Phu Xuan University Library
|
PXU E-LIB
Sign in
MAT 2561 Differential Equations with Engineering Applications

External

MAT 2561 Differential Equations with Engineering Applications

Mathematics
Author
Matthew Watts
Publisher
Red Rocks Community College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 183 sections
  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. 2.1.01: Cooling and Mixing
  10. 2.1.1E: Cooling and Mixing (Exercises)
  11. 2.1.02: Cooling and Mixing (Exercises)
  12. 2.1E: Linear First Order Equations (Exercises)
  13. 2.02: Separable Equations
  14. 2.2E: Separable Equations (Exercises)
  15. 2.03: Substitution Methods - Transformation of Nonlinear Equations into Separable Equations
  16. 2.3.01: Autonomous Second Order Equations
  17. 2.3.02: Autonomous Second Order Equations (Exercises)
  18. 2.04: Existence and Uniqueness of Solutions of Nonlinear Equations
  19. 2.4.01: Elementary Mechanics
  20. 2.4.1.01: Elementary Mechanics (Exercises)
  21. 2.4E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  22. 2.05: Transformation of Nonlinear Equations into Separable Equations
  23. 2.5.01: Autonomous Second Order Equations
  24. 2.5.1E: Autonomous Second Order Equations (Exercises)
  25. 2.5E: Transformation of Nonlinear Equations into Separable Equations (Exercises)
  26. 2.06: Exact Equations
  27. 2.6E: Exact Equations (Exercises)
  28. 2.07: Integrating Factors
  29. 2.7E: Integrating Factors (Exercises)
  30. 03: Numerical Methods
  31. 3.01: Euler's Method
  32. 3.1.01: Eulers Method (Exercises)
  33. 3.02: The Improved Euler Method and Related Methods
  34. 3.2.01: The Improved Euler Method and Related Methods (Exercises)
  35. 3.03: The Runge-Kutta Method
  36. 3.3.01: The Runge-Kutta Method (Exercises)
  37. 04: Applications of First Order Equations
  38. 4.01: Growth and Decay
  39. 4.1.01: Growth and Decay (Exercises)
  40. 4.02: Elementary Mechanics
  41. 4.2.01: Elementary Mechanics (Exercises)
  42. 4.03: Applications to Curves
  43. 4.3.01: Applications to Curves (Exercises)
  44. 05: Linear Second Order Equations
  45. 5.01: Homogeneous Linear Equations
  46. 5.1.01: Homogeneous Linear Equations (Exercises)
  47. 5.02: Constant Coefficient Homogeneous Equations
  48. 5.2.01: Constant Coefficient Homogeneous Equations (Exercises)
  49. 5.03: Nonhomgeneous Linear Equations
  50. 5.3.01: Nonhomgeneous Linear Equations (Exercises)
  51. 5.3.02: Spring Problems I
  52. 5.3.03: Spring Problems I (Exercises)
  53. 5.3.04: Spring Problems II
  54. 5.3.05: Spring Problems II (Exercises)
  55. 5.04: The Method of Undetermined Coefficients I
  56. 5.4.01: The Method of Undetermined Coefficients I (Exercises)
  57. 5.05: The Method of Undetermined Coefficients II
  58. 5.5.01: The Method of Undetermined Coefficients II (Exercises)
  59. 5.06: Reduction of Order
  60. 5.6.01: Reduction of Order (Exercises)
  61. 5.07: Variation of Parameters
  62. 5.7.01: Variation of Parameters (Exercises)
  63. 5.08: The RLC Circuit
  64. 5.8.01: The RLC Circuit (Exercises)
  65. 06: Applications of Linear Second Order Equations
  66. 6.01: Motion Under a Central Force
  67. 6.1.01: Motion Under a Central Force (Exercises)
  68. 07: Series Solutions of Linear Second Order Equations
  69. 7.01: Prelude to Series Solutions of Linear Second Order Equations
  70. 7.02: Review of Power Series
  71. 7.2.01: Review of Power Series (Exercises)
  72. 7.03: Series Solutions Near an Ordinary Point I
  73. 7.3E: Series Solutions Near an Ordinary Point I (Exercises)
  74. 7.04: Series Solutions Near an Ordinary Point II
  75. 7.4.01: Series Solutions Near an Ordinary Point II (Exercises)
  76. 7.05: Regular Singular Points Euler Equations
  77. 7.5.01: Regular Singular Points Euler Equations (Exercises)
  78. 7.06: The Method of Frobenius I
  79. 7.6.01: The Method of Frobenius I (Exercises)
  80. 7.07: The Method of Frobenius II
  81. 7.7.01: The Method of Frobenius II (Exercises)
  82. 7.08: The Method of Frobenius III
  83. 7.8.01: The Method of Frobenius III (Exercises)
  84. 08: Laplace Transforms
  85. 8.01: Introduction to the Laplace Transform
  86. 8.1.01: Introduction to the Laplace Transform (Exercises)
  87. 8.02: The Inverse Laplace Transform
  88. 8.2.01: The Inverse Laplace Transform (Exercises)
  89. 8.03: Solution of Initial Value Problems
