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
MP4 Video: Part 1 (pages 1-5) (Since video, I added a blank page for workspace.)
MP4 Video: Part 2 (pages 6-13) (Since video, I have amended instructions for example 5 to save work and added room for the last example. I also renamed the worksheet.)

2.6
(mentioned at beginning of Section 3.2 notes) 3.1

Compartmental Analysis
MP4 video: Section 3.2 Notes Part 1 (pages 1-4) (If you cannot see whole work area, do not use "full screen" mode.)
MP4 video: Section 3.2 Notes Part 2 (pages 5-7) (If you cannot see whole work area, do not use "full screen" mode.)

3.2
Heating and Cooling of Buildings
MP4 video
3.3
Newtonian Mechanics
MP4 video
3.4

Electric Circuits

Completed version (PDF) from Spring 2024

3.5

Numerical Methods: A Closer Look at Euler’s Algorithm
MP4 video

3.6

Introduction: The Mass-Spring Oscillator
MP4 video

4.1

Homogeneous Linear Equations: The General Solution
MP4 video
Added page to give guidance for #7 in MML Homework

4.2
Auxiliary Equations with Complex Roots
MP4 video
4.3

Nonhomogeneous Equations: The Method of Undetermined Coefficients

Completed version (PDF) from Spring 2024

4.4

The Superposition Principle and Undetermined Coefficients Revisited

Completed version (PDF) from Spring 2024

4.5

Introduction to Systems: Interconnected Fluid Tanks

Completed version (PDF) from Spring 2024

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

Properties of Laplace Transforms

Completed version (PDF) from Spring 2024

7.3

Inverse Laplace Transforms

Completed version (PDF) from Spring 2024

7.4

Solving Initial Value Problems with Laplace Transforms

Completed version (PDF) from Spring 2024

7.5