Phu Xuan University Library
|
PXU E-LIB
Sign in
Differential Equations for Engineers

External

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.

Mathematics
Author
Jiří Lebl
Publisher
Oklahoma State University
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 63 sections
  1. 1: First order ODEs
  2. 1.1 Integrals as solutions
  3. 1.2: Slope fields
  4. 1.3 Separable Equations
  5. 1.4 Linear equations and the integrating factor
  6. 1.5: Substitution
  7. 1.6 Autonomous equations
  8. 1.7: Numerical methods: Euler’s method
  9. 1.E: First order ODEs (Exercises)
  10. 2: Higher order linear ODEs
  11. 2.1: Second order linear ODEs
  12. 2.2: Constant coefficient second order linear ODEs
  13. 2.3: Higher order linear ODEs
  14. 2.4: Mechanical Vibrations
  15. 2.5: Nonhomogeneous Equations
  16. 2.6: Forced Oscillations and Resonance
  17. 2.E: Higher order linear ODEs (Exercises)
  18. 3: Systems of ODEs
  19. 3.1: Introduction to Systems of ODEs
  20. 3.2: Matrices and linear systems
  21. 3.3: Linear systems of ODEs
  22. 3.4: Eigenvalue Method
  23. 3.5: Two dimensional systems and their vector fields
  24. 3.6: Second order systems and applications
  25. 3.7: Multiple Eigenvalues
  26. 3.8: Matrix exponentials
  27. 3.9: Nonhomogeneous systems
  28. 3.E: Systems of ODEs (Exercises)
  29. 4: Fourier series and PDEs
  30. 4.1: Boundary value problems
  31. 4.2: The Trigonometric Series
  32. 4.3: More on the Fourier Series
  33. 4.4: Sine and cosine series
  34. 4.5: Applications of Fourier series
  35. 4.6: PDEs, separation of variables, and the heat equation
  36. 4.7: One dimensional wave equation
  37. 4.8: D’Alembert solution of the wave equation
  38. 4.9: Steady state temperature and the Laplacian
  39. 4.10: Dirichlet problem in the circle and the Poisson kernel
  40. 4.E: Fourier series and PDEs (Exercises)
  41. 5: Eigenvalue problems
  42. 5.1: Sturm-Liouville problems
  43. 5.2: Application of eigenfunction series
  44. 5.3: Steady periodic solutions
  45. 5.E: Eigenvalue Problems (Exercises)
  46. 6: The Laplace Transform
  47. 6.1: The Laplace Transform
  48. 6.2: Transforms of derivatives and ODEs
  49. 6.3: Convolution
  50. 6.4: Dirac delta and impulse response
  51. 6.E: The Laplace Transform (Exercises)
  52. 7: Power series methods
  53. 7.1: Power Series
  54. 7.2: Series solutions of linear second order ODEs
  55. 7.3: Singular Points and the Method of Frobenius
  56. 7.E: Power series methods (Exercises)
  57. 8: Nonlinear Equations
  58. 8.1: Linearization, critical points, and equilibria
  59. 8.2: Stability and classification of isolated critical points
  60. 8.3: Applications of nonlinear systems
  61. 8.4: Limit cycles
  62. 8.5: Chaos
  63. 8.E: Nonlinear Equations (Exercises)