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Math 420: Differential Equations

Nguồn ngoài

Math 420: Differential Equations

This text is written for students in science, engineering, and mathematics who have completed single variable calculus. This course will cover the theory and the applications of the solutions of ordinary differential equations and systems of ordinary differential equations. The course will introduce students to various topics useful in the solution of differential equations including power series, Laplace transforms, matrices, eigenvalues and eigenvectors, and numerical methods.

Mathematics
Tác giả
Ron Breitenbach
Nhà xuất bản
Cosumnes College
Nguồn
LibreTexts
Giấy phép
CC BY-NC-SA
Ngôn ngữ
EN
Danh mục
Khoa học cơ bản
Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 154 mục
  1. 01: Introduction
  2. 1.01: Basic Concepts
  3. 1.1E: Basic Concepts (Exercises)
  4. 1.02: Existence and Uniqueness of Solutions
  5. 1.2E: Existence and Uniqueness of Solutions (Exercises)
  6. 1.03: Direction Fields
  7. 1.3E: Direction Fields (Exercises)
  8. 02: First Order Equations
  9. 2.01: Separable Equations
  10. 2.1E: Separable Equations (Exercises)
  11. 2.02: Exact Equations
  12. 2.2E: Exact Equations (Exercises)
  13. 2.03: Linear First Order Equations
  14. 2.3E: Linear First Order Equations (Exercises)
  15. 2.04: Solving Differential Equations by Substitutions
  16. 2.4E: Solving Differential Equations by Substitution (Exercises)
  17. 03: Numerical Methods
  18. 3.01: Euler's Method
  19. 3.1E: Eulers Method (Exercises)
  20. 3.02: The Improved Euler Method
  21. 3.2E: The Improved Euler Method (Exercises)
  22. 3.03: The Runge-Kutta Method
  23. 3.3E: The Runge-Kutta Method (Exercises)
  24. 04: Applications of First Order Equations
  25. 4.01: Growth and Decay
  26. 4.1E: Growth and Decay (Exercises)
  27. 4.02: Cooling and Mixing
  28. 4.2E: Cooling and Mixing (Exercises)
  29. 4.03: Elementary Mechanics
  30. 4.3E: Elementary Mechanics (Exercises)
  31. 05: Linear Second Order Equations
  32. 5.01: Homogeneous Linear Equations
  33. 5.1.01: Homogeneous Linear Equations (Exercises)
  34. 5.02: Reduction of Order
  35. 5.2.01: Reduction of Order (Exercises)
  36. 5.03: Constant Coefficient Homogeneous Equations
  37. 5.3.01: Constant Coefficient Homogeneous Equations (Exercises)
  38. 5.04: Nonhomogeneous Linear Equations
  39. 5.4.01: Nonhomgeneous Linear Equations (Exercises)
  40. 5.05: Annihilation
  41. 5.5.01: Annihilation (Exercises)
  42. 5.06: Variation of Parameters
  43. 5.6.01: Variation of Parameters (Exercises)
  44. 5.07: Cauchy-Euler Equations
  45. 5.7.01: Cauchy-Euler Equations (Exercises)
  46. 06: Applications of Linear Second Order Equations
  47. 6.01: Spring-Mass Problems (Without Damping)
  48. 6.1E: Spring-Mass Problems (Without Damping) (Exercises)
  49. 6.02: Spring-Mass Problems (With Damping)
  50. 6.2E: Spring-Mass Problems (With Damping) (Exercises)
  51. 6.03: The RLC Circuit
  52. 6.3E: The RLC Circuit (Exercises)
  53. 07: Linear Higher Order Differential Equations
  54. 7.01: Introduction to Linear Higher Order Equations
  55. 7.1.01: Introduction to Linear Higher Order Equations (Exercises)
  56. 7.02: Higher Order Homogeneous Equations
  57. 7.2.01: Higher Order Homogeneous Equations (Exercises)
  58. 7.03: Annihilation for Higher Order Equations
  59. 7.3.01: Annihilation for Higher Order Equations (Exercises)
  60. 7.04: Variation of Parameters for Higher Order Equations
  61. 7.4.01: Variation of Parameters for Higher Order Equations (Exercises)
  62. 08: Series Solutions of Linear Second Order Equations
  63. 8.01: Prelude to Series Solutions of Linear Second Order Equations
  64. 8.02: Review of Power Series
  65. 8.2.01: Review of Power Series (Exercises)
