Mathematical Methods

by Pamini Thangarajah

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Mathematical Methods provides an introduction to vector calculus, ordinary differential equations, and partial differential equations including a variety of applications. Topics include: optimization, line and surface integrals, Green’s theorem, Stokes’ theorem, the Divergence theorem, and the theory of systems of linear differential equations.

Description from LibreTexts.

Publisher
Mount Royal University
Subjects
Mathematics
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Power Series
  7. 1.1: Power Series
  8. 1.1E: Exercises
  9. 1.2: Properties of Power Series
  10. 1.2E: Exercises
  11. 1.3: Taylor and Maclaurin Series
  12. 1.3E: Exercises
  13. 1.4: Working with Taylor Series
  14. 1.4E: Exercises
  15. 1 E: Chapter Exercises
  16. 2: Ordinary differential equations
  17. 2.1: Linear Second Order Homogeneous Equations
  18. 2.1E: Exercises
  19. 2.2: Linear Second Order Constant Coefficient Homogeneous Equations
  20. 2.2E: Exercises
  21. 2.3: Linear Second Order Nonhomogeneous Linear Equations
  22. 2.3E: Exercises
  23. 2.4: The Method of Undetermined Coefficient
  24. 2.4E: Exercises
  25. 2E: Exercises
  26. 3: Series Solutions of Linear Second order Equations
  27. 3.1: Review of Power Series
  28. 3.1E: Exercises
  29. 3.2: Series Solutions Near an Ordinary Point I
  30. 3.2E: Exercises
  31. 3.3: Series Solutions Near an Ordinary Point II
  32. 3.3E: Exercises
  33. 3.4: Regular Singular Points: Euler Equations
  34. 3.4E: Exercises
  35. 3.5: The Method of Frobenius I
  36. 3.5E: Exercises
  37. 3.6: The Method of Frobenius II
  38. 3.6E: Exercises
  39. 3.7: The Method of Frobenius III
  40. 3.7E: Exercises
  41. 4: Linear Systems of Ordinary Differential Equations (LSODE)
  42. 4.1: Introduction to Systems of Differential Equations
  43. 4.1E: Exercises
  44. 4.2: Linear Systems of Differential Equations
  45. 4.2E: Exercises
  46. 4.3: Basic Theory of Homogeneous Linear System
  47. 4.3E: Exercises
  48. 4.4: Constant Coefficient Homogeneous Systems I
  49. 4.4E: Exercises
  50. 4.5: Constant Coefficient Homogeneous Systems II
  51. 4.5E: Exercises
  52. 4.6: Constant Coefficient Homogeneous Systems III
  53. 4.6E: Exercises
  54. 4.7: Variation of Parameters for Nonhomogeneous Linear Systems
  55. 4.7E: Exercises
  56. 5: Vector-Valued Functions
  57. 5.1: Vector-Valued Functions and Space Curves
  58. 5.1E:
  59. 5.2: Calculus of Vector-Valued Functions
  60. 5.2E:
  61. 5.3: Arc Length and Curvature
  62. 5.3E: Exercises
  63. 5.4: Motion in Space
  64. 5.4E:Exercises
  65. 5E: Excercises
  66. 6: Differentiation of Functions of Several Variables
  67. 6.1: Functions of Several Variables
  68. 6.1E:
  69. 6.2: Limits and Continuity
  70. 6.2E:
  71. 6.3: Partial Derivatives
  72. 6.3E:
  73. 6.4: Tangent Planes and Linear Approximations
  74. 6.4E:Exercises
  75. 6.5: The Chain Rule for Multivariable Functions
  76. 6.5E: Exercises
  77. 6.6: Directional Derivatives and the Gradient
  78. 6.6E: Exercises
  79. 6.7: Maxima/Minima Problems
  80. 6.7E:
  81. 6.8: Lagrange Multipliers
  82. 6.8E:
  83. 6E: Chapter Review Excersies
  84. 7: Multiple Integration
  85. 7.1 :Double Integrals over Rectangular Regions
  86. 7.1E: Exercises
  87. 7.2: Double Integrals over General Regions
  88. 7.2E: Exercises
  89. 7.3: Double Integrals in Polar Coordinates
  90. 7.3E:
  91. 7.4: Triple Integrals
  92. 7.4E:
  93. 7.5: Triple Integrals in Cylindrical and Spherical Coordinates
  94. 7.5E:
  95. 7.6: Calculating Centers of Mass and Moments of Inertia
  96. 7.6E
  97. 7.7: Change of Variables in Multiple Integrals
  98. 7.7E:
  99. 7E: Chapter Review Excersies
  100. 8: Partial Differential Equations
  101. 8.1: Laplace Equations
  102. 8.2: The heat equation
  103. 8.3: Wave Equations
  104. 8E: Excercise
  105. 9: Vector Calculus
  106. 9.1: Vector Fields
  107. 9.1E: Exercises
  108. 9.2: Line Integrals
  109. 9.2E: Exercises
  110. 9.3: Conservative vector Fields
  111. 9.3E: EXERCISES
  112. 9.4: Green's Theorem
  113. 9.4E: EXERCISES
  114. 9.5: Divergence and Curl
  115. 9.5E: EXERCISES
  116. 9.6: Surface Integrals
  117. 9.6E: Exercises
  118. 9.7: Stoke's Theorem
  119. 9.7E: EXERCISES
  120. 9.8: The Divergence Theorem
  121. 9.8E: Exercises
  122. 9E: Chapter Exercises
  123. Summary Tables
  124. 3-D Coordinate Systems
  125. Summary of Convergence Tests
  126. Summary of Theorems
  127. Summary table of derivatives
  128. Summary Table Of Integrals
  129. Back Matter
  130. Index
  131. Glossary
  132. Detailed Licensing