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Differential Equations

Differential Equations

Dr Juan Klopper via YouTube Direct link

A1 Introduction

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A1 Introduction

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Differential Equations

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  1. 1 A1 Introduction
  2. 2 B01 An introduction to separable variables
  3. 3 B02 Example problem with separable variables
  4. 4 B03 Example problem with separable variables
  5. 5 B04 Example problem with separable variables
  6. 6 B05 Example problem with separable variables
  7. 7 B06 Example problem with separable variables
  8. 8 B07 Example problem with separable variables
  9. 9 B08 Introduction to linear equations
  10. 10 B09 Example problem with a linear equation
  11. 11 B10 Example problem with a linear equation
  12. 12 B11 Example problem with a linear equation
  13. 13 B12 Example problem with a linear equation
  14. 14 B13 Example problem with a linear equation
  15. 15 B15 Example problem with a linear equation using the error function
  16. 16 2_2_8 Example problem with a linear equation modeling a real world situation
  17. 17 B16 Introduction to exact equations
  18. 18 B17 Example problem solving an exact DE
  19. 19 B18 Example problem solving an exact equation
  20. 20 B19 Example problem solving for an exact equation
  21. 21 B20 Creating an exact equation by using an integrating factor
  22. 22 B21 Example problem where an exact DE has to be created
  23. 23 B22 Introduction to Substitutions
  24. 24 B23 Example problem solving for a homogeneous DE
  25. 25 B24 Introduction to the Bernoulli Equation
  26. 26 B25 Example problem solving for a Bernoulli equation
  27. 27 B26 U substitution
  28. 28 B27 Introduction to linear models
  29. 29 B28 An example problem of a linear model
  30. 30 C01 Preliminaries
  31. 31 C02 Reduction of order
  32. 32 C03 Example problem using reduction of order
  33. 33 C04 Example problem using reduction of order
  34. 34 C05 Example problem using reduction of order
  35. 35 C06 Example problem using reduction of order
  36. 36 C07 Homogeneous linear differential equations with constant coefficients
  37. 37 C08 Homogeneous linear differential equations with constant coefficients
  38. 38 C09 Example problem solving a second order LDE with constant coefficients
  39. 39 C10 Example problem solving a second order LDE with constant coefficients
  40. 40 C11 Example problem solving a second order LDE with constant coefficients
  41. 41 C12 Example problem solving a second order LDE with constant coefficients
  42. 42 C13 Third and higher order linear DE with constant coefficients
  43. 43 C14 Example problem with a third order linear DE with constant coefficients
  44. 44 C15 Initial value problem solving a homogeneous linear SOODE with constant coefficients
  45. 45 C16 Example of solving a homogeneous higher order linear ODE with constant coefficients
  46. 46 C17 Non homogeneous higher order linear ODEs with constant coefficients
  47. 47 C18 Example problem using the superposition approach
  48. 48 C19 Example problem using the superposition principle
  49. 49 C20 Example problem using the superposition principle
  50. 50 C21 The annihilator approach
  51. 51 C22 Simple examples finding the annihilator
  52. 52 C23 More about the annihilator approach
  53. 53 C24 Finding the differential annihilator
  54. 54 C25 Solving a DE with the annihilator approach
  55. 55 C26 Example problem finding the form of the particular solution
  56. 56 C27 Example problem finding the form of the particular solution
  57. 57 C28 Variation of parameters Part 1
  58. 58 C29 Variation of parameters Part 2
  59. 59 C30 Solving a linear DE by the annihilator approach
  60. 60 C31 The same problem but using variation of parameters
  61. 61 C32 Example problem using variation of parameters
  62. 62 C33 Example problem using variation of parameters
  63. 63 C34 Expanding this method to higher order linear differential equations
  64. 64 C35 The Cauchy Euler Equation
  65. 65 C36 Example problem solving a Cauchy Euler equation
  66. 66 C37 Example problem solving a Cauchy Euler equation
  67. 67 C38 Example problem solving a Cauchy Euler equation with initial values
  68. 68 C39 A Cauchy Euler equation that is nonhomogeneous
  69. 69 C40 Example problem solving a nonhomogeneous Cauchy Euler equation
  70. 70 C41 Using substitution to solve a Cauchy Euler equation
  71. 71 C42 Example problem solving a Cauchy Euler equation with substitution
  72. 72 C43 Example problem solving a Cauchy Euler equation
  73. 73 C44 Example problem solving a Cauchy Euler equation
  74. 74 C45 Example problem solving a Cauchy Euler equation
  75. 75 C46 Solving the previous problem by another method
  76. 76 C47 Example problem solving a Cauchy Euler equation
  77. 77 C48 Systems of linear differential equations
  78. 78 C49 Example problem solving a system of linear DEs Part 1
  79. 79 C50 Example problem solving a system of linear DEs Part 2
  80. 80 C51 Example problem of a system of linear DEs
  81. 81 C52 Introduction to nonlinear DEs
  82. 82 C53 Introduction to modelling
  83. 83 C54 Free undamped motion
  84. 84 C55 Example problem of free undamped motion
  85. 85 C56 Continuation of previous problem
  86. 86 C57 Alternate form of the solution
  87. 87 C58 Example problem using the alternate form
  88. 88 C59 Free damped motion
  89. 89 C60 Example problem involving free damped motion
  90. 90 C61 Another problem involving free undamped motion
  91. 91 C62 Driven motion with damping
  92. 92 C63 Example problem involving driven motion with damping
  93. 93 C64 Transient and steady state terms
  94. 94 C65 Exampe problem illustrating transient and steady state terms
  95. 95 C66 Resonance
  96. 96 C67 The physics of simple harmonic motion
  97. 97 C68 The physics of damped motion
  98. 98 C69 Introduction to power series
  99. 99 C70 The ratio test for power series
  100. 100 C71 Adding to power series in sigma notation
  101. 101 C72 What to do about the singular point
  102. 102 C73 Introducing the theorem of Frobenius
  103. 103 C74 Example problem
  104. 104 C75 Introduction to the Laplace Transform
  105. 105 C76 A first example problem calculating the Laplace transform
  106. 106 C77 Another example problem calculating the Laplace transform
  107. 107 C78 Another example problem calculating the Laplace transform
  108. 108 C79 Linear properties of the Laplace transform
  109. 109 C80 Solving a linear DE with Laplace transformations
  110. 110 C81 More complex Laplace tranformations
  111. 111 C82 Example problem using inverse Laplace transforms Part 1
  112. 112 C83 Example problem using inverse Laplace transforms Part 2
  113. 113 C84 Example problem using inverse Laplace transforms Part 3

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