  66. 8.03: Series Solutions Near an Ordinary Point
  67. 8.3.01: Series Solutions Near an Ordinary Point (Exercises)
  68. 8.04: Series Solutions Near a Regular Singular Point
  69. 8.4.01: Series Solutions near a Regular Singular Point (Exercises)
  70. 09: Laplace Transforms
  71. 9.01: Introduction to the Laplace Transform
  72. 9.1.01: Introduction to the Laplace Transform (Exercises)
  73. 9.02: The Inverse Laplace Transform
  74. 9.2.01: The Inverse Laplace Transform (Exercises)
  75. 9.03: Solution of Initial Value Problems
  76. 9.3.01: Solution of Initial Value Problems (Exercises)
  77. 9.04: The Shifting Theorems
  78. 9.4.01: The Shifting Theorems (Exercises)
  79. 9.05: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  80. 9.5.01: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  81. 9.06: Convolution
  82. 9.6.01: Convolution (Exercises)
  83. 10: Linear Systems of Differential Equations
  84. 01: Linear Systems of Differential Equations
  85. 1.01: Linear Systems of Differential Equations (Exercises)
  86. 02: Basic Theory of Homogeneous Linear Systems
  87. 2.01: Basic Theory of Homogeneous Linear Systems (Exercises)
  88. 03: Constant Coefficient Homogeneous Systems I
  89. 3.01: Constant Coefficient Homogeneous Systems I (Exercises)
  90. 04: Constant Coefficient Homogeneous Systems II
  91. 4.01: Constant Coefficient Homogeneous Systems II (Exercises)
  92. 05: Constant Coefficient Homogeneous Systems III
  93. 5.01: Constant Coefficient Homogeneous Systems III (Exercises)
  94. 06: Variation of Parameters for Nonhomogeneous Linear Systems
  95. 6.01: Variation of Parameters for Nonhomogeneous Linear Systems (Exercises)
  96. 11: Appendices
  97. 01: Functions of Several Variables
  98. 1.01: Functions of Several Variables (Exercises)
  99. 02: Partial Derivatives
  100. 2.01: Partial Derivatives (Exercises)
  101. 03: Determinants and Cramer's Rule for 2 X 2 Matrices
  102. 11.3.1: Determinants and Cramer's Rule for 2 X 2 Matrices (Exercises)
  103. 04: Determinants and Cramer's Rule for n x n Matrices
  104. 11.4.1: Determinants and Cramer's Rule for n x n Matrices (Exercises)
  105. 05: Elementary Row Operations and Gaussian Elimination
  106. 5.01: Exercises 1.3
  107. 06: Eigenvalues and Eigenvectors
  108. 6.01: Exercises 4.1
  109. 07: A Brief Table of Integrals
  110. 08: A Brief Table of Trigonometric Identities and Logarithmic Laws
  111. 12: Answers to Exercises and Index
  112. 01: Section 1.1 Answers
  113. 02: Section 1.2 Answers
  114. 03: Section 1.3 Answers
  115. 04: Section 2.1 Answers
  116. 05: Section 2.2 Answers
  117. 06: Section 2.3 Answers
  118. 07: Section 2.4 Answers
  119. 08: Section 3.1 Answers
  120. 09: Section 3.2 Answers
  121. 10: Section 3.3 Answers
  122. 11: Section 4.1 Answers
  123. 12: Section 4.2 Answers
  124. 13: Section 4.3 Answers
  125. 14: Section 5.1 Answers
  126. 15: Section 5.2 Answers
  127. 16: Section 5.3 Answers
  128. 17: Section 5.4 Answers
  129. 18: Section 5.5 Answers
  130. 19: Section 5.6 Answers
  131. 20: Section 5.7 Answers
  132. 21: Section 6.1 Answers
  133. 22: Section 6.2 Answers
  134. 23: Section 6.3 Answers
  135. 24: Section 7.1 Answers
  136. 25: Section 7.2 Answers
  137. 26: Section 7.3 Answers
  138. 27: Section 7.4 Answers
  139. 28: Section 8.2 Answers
  140. 29: Section 8.3 Answers
  141. 30: Section 8.4 Answers
  142. 31: Section 9.1 Answers
  143. 32: Section 9.2 Answers
  144. 33: Section 9.3 Answers
  145. 34: Section 9.4 Answers
  146. 35: Section 9.5 Answers
  147. 36: Section 9.6 Answers
  148. 37: Section 10.1 Answers
  149. 38: Section 10.2 Answers
  150. 39: Section 10.3 Answers
  151. 40: Section 10.4 Answers
  152. 41: Section 10.5 Answers
  153. 42: Section 10.6 Answers
  154. 43: Index