Differential Equations for Engineers

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135 pages
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 English
These are the lecture notes for my Coursera course, Differential Equations for Engineers. This course is all about differential equations, and covers material that all engineers should know.
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Om forfatteren

Dr. Jeffrey Chasnov received his BA from UC Berkeley in 1983, and his PhD from Columbia University in 1990. He had postdoctoral appointments at NASA, Stanford University, and the Université Joseph Fourier before expatriating to Hong Kong in 1993, where he is currently a Professor of Mathematics at t...

Description
Content

  • Preface
  1. Introduction to differential equations
  2. Week I First-order differential equations
  3. Euler method
  4. Separable first-order equations
  5. Separable first-order equation: example
  6. Linear first-order equations
  7. Linear first-order equation: example
  8. Application: compound interest
  9. Application: terminal velocity
  10. Application: RC circuit
  11. Week II Second-order differential equations
  12. Euler method for higher-order odes
  13. The principle of superposition
  14. The Wronskian
  15. Homogeneous second-order ode with constant coefficients
  16. Case 1: distinct real roots
  17. Case 2: complex-conjugate roots (Part A)
  18. Case 2: complex-conjugate roots (Part B)
  19. Case 3: Repeated roots (Part A)
  20. Case 3: Repeated roots (Part B)
  21. Inhomogeneous second-order ode
  22. Inhomogeneous term: exponential function
  23. Inhomogeneous term: sine or cosine (Part A)
  24. Inhomogeneous term: sine or cosine (Part B)
  25. Inhomogeneous term: polynomials
  26. Resonance
  27. Application: RLC circuit
  28. Application: mass on a spring
  29. Application: pendulum
  30. Damped resonance
  31. Week III The Laplace Transform and Series Solution Methods
  32. Definition of the Laplace transform
  33. Laplace transform of a constant-coefficient ode
  34. Solution of an initial value problem
  35. The Heaviside step function
  36. The Dirac delta function
  37. Solution of a discontinuous inhomogeneous term
  38. Solution of an impulsive inhomogeneous term
  39. The series solution method
  40. Series solution of the Airy’s equation (Part A)
  41. Series solution of the Airy’s equation (Part B)
  42. Week IV Systems of Differential Equations and Partial Differential Equations
  43. Systems of homogeneous linear first-order odes
  44. Distinct real eigenvalues
  45. Complex-conjugate eigenvalues
  46. Coupled oscillators
  47. Normal modes (eigenvalues)
  48. Normal modes (eigenvectors)
  49. Fourier series
  50. Fourier sine and cosine series
  51. Fourier series: example
  52. The diffusion equation
  53. Solution of the diffusion equation (separation of variables)
  54. Solution of the diffusion equation (eigenvalues)
  55. Solution of the diffusion equation (Fourier series)
  56. Diffusion equation: example
  • Appendix
  • Appendix A Complex numbers
  • Appendix B Nondimensionalization
  • Appendix C Matrices and determinants
  • Appendix D Eigenvalues and eigenvectors
  • Appendix E Partial derivatives
  • Appendix F Table of Laplace transforms
  • Appendix G Problem solutions

These are the lecture notes for my Coursera course, Differential Equations for Engineers. I cover solution methods for first-order differential equations, second-order differential equations with constant coefficients, and discuss some fundamental applications. I also cover the Laplace transform and series solution methods, systems of linear differential equations, including the very important normal modes problem, and partial differential equations and the method of separation of variables, including the use of Fourier series.

About the author

Dr. Jeffrey Chasnov received his BA from UC Berkeley in 1983, and his PhD from Columbia University in 1990. He had postdoctoral appointments at NASA, Stanford University, and the Université Joseph Fourier before expatriating to Hong Kong in 1993, where he is currently a Professor of Mathematics at the Hong Kong University of Science and Technology. Jeff has published over 30 research articles on fluid turbulence, population genetics, and C. elegans biology, and is an experienced lecturer in applied mathematics. One of his favorite courses is Introduction to Differential Equations.