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Elementary Differential Equations with Boundary Values Problems

Nguồn ngoài

Elementary Differential Equations with Boundary Values Problems

This text is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

Differential EquationsMathematics
Tác giả
William F. Trench
Nhà xuất bản
Trinity University
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· 201 mục
  1. 01: Introduction
  2. 1.01: Applications Leading to Differential Equations
  3. 1.02: Basic Concepts
  4. 1.2E: Basic Concepts (Exercises)
  5. 1.03: Direction Fields for First Order Equations
  6. 1.3E: Direction Fields for First Order Equations (Exercises)
  7. 02: First Order Equations
  8. 2.01: Linear First Order Equations
  9. 2.1E: Linear First Order Equations (Exercises)
  10. 2.02: Separable Equations
  11. 2.2E: Separable Equations (Exercises)
  12. 2.03: Existence and Uniqueness of Solutions of Nonlinear Equations
  13. 2.3E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  14. 2.04: Transformation of Nonlinear Equations into Separable Equations
  15. 2.4E: Transformation of Nonlinear Equations into Separable Equations (Exercises)
  16. 2.05: Exact Equations
  17. 2.5E: Exact Equations (Exercises)
  18. 2.06: Integrating Factors
  19. 2.6E: Integrating Factors (Exercises)
  20. 03: Numerical Methods
  21. 3.01: Euler's Method
  22. 3.1E: Eulers Method (Exercises)
  23. 3.02: The Improved Euler Method and Related Methods
  24. 3.2E: The Improved Euler Method and Related Methods (Exercises)
  25. 3.03: The Runge-Kutta Method
  26. 3.3E: The Runge-Kutta Method (Exercises)
  27. 04: Applications of First Order Equations
  28. 4.01: Growth and Decay
  29. 4.1E: Growth and Decay (Exercises)
  30. 4.02: Cooling and Mixing
  31. 4.2E: Cooling and Mixing (Exercises)
  32. 4.03: Elementary Mechanics
  33. 4.3E: Elementary Mechanics (Exercises)
  34. 4.04: Autonomous Second Order Equations
  35. 4.4E: Autonomous Second Order Equations (Exercises)
  36. 4.05: Applications to Curves
  37. 4.5E: Applications to Curves (Exercises)
  38. 05: Linear Second Order Equations
  39. 5.01: Homogeneous Linear Equations
  40. 5.1E: Homogeneous Linear Equations (Exercises)
  41. 5.02: Constant Coefficient Homogeneous Equations
  42. 5.2E: Constant Coefficient Homogeneous Equations (Exercises)
  43. 5.03: Nonhomogeneous Linear Equations
  44. 5.3E: Nonhomgeneous Linear Equations (Exercises)
  45. 5.04: The Method of Undetermined Coefficients I
  46. 5.4E: The Method of Undetermined Coefficients I (Exercises)
  47. 5.05: The Method of Undetermined Coefficients II
  48. 5.5E: The Method of Undetermined Coefficients II (Exercises)
  49. 5.06: Reduction of Order
  50. 5.6E: Reduction of Order (Exercises)
  51. 5.07: Variation of Parameters
  52. 5.7E: Variation of Parameters (Exercises)
  53. 06: Applications of Linear Second Order Equations
  54. 6.01: Spring Problems I
  55. 6.1E: Spring Problems I (Exercises)
  56. 6.02: Spring Problems II
  57. 6.2E: Spring Problems II (Exercises)
  58. 6.03: The RLC Circuit
  59. 6.3E: The RLC Circuit (Exercises)
  60. 6.04: Motion Under a Central Force
  61. 6.4E: Motion Under a Central Force (Exercises)
