Differential Equations Class Notes
You should print out the Class Notes and complete them as you watch the videos.
Name of Section |
Section of Nagle, et al, Fundamentals of Differential Equations , 9th edition |
| Introduction and Background MP4 Video (I have since added a few handouts on page 2.) |
1.1 |
| Solutions and Initial Value Problems MP4 Video (Since video, I added a page after example 2, exploring its interval.) |
1.2 |
| Direction Fields MP4 Video |
1.3 |
| The Approximation Method of Euler MP4 Video (Since video, I added an expanatory paragraph for example 3 and leading zeros throughout.) |
1.4 |
| Introduction: Motion of a Falling Body MP4 Video (I have since amended the handouts.) |
2.1 |
| Separable Equations MP4 Video (I have since added room for example 3.) |
2.2 |
| Linear Equations MP4 Video (I have since amended a thought bubble on page 2.) |
2.3 |
| Exact Equations MP4 Video (Since video, I slightly rewrote comment on bottom of page 6.) |
2.4 |
| Special Integrating Factors MP4 Video (Since video, I rewrote some to clarify lost and gained solutions.) |
2.5 |
Substitutions and Transformations |
2.6 |
| (mentioned at beginning of Section 3.2 notes) | 3.1 |
Compartmental Analysis |
3.2 |
| Heating and Cooling of Buildings MP4 video |
3.3 |
| Newtonian Mechanics MP4 video |
3.4 |
| 3.5 | |
Numerical Methods: A Closer Look at Euler’s Algorithm |
3.6 |
| 4.1 | |
Homogeneous Linear Equations: The General Solution |
4.2 |
| Auxiliary Equations with Complex Roots MP4 video |
4.3 |
Nonhomogeneous Equations: The Method of Undetermined Coefficients |
4.4 |
The Superposition Principle and Undetermined Coefficients Revisited |
4.5 |
| 5.1 | |
Differential Operators and the Elimination Method for Systems Completed version (PDF) from Spring 2024 (On example 5, page 5 of completed version, I erroneously labeled "add" on the step above the step where I actually did the addition.) |
5.2 |
Basic Theory of Linear Differential Equations (Higher-Order Including Variable Coefficients) Completed version (PDF) from Spring 2024 (More space was given for work since this copy.) |
6.1 |
Laplace Transforms for Differential Equations Completed version (PDF) from Spring 2024 (A small typo on page 1 was fixed and more room was given for example 2 since this copy.) There is a mistake I have not fixed yet. On example 2, page 3, when I used u-substitution in the first half, I should have left off the limits of integration from the step before. Those are t-values, not u-values. |
7.1/7.2 |
| 7.3 | |
| 7.4 | |
| 7.5 |