
Some examples
General form of linear first order
Direction Fields
First Order Differential Equations
Modeling common problems
Existence and uniqueness
Integrating factor
Separation of variables (non-linear)
Applications to mechanics
Numerical methods
General solution and particular solution
Constant coefficient homogeneous equations
Special focus: vibration problem
Non-homogeneous equations
Repeated Roots and reduction of order
Method of Undetermined Coefficients
Method of Variation of Parameters
Linear Algebra Review
Determinants
Row reduction and linear independence
Eigenpairs
Intro to Higher Order Differential Equations
Abel’s Theorem
Calculus of Matrices
Intro First Order Linear Systems
Converting Higher Order ODE to First Order Linear System
Eigenvalue Problem for Linear Systems
Phase Plane
Variation of Parameters for Linear Systems
Equilibrium Points and Nullclines
Classifying Equilibrium Points
Linearization of Nonlinear System
Revisit the population logistics model to analyze the equilibrium points of a nonlinear, first order, differential equation.
Differential Equations are commonly used to describe real life phenomenon such as: tank mixing, vibrations, population dynamics, radioactive decay, falling with air resistance, etc. We will study common differential equations and how to solve them.
I find too often that students don’t know why they are learning something or how it relates to future classes or career. Some professors are too focused on getting the material over to you and giving you the test. Sound familiar? I will teach you how to think like an engineer, which means being able to break down complicated problems into simple pieces that you already know how to do! I recognize that students value simplicity and logic over complicated derivations and memorized processes. I will teach you the simplest way that has helped my students become successful for the past 5 years.
By the end of the course, you will know how to approach fundamental problems in each of the major topics and explain why they are relevant in engineering. The course is designed to also be used as a reference when you are taking the full version of the course as well, so don’t be afraid if you don’t pick everything up the first time you see it! My hope is that you have the “ah-ha that’s why Scott approached it that way” moment when you take the real course.