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Differential Equations for Engineers

A one semester first course on differential equations, aimed at engineering students. This course covers techniques of solving ordinary differential equations including exact, separable, and linear equations; integrating factors; the method of undetermined coefficients; variation of parameters; Laplace transforms; series solutions; systems of differential equations; and applications.

Mathematics
Author
Jiří Lebl
Publisher
Oklahoma State University
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 97 sections
  1. 01: Introduction
  2. 1.01: Notes About These Notes
  3. 1.02: Introduction to Differential Equations
  4. 1.03: Classification of Differential Equations
  5. 1.E: Introduction (Exercises)
  6. 02: First order ODEs
  7. 2.01: Integrals as solutions
  8. 2.02: Slope fields
  9. 2.03: Separable Equations
  10. 2.04: Linear equations and the integrating factor
  11. 2.05: Existence and Uniqueness of Solutions of Nonlinear Equations
  12. 2.5E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  13. 2.06: Substitution
  14. 2.07: Autonomous equations
  15. 2.08: Numerical methods- Eulers method
  16. 2.09: Exact Equations
  17. 2.10: First Order Linear PDE
  18. 2.E: First order ODEs (Exercises)
  19. 03: Applications of First Order Equations
  20. 3.01: Growth and Decay
  21. 3.1E: Growth and Decay (Exercises)
  22. 3.02: Cooling and Mixing
  23. 3.2E: Cooling and Mixing (Exercises)
  24. 3.03: Elementary Mechanics
  25. 3.3E: Elementary Mechanics (Exercises)
  26. 04: Higher order linear ODEs
  27. 4.01: Second order linear ODEs
  28. 4.02: The Method of Undetermined Coefficients I
  29. 4.2E: The Method of Undetermined Coefficients I (Exercises)
  30. 4.03: The Method of Undetermined Coefficients II
  31. 4.3E: The Method of Undetermined Coefficients II (Exercises)
  32. 4.04: Constant coefficient second order linear ODEs
  33. 4.05: Higher order linear ODEs
  34. 4.06: Reduction of Order
  35. 4.6E: Reduction of Order (Exercises)
  36. 4.07: Variation of Parameters
  37. 4.7E: Variation of Parameters (Exercises)
  38. 4.08: Mechanical Vibrations
  39. 4.09: Nonhomogeneous Equations
  40. 4.10: Forced Oscillations and Resonance
  41. 4.E: Higher order linear ODEs (Exercises)
  42. 05: Systems of ODEs
  43. 5.01: Introduction to Systems of ODEs
  44. 5.02: Matrices and linear systems
  45. 5.03: Linear systems of ODEs
  46. 5.04: Eigenvalue Method
  47. 5.05: Two dimensional systems and their vector fields
  48. 5.06: Second order systems and applications
  49. 5.07: Multiple Eigenvalues
  50. 5.08: Matrix exponentials
  51. 5.09: Nonhomogeneous systems
  52. 5.E: Systems of ODEs (Exercises)
  53. 06: Fourier series and PDEs
  54. 6.01: Boundary value problems
  55. 6.02: The Trigonometric Series
  56. 6.03: More on the Fourier Series
  57. 6.04: Sine and Cosine Series
  58. 6.05: Applications of Fourier Series
  59. 6.06: PDEs Separation of Variables and The Heat Equation
  60. 6.07: One Dimensional Wave Equation
  61. 6.08: DAlembert Solution of The Wave Equation
  62. 6.09: Steady State Temperature and the Laplacian
  63. 6.10: Dirichlet Problem in the Circle and the Poisson Kernel
  64. 6.E: Fourier Series and PDEs (Exercises)
  65. 07: Eigenvalue problems
  66. 7.01: Sturm-Liouville problems
  67. 7.02: Application of Eigenfunction Series
  68. 7.03: Steady Periodic Solutions
  69. 7.E: Eigenvalue Problems (Exercises)
  70. 08: The Laplace Transform
  71. 8.01: The Laplace Transform
  72. 8.02: Transforms of derivatives and ODEs
  73. 8.03: Convolution
  74. 8.04: Dirac Delta and Impulse Response
  75. 8.05: Solving PDEs with the Laplace Transform
  76. 8.E: The Laplace Transform (Exercises)
  77. 09: Power series methods
  78. 9.01: Power Series
  79. 9.02: Series Solutions of Linear Second Order ODEs
  80. 9.03: Singular Points and the Method of Frobenius
  81. 9.E: Power series methods (Exercises)
  82. 10: Nonlinear Systems
  83. 10.01: Linearization Critical Points and Equilibria
  84. 10.02: Stability and Classication of Isolated Critical Points
  85. 10.03: Applications of Nonlinear Systems
  86. 10.04: Limit cycles
  87. 10.05: Chaos
  88. 10.E: Nonlinear Equations (Exercises)
  89. 11: Appendix A- Linear Algebra
  90. 11.01: A.1- Vectors Mappings and Matrices
  91. 11.02: A.2- Matrix Algebra
  92. 11.03: A.3- Elimination
  93. 11.04: A.4- Subspaces Dimension and The Kernel
  94. 11.05: A.5- Inner Product and Projections
  95. 11.06: A.6- Determinant
  96. 11.07: A.E- Linear Algebra (Exercises)
  97. 12: Appendix B- Table of Laplace Transforms