Lecture Materials

Below you will find copies of overheads and materials that I use in lecture. Most of lecture I write out during class, so if you missed class, then you will want to get a copy of the notes from a classmate.

Ch 1 Lecture 1 Outline - Handwritten Notes: Terminology, Checking Solutions, Units, Motivational Examples.
Ch 1 Lecture 2 Outline - Notes: More Motivationing Examples and Slope/Direction Fields.
2.2 Lecture 1 Outline - Notes: Motivation and several examples of separable equations.
2.2 Lecture 2 Outline - Notes: With applications, Slope fields, and change of variable.
- 2.2 Review with Examples
2.1 Outline - Notes:: How to solve linear, 1st order ODEs, several examples (integrating factors).
- 2.1 Review with Examples
2.3 Lecture Outline - Notes: Case studies of some important applications.
- 2.3 Lecture Examples
- 2.3 Application Packet
2.5 Lecture Visuals - Notes: Equilibriums Solutions (Stable, Unstable, Semistable), Autonomous equations.
- 2.5 Review with Examples
2.7 Lecture Outline - Notes: Euler's Method, approximating solutions
- 2.7 Review with Examples
Exam 1 Rules and Topics
Exam 1 Review Sheet

The notes below are my personal notes (sorry they are rough, I didn't make them thinking I would post them, but I've found it difficult this quarter to find the time to retype all my notes. So I'm going to post them "as is" right now so you can see more examples, but apologies that they are rough looking):

3.1 Notes: Terminology of second order equations, characteristic equations with two real roots
- 3.1 review with additional examples
3.2 Notes: Discussion of Linearity and combinations of solutions
- 3.2 review
3.3 Notes: Characteristic equations with two complex roots, waves
- 3.3 review with additional examples
3.4 Notes: Characteristic equations with one repeated roots
- 3.4 review with additional examples
- Homogeneous Solving Summary (3.1-3.4) With Six Practice Problems
3.7 Notes: Free Vibrations (an explanation of mass-spring systems)
- Summary of Set-Up for mass-spring
- Summary of Analysis of Free Vibrations (3.7)
3.5 Notes: NONhomogeneous equations, particular solutions, method of undetermined coefficients
3.5 Day 2 Notes: More discussion of undetermined coefficients
- Extensive Summary of undetermined coefficients with many practice problems
3.8 Notes: Mass-Spring Systems with External Forcing (of the form cos(wt))
3.8 Notes 2: Mass-Spring System with External Forcing AND Damping
3.7/3.8 Analysis Full Summary: Carefully goes through analysis of all four cases (with and without damping in combination of with and without forcing).
- Summary of Analysis of Forced Vibrations (3.8)
- 3.8 Solutions with two different frequency waves ("beats") Overview
- Pictures of "beats" example from Lecture on 3.8
Exam 2 Full Review: Contains a review, plus a copy of all the original review sheets that I have created this year. Hope this helps to get in all in one place.

Brief Review Lecture Notes: Full example of undetermined coefficients and full example of reduction of order.

6.1 Notes: The LaPlace Transform.
- LaPlace Transform Practice Sheet with Practice Problems/Solutions
6.2 Notes: The inverse LaPlace Transform and solving.
- Inverse LaPlace Transform Practice Sheet with Practice Problems/Solutions
- Full Big Example of solving with LaPlace Transforms
6.3 Notes: Solving and step-functions.
- Step Functions with practice problems
- More Notes on Step Functions plus HW 9 Hints
6.3 Notes 2: More on step-functions.
- LaPlace Transform Fact Sheet: Full Table plus several worked out examples
6.4 Notes: Discontinuous Forcing.
- 6.4 Example from Lecture
6.5 & 6.6 Notes: Some terminology - Transfer function, impulse response, convolutions.
6.5 & 6.6 Notes 2: More Examples with the Delta Function.
- Full Review of 6.5 and 6.6 with Examples - Also contains proof for the convolution solution.

Final Exam List of Topics

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