Math 3D Resources

Math 3D - Intro to Differential Equations (Winter '26)

The course loosely follows the structure of the free text found here. You can download the pdf for free, or link directly to it or to an online html version.

Homework

These files are for the weekly homework exercises. Solutions to these, and some of the exercises from the course text, can be found in Canvas.

Homework 1
Homework 2
Extra Questions to prepare for Midterm 1
Homework 3
Homework 4
Extra Questions to prepare for Midterm 2
Homework 5
Homework 6

Other Resources

Some of these are pictures shown in lectures. Sometimes these are more advanced problems/ideas.

Pre-requisite quiz Some of this might be used in the first discussion. It won't be collected or graded. If you don't understand what's being asked, ask. In particular, you must know how to work with matrices before we get to chapter 3.
1.2 Slope Fields and Euler's Method.
1.2 Existence and Uniqueness of 1st order equations: three initial value problems for which Picard's Theorem does not apply.
1.3 General/singular solutions example
1.4 The Reservoir Problem
1.6 Population models (mostly for interest & homework --- should know the logistic equation and basic birth/death rate concepts)
2.1 Second-order existence/uniqueness problem - hard! (pdf)
2.4 Mechanical Vibrations Summary. Contains a lot of terminology: don't memorize all the formulas and do the exercises open-book! Some animations where spring stiffness and damping are changed.
2.5 Non-homogeneous equation A nasty initial value problem with repeated roots
2.6 Damped Vibrations Summary: also open-book
3.1 The Brine Tanks problem
3.5 Linear Systems and their vector fields
Non-linear Systems some overlap with section 8 in the text
Translation in Laplace transforms: a step-function force applied to a spring.