# Notes on Diffy Qs (Lebl)

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## Info

This is an online homework companion to Notes on Diffy Qs: Differential Equations for Engineers by Jiri Lebl. It comprises hundreds of algorithmic problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other catalog courses, add problems from the Edfinity problem repository, or write your own

How to use this course

1. Homework: Assign high quality problems with hints and personalized feedback to develop problem-solving skills.
2. Testing: Create summative secure online quizzes and tests in minutes.
3. Supplementary resources: Embed videos, class notes, and applets alongside assignments.
4. Intervention: Use rich analytics to identify and monitor at-risk students for timely intervention.
5. Analytics: Drill down into student performance and identify problematic or difficult topics.
6. Flipped classroom: Assign pre-class assignments. Save precious class time for discussions.
7. Emporium classes: Use Edfinity for individual/group work for large enrollment sections in labs.
Interactive, algorithmic problems
Algebraic, graphing, open response; randomized variants, hints, and tips
to fill learning gaps.
Corequisite course structures
Use pre-built corequisite content,
LMS integration and accessibility
Connect to your LMS in minutes. VPAT here.
WeBWorK-compatible
Import and author WeBWorK problems.

## Syllabus

1. Edfinity Demo
2. Sec 0.2: Introduction to differential equations
3. Sec 0.3: Classification of differential equations
4. Sec 1.1: Integrals as solutions
5. Sec 1.2: Slope fields
6. Sec 1.3: Separable equations
7. Sec 1.4: Linear equations and the integrating factor
8. Sec 1.5: Substitution
9. Sec 1.6: Autonomous equations
10. Sec 1.7: Numerical methods
11. Sec 1.8: Exact equations
12. Sec 1.9: First order linear PDE
13. Sec 2.1: Second order linear ODEs
14. Sec 2.2: Constant coefficient second order linear ODEs
15. Sec 2.3: Higher order linear ODEs
16. Sec 2.4: Mechanical vibrations
17. Sec 2.5: Nonhomogeneous equations
18. Sec 2.6: Forced oscillations and resonance
19. Sec 3.1: Introduction to systems of ODEs
20. Sec 3.2: Matrices and linear systems
21. Sec 3.3: Linear systems of ODEs
22. Sec 3.4: Eigenvalue method
23. Sec 3.5: Two dimensional systems and their vector fields
24. Sec 3.6: Second order systems and applications
25. Sec 3.7: Multiple eigenvalues
26. Sec 3.8: Matrix exponentials
27. Sec 3.9: Nonhomogeneous systems
28. Sec 4.10: Dirichlet problem in the circle and the Poisson kernel
29. Sec 4.1: Boundary value problems
30. Sec 4.2: The trigonometric series
31. Sec 4.3: More on the Fourier series
32. Sec 4.4: Sine and cosine series
33. Sec 4.5: Applications of Fourier series
34. Sec 4.6: PDEs, separation of variables, and the heat equation
35. Sec 4.7: One dimensional wave equation
36. Sec 4.8: D’Alembert solution of the wave equation
37. Sec 4.9: Steady state temperature and the Laplacian
38. Sec 5.1: Sturm-Liouville problems
39. Sec 6.1: The Laplace transform
40. Sec 6.2: Transforms of derivatives and ODEs
41. Sec 6.3: Convolution
42. Sec 6.4: Dirac delta and impulse response
43. Sec 6.5: Solving PDEs with the Laplace transform
44. Sec 7.1: Power series
45. Sec 7.2: Series solutions of linear second order ODEs
46. Sec 7.3: Singular points and the method of Frobenius
47. Sec 8.1: Linearization, critical points, and equilibria
48. Sec 8.2: Stability and classification of isolated critical points
49. Sec 8.3: Applications of nonlinear systems
50. Sec 8.4: Limit cycles
51. Sec A.1: Vectors, mappings, and matrices
52. Sec A.2: Matrix algebra
53. Sec A.3: Elimination
54. Sec A.4: Subspaces, dimension, and the kernel
55. Sec A.5: Inner product and projections
56. Sec A.6: Determinant