See Books & Online Resources Lists for the readings & practice materials.

The reading materials are not mandatory but it is encouraged.


The “Reading” column in the table below contains page numbers (Pg.) or chapters (ch.) on which it refers to a label in the Books & Online Resources List. For example “Pg. 1-5 [H]” refers to pages 1-5 of the first item in the list, which is the textbook titled “Ordinary Differential Equations: A Primer on Dynamics and Systems”.


Topics and Materials

Week Day Topic Worksheet Homework Reading
1 Tu 8/27 Introduction and Orientation to ODEs Review Algebra and Calculus - Syllabus
Th 8/29 Modeling Physical Systems,
Classification of Equations, &
Principles of Solutions		 Classify ODEs and Verify Solutions - Ch. 1.1 [T]
2 Tu 9/3 1st-Order ODEs,
Existence and Uniqueness, &
Analyzing Equilibriums of 1st-Order ODEs		 Analyze 1st-Order ODEs Qualitatively Assigned: Homework 1 Ch. 1.2 & 2.1 [T]
Th 9/5 Nullclines and Isoclines &
Euler’s Method for solving 1st-Order ODEs		 Solve 1st-Order ODEs Graphically and Numerically - Ch. 1.3 & 3.1 [T]
3 Tu 9/10 Separation of Variables for Solving 1st-Order ODEs Separate the Variables Assigned: Homework 2 Ch. 2.2 [T]
Th 9/12 Integrating Factors for Solving 1st-Order ODEs Choose an Integrating Factor - Ch. 2.6 [T]
4 Tu 9/17 Laplace Transforms for Solving 1st-Order ODEs Introduce the Laplace Transform - Ch. 8.1-8.2 [T]
Th 9/19 Bifurcations in One Dimension Apply Bifurcation Analysis to Physical Systems - Ch. 4.1-4.3 [T]
5 Tu 9/24 Review Exam 1 Examples - Exam 1 Topics
Th 9/26 Exam 1 - - -
6 Tu 10/1 Systems of 1st-Order ODEs,
Existence and Uniqueness, &
Modeling Physical Processes		 Interpret 1st-Order System of ODEs - Ch. 10.1 [T]
Th 10/3 Analyzing Equilibriums to 1st-Order System of ODEs Find Equilibriums of 1st-Order System of ODEs Assigned: Homework 3 Ch. 10.2 [T]
7 Tu 10/8 Stability Analysis by Linearization & Eigentheory Use Eigentheory to Analyze Equilibrium Stability - Ch. 10.3 [T]
Th 10/10 Analytical Solutions to 1st-Order System of ODEs Use Eigentheory to Solve 1st-Order Linear System of ODEs - Ch. 10.4 [T]
8 Tu 10/15 Fall Vacation - - -
Th 10/17 Fall Vacation - - -
9 Tu 10/22 Eigenvalues and Eigenvectors for Solving 1st-Order Linear Systems Use Distinct or Repeated Eigenvalues - Ch. 10.5 [T]
Th 10/24 Complex Solutions of 1st-Order Linear Systems Use Complex Exponentials Assigned: Homework 4 Ch. 10.6 [T]
10 Tu 10/29 Review Exam 2 Examples - Exam 2 Topics
Th 10/31 Exam 2 - - -
11 Tu 11/5 Higher-Order ODEs,
Classification of Equations, &
Modeling Physical Processes		 Find Homogeneous and Particular Solutions - Ch. 5.1-5.3 & 6.1 [T]
Th 11/7 Undetermined Coefficients for Solving Linear Higher-Order ODEs Determine the Undetermined Assigned: Homework 5 Ch. 5.4-5.5 & 6.2 [T]
12 Tu 11/12 Variation of Parameters for Solving Linear Higher-Order ODEs Vary the Parameters - Ch. 5.7 & 6.3 [T]
Th 11/14 Laplace Transforms for Solving Linear Higher-Order ODEs Transform the Derivatives Assigned: Homework 6 Ch. 8.3 & 8.5 [T]
13 Tu 11/19 Analyzing Higher-Order Linear ODEs Use Substitutions and Reduce the Order - Ch. 5.6 [T]
Th 11/21 Review Exam 3 Examples - Exam 3 Topics
14 Tu 11/26 Exam 3 - - -
Th 11/28 Thanksgiving Vacation - - -
15 Tu 12/3 Series Solutions for Solving Linear ODEs Use Power Series - Ch. 7.1-7.3 [T]
Th 12/5 Review Final Exam Examples - Final Exam Topics
16 Tu 12/11 Final Exam Section A - - -
Th 12/12 Final Exam Section B - - -


Along with the textbook [T], and websites [C] and [P], most of the course materials (contents of worksheets and homework) of each topic was taken from these following sources:

  • Inquiry oriented differential equations (IODE) by Rasmussen et al. (2018)
  • Differential equations and linear algebra by Strang (2014)
  • Applied differential equations: The primary course by Dobrushkin (2022)
  • Differential Equations by MIT Open Courseware (2015)


Books & Online Resources Lists

Click on the link to access the resources.

Textbooks

[T] Trench WF (2013). Elementary Differential Equations. Faculty Authored, and Edited Books & CDs. 8., https://digitalcommons.trinity.edu/mono/8/.

Websites

[C] Clontz S (2022). “Differential Equations - Checkit.”, https://stevenclontz.github.io/checkit-clontz-diff-eq.

[P] Dawkins P (2023). “Paul’s Online Notes on Differential Equations.”, https://tutorial.math.lamar.edu/Classes/DE/DE.aspx.


References

Dobrushkin, V. A. (2022). Applied differential equations: The primary course (2nd ed.). Chapman; Hall/CRC.
MIT Open Courseware. (2015). Differential equations. https://ocw.mit.edu/courses/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/
Rasmussen, C., Keene, K. A., Dunmyre, J., & Fortune, N. (2018). Inquiry oriented differential equations: Course materials. https://iode.sdsu.edu
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. http://creativecommons.org/licenses/by-nc-sa/4.0/
Strang, G. (2014). Differential equations and linear algebra. Wellesley-Cambridge Press.