Applied Mathematical Methods

Table of contents

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
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 11
    11. Chapter 12
    12. Chapter 14
    13. Chapter 15
    14. Chapter 16
    15. Chapter 17
    16. Chapter 18
    17. Chapter 19
    18. Chapter 20
    19. Chapter 21
    20. Chapter 22
    21. Chapter 23
    22. Chapter 24
    23. Chapter 25
    24. Chapter 26
    25. Chapter 27
    26. Chapter 28
    27. Chapter 29
    28. Chapter 30
    29. Chapter 31
    30. Chapter 32
    31. Chapter 33
    32. Chapter 35
    33. Chapter 36
    34. Chapter 37
    35. Chapter 38
    36. Chapter 39
    37. Chapter 40
    38. Chapter 41
    39. Chapter 42
    40. Chapter 43
    41. Chapter 44
    42. Chapter 45
    43. Chapter 46
    44. Chapter 48
59. Acknowledgements
60. Copyright