 # 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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A propos de l'auteur

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

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• 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.