  62. 07: Series Solutions of Linear Second Order Equations
  63. 7.01: Prelude to Series Solutions of Linear Second Order Equations
  64. 7.02: Review of Power Series
  65. 7.2E: Review of Power Series (Exercises)
  66. 7.03: Series Solutions Near an Ordinary Point I
  67. 7.3E: Series Solutions Near an Ordinary Point I (Exercises)
  68. 7.04: Series Solutions Near an Ordinary Point II
  69. 7.4E: Series Solutions Near an Ordinary Point II (Exercises)
  70. 7.05: Regular Singular Points Euler Equations
  71. 7.5E: Regular Singular Points Euler Equations (Exercises)
  72. 7.06: The Method of Frobenius I
  73. 7.6E: The Method of Frobenius I (Exercises)
  74. 7.07: The Method of Frobenius II
  75. 7.7E: The Method of Frobenius II (Exercises)
  76. 7.08: The Method of Frobenius III
  77. 7.8E: The Method of Frobenius III (Exercises)
  78. 08: Laplace Transforms
  79. 8.01: Introduction to the Laplace Transform
  80. 8.1E: Introduction to the Laplace Transform (Exercises)
  81. 8.02: The Inverse Laplace Transform
  82. 8.2E: The Inverse Laplace Transform (Exercises)
  83. 8.03: Solution of Initial Value Problems
  84. 8.3E: Solution of Initial Value Problems (Exercises)
  85. 8.04: The Unit Step Function
  86. 8.4E: The Unit Step Function (Exercises)
  87. 8.05: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  88. 8.5E: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  89. 8.06: Convolution
  90. 8.6E: Convolution (Exercises)
  91. 8.07: Constant Coefficient Equations with Impulses
  92. 8.7E: Constant Coefficient Equations with Impulses (Exercises)
  93. 8.08: A Brief Table of Laplace Transforms
  94. 09: Linear Higher Order Differential Equations
  95. 9.01: Introduction to Linear Higher Order Equations
  96. 9.1E: Introduction to Linear Higher Order Equations (Exercises)
  97. 9.02: Higher Order Constant Coefficient Homogeneous Equations
  98. 9.2E: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
  99. 9.03: Undetermined Coefficients for Higher Order Equations
  100. 9.3E: Undetermined Coefficients for Higher Order Equations (Exercises)
  101. 9.04: Variation of Parameters for Higher Order Equations
  102. 9.4E: Variation of Parameters for Higher Order Equations (Exercises)
  103. 10: Linear Systems of Differential Equations
  104. 10.01: Introduction to Systems of Differential Equations
  105. 10.1E: Introduction to Systems of Differential Equations (Exercises)
  106. 10.02: Linear Systems of Differential Equations
  107. 10.2E: Linear Systems of Differential Equations (Exercises)
  108. 10.03: Basic Theory of Homogeneous Linear Systems
  109. 10.3E: Basic Theory of Homogeneous Linear Systems (Exercises)
  110. 10.04: Constant Coefficient Homogeneous Systems I
  111. 10.4E: Constant Coefficient Homogeneous Systems I (Exercises)
  112. 10.05: Constant Coefficient Homogeneous Systems II
  113. 10.5E: Constant Coefficient Homogeneous Systems II (Exercises)
  114. 10.06: Constant Coefficient Homogeneous Systems III
  115. 10.6E: Constant Coefficient Homogeneous Systems III (Exercises)
  116. 10.07: Variation of Parameters for Nonhomogeneous Linear Systems
  117. 10.7E: Variation of Parameters for Nonhomogeneous Linear Systems (Exercises)
