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Differential Equations for Engineers

A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.

Differential EquationsMathematics
Author
Jiří Lebl
Publisher
Oklahoma State University
Source
LibreTexts
License
CC BY-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 80 sections
  1. 0: Introduction
  2. 0.1: Notes About These Notes
  3. 0.2: Introduction to Differential Equations
  4. 0.3: Classification of Differential Equations
  5. 0.E: Introduction (Exercises)
  6. 1: First order ODEs
  7. 1.1: Integrals as solutions
  8. 1.2: Slope fields
  9. 1.3: Separable Equations
  10. 1.4: Linear equations and the integrating factor
  11. 1.5: Substitution
  12. 1.6: Autonomous equations
  13. 1.7: Numerical methods: Eulers method
  14. 1.8: Exact Equations
  15. 1.9: First Order Linear PDE
  16. 1.E: First order ODEs (Exercises)
  17. 2: Higher order linear ODEs
  18. 2.1: Second order linear ODEs
  19. 2.2: Constant coefficient second order linear ODEs
  20. 2.3: Higher order linear ODEs
  21. 2.4: Mechanical Vibrations
  22. 2.5: Nonhomogeneous Equations
  23. 2.6: Forced Oscillations and Resonance
  24. 2.E: Higher order linear ODEs (Exercises)
  25. 3: Systems of ODEs
  26. 3.1: Introduction to Systems of ODEs
  27. 3.2: Matrices and linear systems
  28. 3.3: Linear systems of ODEs
  29. 3.4: Eigenvalue Method
  30. 3.5: Two dimensional systems and their vector fields
  31. 3.6: Second order systems and applications
  32. 3.7: Multiple Eigenvalues
  33. 3.8: Matrix exponentials
  34. 3.9: Nonhomogeneous systems
  35. 3.E: Systems of ODEs (Exercises)
  36. 4: Fourier series and PDEs
  37. 4.01: Boundary value problems
  38. 4.02: The trigonometric series
  39. 4.03: More on the Fourier series
  40. 4.04: Sine and cosine series
  41. 4.05: Applications of Fourier series
  42. 4.06: PDEs separation of variables and the heat equation
  43. 4.07: One dimensional wave equation
  44. 4.08: DAlembert solution of the wave equation
  45. 4.09: Steady state temperature and the Laplacian
  46. 4.10: Dirichlet Problem in the Circle and the Poisson Kernel
  47. 4.E: Fourier Series and PDEs (Exercises)
  48. 5: Eigenvalue problems
  49. 5.1: Sturm-Liouville problems
  50. 5.2: Application of Eigenfunction Series
  51. 5.3: Steady Periodic Solutions
  52. 5.E: Eigenvalue Problems (Exercises)
  53. 6: The Laplace Transform
  54. 6.1: The Laplace Transform
  55. 6.2: Transforms of derivatives and ODEs
  56. 6.3: Convolution
  57. 6.4: Dirac Delta and Impulse Response
  58. 6.5: Solving PDEs with the Laplace Transform
  59. 6.E: The Laplace Transform (Exercises)
  60. 7: Power series methods
  61. 7.1: Power Series
  62. 7.2: Series Solutions of Linear Second Order ODEs
  63. 7.3: Singular Points and the Method of Frobenius
  64. 7.E: Power series methods (Exercises)
  65. 8: Nonlinear Systems
  66. 8.1: Linearization critical points and equilibria
  67. 8.2: Stability and classication of isolated critical points
  68. 8.3: Applications of Nonlinear Systems
  69. 8.4: Limit cycles
  70. 8.5: Chaos
  71. 8.E: Nonlinear Equations (Exercises)
  72. Appendix A: Linear Algebra
  73. A.1: Vectors Mappings and Matrices
  74. A.2: Matrix Algebra
  75. A.3: Elimination
  76. A.4: Subspaces Dimension and The Kernel
  77. A.5: Inner Product and Projections
  78. A.6: Determinant
  79. A.E: Linear Algebra (Exercises)
  80. Appendix B: Table of Laplace Transforms