Additional Topics
This page is a compendium of additional topics for MATH 341 Differential Equations.
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).