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 1/16 Cancelled - - -
Th 1/18 Introduction and Orientation to ODEs
(Temporarily Asynchronous)		 Algebra and Calculus Review - Syllabus
2 Tu 1/23 Modeling Physical Systems,
Classification of Equations, &
Principles of Solutions		 Classifying ODEs and Verifying Solutions - Ch. 1.1 [T], Ch. 1.1 [H], & Ch. 1.2.3 [H]
Th 1/25 1st-Order ODEs,
Existence and Uniqueness, &
Analyzing Equilibriums of Linear and Non-Linear 1st-Order ODEs		 Qualitative and Graphical Approaches Assigned: Homework 1 Ch. 1.2 [T], Ch. 2.1 [T], Ch. 1.3.1 [H], & Ch. 1.4 [H]
3 Tu 1/30 Nullclines and Isoclines &
Euler’s Method for solving 1st-Order ODEs		 Graphical and Numerical Methods - Ch. 1.3 [T] & Ch. 3.1 [T]
Th 2/1 Separation of Variables &
Integrating Factors for Solving 1st-Order ODEs		 Analytical Methods Assigned: Homework 2 Ch. 2.2 [T], Ch. 2.6 [T], & Ch. 2.1 [H]
4 Tu 2/6 Laplace Transforms for Solving 1st-Order ODEs Laplace Transforms for 1st-Order ODEs - Ch. 8.1 [T], Ch. 8.2 [T], & Ch. 5.1 [H]
Th 2/8 Bifurcations in One Dimension Bifurcations and Applications - TBA
5 Tu 2/13 Review Exam 1 Examples - Exam 1 Topics
Th 2/15 Exam 1 - - -
6 Tu 2/20 Systems of 1st-Order ODEs &
Modeling Physical Processes		 Interpreting 1st-Order System of ODEs - TBA
Th 2/22 Cancelled - Assigned: Homework 3 -
7 Tu 2/27 Analyzing Equilibriums to 1st-Order Linear and Non-Linear Systems Equilibriums of 1st-Order System of ODEs - TBA
Th 2/29 Linear Transformations &
Stability Analysis of 1st-Order Linear Systems		 Linearization and Stability Analysis Assigned: Homework 4 TBA
8 Tu 3/5 Spring Vacation - - -
Th 3/7 Spring Vacation - - -
9 Tu 3/12 Eigenvalues and Eigenvectors for solving 1st-Order Linear Systems Analytical Methods for 1st-Order System of ODEs - TBA
Th 3/14 Complex Solutions of 1st-Order Linear Systems Repeated Eigenvalues and Complex Exponentials - TBA
10 Tu 3/19 Review Exam 2 Examples - Exam 2 Topics
Th 3/21 Exam 2 - - -
11 Tu 3/26 Higher Order ODEs &
Modeling Physical Processes		 Particular Solutions - TBA
Th 3/28 Analyzing Linear and Non-Linear 2nd-Order ODEs Substitution and Non-Dimensionalization Assigned: Homework 5 TBA
12 Tu 4/2 Undetermined Coefficients for Solving Linear 2nd-Order ODEs Determining the Undetermined - TBA
Th 4/4 Variation of Parameters for Solving Linear 2nd-Order ODEs Varying the Parameters Assigned: Homework 6 TBA
13 Tu 4/9 Founder’s Day (No Class) - - -
Th 4/11 Laplace Transforms for Solving Linear 2nd-Order ODEs Transforming Derivatives à la Laplace - TBA
14 Tu 4/16 Review Exam 3 Examples - Exam 3 Topics
Th 4/18 Exam 3 - - -
15 Tu 4/23 Bifurcations in Two Dimensions Bifurcation Analysis - TBA
Th 4/25 Analyzing the Lorenz System Dynamics and Chaos Theory - TBA
16 Tu 4/30 Final Exam Section B - - -
Th 5/2 Final Exam Section C - - -


Along with textbooks [H] and [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

[H] Hallstrom C (2018). Ordinary Differential Equations: A Primer on, Dynamics and Systems. online. Version 2.3. [pdf]

[T] Trench WF (2013). Elementary Differential Equations. Faculty Authored, and Edited Books & CDs. 8. [pdf]

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.