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Applied Mathematical Methods

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.

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