Systems
14. Chapter 8. Eigenvalues and Eigenvectors
15. Chapter 9. Diagonalization and Similarity Transformations
16. Chapter 10. Jacobi and Givens Rotation Methods
17. Chapter 11. Householder Transformation and Tridiagonal Matrices
18. Chapter 12. QR Decomposition Method
19. Chapter 13. Eigenvalue Problem of General Matrices
20. Chapter 14. Singular Value Decomposition
21. Chapter 15. Vector Spaces: Fundamental Concepts*
22. Chapter 16. Topics in Multivariate Calculus
23. Chapter 17. Vector Analysis: Curves and Surfaces
24. Chapter 18. Scalar and Vector Fields
25. Chapter 19. Polynomial Equations
26. Chapter 20. Solution of Nonlinear Equations and Systems
27. Chapter 21. Optimization: Introduction
28. Chapter 22. Multivariate Optimization
29. Chapter 23. Methods of Nonlinear Optimization*
30. Chapter 24. Constrained Optimization
31. Chapter 25. Linear and Quadratic Programming Problems*
32. Chapter 26. Interpolation and Approximation
33. Chapter 27. Basic Methods of Numerical Integration
34. Chapter 28. Advanced Topics in Numerical Integration*
35. Chapter 29. Numerical Solution of Ordinary Differential Equations
36. Chapter 30. ODE Solutions: Advanced Issues
37. Chapter 31. Existence and Uniqueness Theory
38. Chapter 32. First Order Ordinary Differential Equations
39. Chapter 33. Second Order Linear Homogeneous ODE’s
40. Chapter 34. Second Order Linear Non-Homogeneous ODE’s
41. Chapter 35. Higher Order Linear ODE’s
42. Chapter 36. Laplace Transforms
43. Chapter 37. ODE Systems
44. Chapter 38. Stability of Dynamic Systems
45. Chapter 39. Series Solutions and Special Functions
46. Chapter 40. Sturm-Liouville Theory
47. Chapter 41. Fourier Series and Integrals
48. Chapter 42. Fourier Transforms
49. Chapter 43. Minimax Approximation*
50. Chapter 44. Partial Differential Equations
51. Chapter 45. Analytic Functions
52. Chapter 46. Integrals in the Complex Plane
53. Chapter 47. Singularities of Complex Functions
54. Chapter 48. Variational Calculus*
55. Bibliography
56. Epilogue
57. Appendix
58. Notes
59. Acknowledgements