  118. 11: Boundary Value Problems and Fourier Expansions
  119. 11.01: Eigenvalue Problems for y'' y 0
  120. 11.1E: Eigenvalue Problems for y'' y 0 (Exercises)
  121. 11.02: Fourier Series I
  122. 11.2E: Fourier Series I (Exercises)
  123. 11.03: Fourier Series II
  124. 11.3E: Fourier Series II (Exercises)
  125. 12: Fourier Solutions of Partial Differential Equations
  126. 12.01: The Heat Equation
  127. 12.1E: The Heat Equation (Exercises)
  128. 12.02: The Wave Equation
  129. 12.2E: The Wave Equation (Exercises)
  130. 12.03: Laplace's Equation in Rectangular Coordinates
  131. 12.3E: Laplace's Equation in Rectangular Coordinates (Exercises)
  132. 12.04: Laplace's Equation in Polar Coordinates
  133. 12.4E: Laplace's Equation in Polar Coordinates (Exercises)
  134. 13: Boundary Value Problems for Second Order Linear Equations
  135. 13.01: Boundary Value Problems
  136. 13.1E: Boundary Value Problems (Exercises)
  137. 13.02: Sturm-Liouville Problems
  138. 13.2E: Sturm-Liouville Problems (Exercises)
  139. A: Appendices and Answers to Exercises
  140. A Brief Table of Integrals (by Trench)
  141. A.1.2: Section 1.2 Answers
  142. A.2.1: Section 2.1 Answers
  143. A.2.2: Section 2.2 Answers
  144. A.2.3: Section 2.3 Answers
  145. A.2.4: Section 2.4 Answers
  146. A.2.5: Section 2.5 Answers
  147. A.2.6: Section 2.6 Answers
  148. A.3.1: Section 3.1 Answers
  149. A.3.2: Section 3.2 Answers
  150. A.3.3: Section 3.3 Answers
  151. A.4.1: Section 4.1 Answers
  152. A.4.2: Section 4.2 Answers
  153. A.4.3: Section 4.3 Answers
  154. A.4.4: Section 4.4 Answers
  155. A.4.5: Section 4.5 Answers
  156. A.5.1: Section 5.1 Answers
  157. A.5.2: Section 5.2 Answers
  158. A.5.3: Section 5.3 Answers
  159. A.5.4: Section 5.4 Answers
  160. A.5.5: Section 5.5 Answers
  161. A.5.6: Section 5.6 Answers
  162. A.5.7: Section 5.7 Answers
  163. A.6.1: Section 6.1 Answers
  164. A.6.2: Section 6.2 Answers
  165. A.6.3: Section 6.3 Answers
  166. A.6.4: Section 6.4 Answers
  167. A.7.1: Section 7.1 Answers
  168. A.7.2: Section 7.2 Answers
  169. A.7.3: Section 7.3 Answers
  170. A.7.4: Section 7.4 Answers
  171. A.7.5: Section 7.5 Answers
  172. A.7.6: Section 7.6 Answers
  173. A.7.7: Section 7.7 Answers
  174. A.8.1: Section 8.1 Answers
  175. A.8.2: Section 8.2 Answers
  176. A.8.3: Section 8.3 Answers
  177. A.8.4: Section 8.4 Answers
  178. A.8.5: Section 8.5 Answers
  179. A.8.6: Section 8.6 Answers
  180. A.8.7: Section 8.7 Answers
  181. A.9.1: Section 9.1 Answers
  182. A.9.2: Section 9.2 Answers
  183. A.9.3: Section 9.3 Answers
  184. A.9.4: Section 9.4 Answers
  185. A10.1: Section 10.1 Answers
  186. A10.2: Section 10.2 Answers
  187. A10.3: Section 10.3 Answers
  188. A10.4: Section 10.4 Answers
  189. A10.5: Section 10.5 Answers
  190. A10.6: Section 10.6 Answers
  191. A10.7: Section 10.7 Answers
  192. A11.1: Section 11.1 Answers
  193. A11.2: Section 11.2 Answers
  194. A11.3: Section 11.3 Answers
  195. A12.1: Section 12.1 Answers
  196. A12.2: Section 12.2 Answers
  197. A12.3: Section 12.3 Answers
  198. A12.4: Section 12.4 Answers
  199. A13.1: Section 13.1 Answers
  200. A13.2: Section 13.2 Answers
  201. z Index