# Notes on Diffy Qs

Educator Edition

 Textbook Pair this course with Notes on Diffy Qs: Differential Equations for Engineers or a differential equations textbook of your choice.

## Overview

This course is designed to be a companion to Notes on Diffy Qs: Differential Equations for Engineers and was prepared by the book's author, Jiri LeblThe problem sets map contain over 310 interactive, algorithmic problems and map directly to textbook sections.

Edfinity is a full-featured homework system that supports mathematically aware problems with algebraic input, evaluation of mathematical expressions, and randomized variants for personalized learning. Use this problem series as-is, or mix-and-match with other series or your own problems as desired. Edfinity gives you complete control over every aspect of students' online assessment experience.

## How to use this course

• Develop problem-solving skills: Use the problem sets to help students develop problem-solving skills. Save hours of grading time.
• Flip your classroom: Have students work on assignments ahead of class to master the basics and save precious class time for discussions and difficult problems.
• Make your own tests and quizzes: Edfinity’s flexible assignment templates allow you to create timed quizzes and tests in minutes. Assessments are auto-scored and provide summary statistics and analytics on student outcomes
• Remix problems: Select problem sets of your choice. Find more problems in the Edfinity repository, or create your own.

## WeBWorK

This course includes algorithmic WeBWorK problems, with support for randomized variants, algebraic expressions, and mathematical objects such as vectors, matrices, intervals, and complex numbers.

## Problem Sets

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: Euler's method
11. Sec 1.8: Exact equations
12. Sec 2.1: Second order linear ODEs
13. Sec 2.2: Constant coefficient second order linear ODEs
14. Sec 2.3: Higher order linear ODEs
15. Sec 2.4: Mechanical vibrations
16. Sec 2.5: Nonhomogeneous equations
17. Sec 2.6: Forced oscillations and resonance
18. Sec 3.1: Introduction to systems of ODEs
19. Sec 3.2: Matrices and linear systems
20. Sec 3.3: Linear systems of ODEs
21. Sec 3.4: Eigenvalue method
22. Sec 3.5: Two dimensional systems and their vector fields
23. Sec 3.6: Second order systems and applications
24. Sec 3.7: Multiple eigenvalues
25. Sec 3.8: Matrix exponentials
26. Sec 3.9: Nonhomogeneous systems
27. Sec 6.1: The Laplace transform
28. Sec 6.2: Transforms of derivatives and ODEs
29. Sec 6.3: Convolution
30. Sec 6.4: Dirac delta and impulse response
31. Sec 7.1: Power series
32. Sec 7.2: Series solutions of linear second order ODEs
33. Sec 7.3: Singular points and the method of Frobenius
34. Sec 8.1: Linearization, critical points, and equilibria
35. Sec 8.2: Stability and classification of isolated critical points
36. Sec 8.3: Applications of nonlinear systems
37. Sec 8.4: Limit cycles