Additional Topics
This page is a compendium of additional topics for MATH 341 Differential Equations during the Fall 2026 semester. Sections may be added or edited as the course progresses. Some but not all of the topics treated here may be covered in lectures depending on time and the interests of the students.
Dimensional Analysis this section will cover the basics of dimensional analysis, which is a powerful tool for understanding the behavior of physical systems and for simplifying mathematical models. We will discuss how to identify the dimensions of physical quantities, how to use dimensional analysis to derive relationships between variables, and how to apply these techniques.
Bernoulli equations discusses Bernoulli equations as covered in Exercises 14 & 15 in Section 1.4.1 of Logan (2015).
Linearity and superposition discusses the concept of linearity carefully, states the superposition principle precisely for differential equations, and then illustrates why it is so important in physics and engineering.
Existence and uniqueness discusses the ideas behind the existence and uniqueness theory for solutions to first-order ODEs.
Classical Mechanics discusses the ideas covered in Section 2.1 of Logan (2015) on the classical mechanics background for the second-order linear ODEs. The material here connects directly to the solution methods of §2.2–2.3 covered in Notes 4.
RLC Circuits, Filters, and the DC Motor develops three progressively richer applications of differential equations to electrical and electro-mechanical devices, each of which illuminates a different aspect of the ODE theory. The material here connects directly to the solution methods of §2.2–2.3 covered in Notes 4.
Series Solutions discusses the method of series solutions for solving second-order linear ODEs, as covered in Chapter 5 of Said-Houari (2015).
Linear Algebra discusses the basic concepts of linear algebra over the real numbers and some of its applications outside of the context of differential equations. Topics include vectors and matrices over \(\mathbb{R}\), systems of linear equations, eigenvectors and eigenvalues, and applications.
Bessel Functions introduces the concepts of Bessel differential equations and Bessel functions.
Draining Tanks, Coupled Reservoirs, and Drag introduces some applications of the concepts/techniques covered in MATH 341 to topics from fluid mechanics.
Thermodynamics and Heat Transfer introduces some applications of the concepts/techniques covered in MATH 341 to topics from thermodynamics.
The Hodgkin–Huxley Equations introduces some applications of the concepts/techniques covered in MATH 341 to topics from electrophysiology.
Access Jupyter Notebooks
Each section of additional topics has an associated Jupyter notebook, which can be run via Google Colab. Just click the “Open in Colab” button below for the notebook you want. The notebooks contain all of the code used in the topics, and can be modified and can be modified for exploring on your own.
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