  90. 8.3.01: Solution of Initial Value Problems (Exercises)
  91. 8.04: The Unit Step Function
  92. 8.4.01: The Unit Step Function (Exercises)
  93. 8.05: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  94. 8.5.01: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  95. 8.06: Convolution
  96. 8.6.01: Convolution (Exercises)
  97. 8.07: Constant Coefficient Equations with Impulses
  98. 8.7.01: Constant Coefficient Equations with Impulses (Exercises)
  99. 8.08: A Brief Table of Laplace Transforms (Trench's)
  100. 8.09: Professor Seeburger's Table of Laplace Transforms
  101. 8.10: Spring Problems I
  102. 8.10.01: Spring Problems I (Exercises)
  103. 8.11: Spring Problems II
  104. 8.11.01: Spring Problems II (Exercises)
  105. 09: Linear Systems of Differential Equations
  106. 9.01: Introduction to Systems of Differential Equations
  107. 9.1.01: Introduction to Systems of Differential Equations (Exercises)
  108. 9.02: Linear Systems of Differential Equations
  109. 9.2.01: Linear Systems of Differential Equations (Exercises)
  110. 9.03: Basic Theory of Homogeneous Linear Systems
  111. 9.3.01: Basic Theory of Homogeneous Linear Systems (Exercises)
  112. 9.04: Constant Coefficient Homogeneous Systems I
  113. 9.4.01: Constant Coefficient Homogeneous Systems I (Exercises)
  114. 9.05: Constant Coefficient Homogeneous Systems II
  115. 9.5.01: Constant Coefficient Homogeneous Systems II (Exercises)
  116. 9.06: Constant Coefficient Homogeneous Systems III
  117. 9.6.01: Constant Coefficient Homogeneous Systems III (Exercises)
  118. 9.07: Variation of Parameters for Nonhomogeneous Linear Systems
  119. 9.7.01: Variation of Parameters for Nonhomogeneous Linear Systems (Exercises)
  120. 10: Answers to Selected Exercises
  121. 10.01: A.1.2- Section 1.2 Answers
  122. 10.02: A.10.1- Section 10.1 Answers
  123. 10.03: A.10.2 Section 10.2 Answers
  124. 10.04: A.10.3- Section 10.3 Answers
  125. 10.05: A.10.4 Section 10.4 Answers
  126. 10.06: A.10.5- Section 10.5 Answers
  127. 10.07: A.10.6 Section 10.6 Answers
  128. 10.08: A.10.7- Section 10.7 Answers
  129. 10.09: A.11.1- Section 11.1 Answers
  130. 10.10: A.11.2- Section 11.2 Answers
  131. 10.11: A.11.3- Section 11.3 Answers
  132. 10.12: A.12.1- Section 12.1 Answers
  133. 10.13: A.12.2- Section 12.2 Answers
  134. 10.14: A.12.3- Section 12.3 Answers
  135. 10.15: A.12.4- Section 12.4 Answers
  136. 10.16: A.13.1- Section 13.1 Answers
  137. 10.17: A.13.2- Section 13.2 Answers
  138. 10.18: A.2.1- Section 2.1 Answers
  139. 10.19: A.2.2- Section 2.2 Answers
  140. 10.20: A.2.3- Section 2.3 Answers
  141. 10.21: A.2.4- Section 2.4 Answers
  142. 10.22: A.2.5- Section 2.5 Answers
  143. 10.23: A.2.6- Section 2.6 Answers
  144. 10.24: A.3.1- Section 3.1 Answers
  145. 10.25: A.3.2- Section 3.2 Answers
  146. 10.26: A.3.3- Section 3.3 Answers
  147. 10.27: A.4.1- Section 4.1 Answers
  148. 10.28: A.4.2- Section 4.2 Answers
  149. 10.29: A.4.3- Section 4.3 Answers
  150. 10.30: A.4.4- Section 4.4 Answers
  151. 10.31: A.4.5- Section 4.5 Answers
  152. 10.32: A.5.1- Section 5.1 Answers
  153. 10.33: A.5.2- Section 5.2 Answers
  154. 10.34: A.5.3- Section 5.3 Answers
  155. 10.35: A.5.4- Section 5.4 Answers
  156. 10.36: A.5.5- Section 5.5 Answers
  157. 10.37: A.5.6- Section 5.6 Answers
  158. 10.38: A.5.7- Section 5.7 Answers
  159. 10.39: A.6.1- Section 6.1 Answers
  160. 10.40: A.6.2- Section 6.2 Answers
  161. 10.41: A.6.3- Section 6.3 Answers
  162. 10.42: A.6.4- Section 6.4 Answers
  163. 10.43: A.7.1- Section 7.1 Answers
  164. 10.44: A.7.2- Section 7.2 Answers
  165. 10.45: A.7.3- Section 7.3 Answers
  166. 10.46: A.7.4- Section 7.4 Answers
  167. 10.47: A.7.5- Section 7.5 Answers
  168. 10.48: A.7.6- Section 7.6 Answers
  169. 10.49: A.7.7- Section 7.7 Answers
  170. 10.50: A.8.1- Section 8.1 Answers
  171. 10.51: A.8.2- Section 8.2 Answers
  172. 10.52: A.8.3- Section 8.3 Answers
  173. 10.53: A.8.4- Section 8.4 Answers
  174. 10.54: A.8.5- Section 8.5 Answers
  175. 10.55: A.8.6- Section 8.6 Answers
  176. 10.56: A.8.7- Section 8.7 Answers
  177. 10.57: A.9.1- Section 9.1 Answers
  178. 10.58: A.9.2- Section 9.2 Answers
  179. 10.59: A.9.3 Section 9.3 Answers
  180. 10.60: A.9.4- Section 9.4 Answers
  181. 10.61: A Brief Table of Integrals (by Trench)
  182. 10.62: A Brief Table of Integrals (edited by Prof. Seeburger)
  183. 10.63: Index