Outline
Differential Equations For The People
This GeoGebra "book" is a set of interactive notes that I use to teach Differential Equations at Vermont State University in the Vermont State College System. Interactive applets replace static figures to illustrate the concepts. Many--but not all--of the algebraic hurdles have been shunted to the GeoGebra Computer Algebra System (CAS). In particular, students are not expected to be skillful in second semester calculus integration techniques, linear algebraic skills associated with solving systems of linear algebraic equations, and simplification of complicated expressions. GeoGebra can take care of most of that for us. That said, a firm understanding of the concept and calculation of derivatives is expected. Similarly, knowledge of the core principle of integration as well as elementary techniques up to about u-substitution is also expected.
This is a sequel (or "second season") of sorts to Calculus for the People -- https://www.geogebra.org/m/x39ys4d7 -- so if you want to brush up on elementary differentiation and integration, check it out.
Email me at greg dot petrics at vermontstate dot edu to learn more, or to offer your comments and suggestions.
These notes are open source. Feel free to use them or modify them in any way. I'd appreciate some credit if you republish these elsewhere.
Table of Contents
First Order Differential Equations
- Differential Equations Day 1 -- Introduction & Slope Fields
- Differential Equations Day 2 -- Separable Differential Equations
- Differential Equations Day 3 -- Initial Conditions and Intro to Modeling
- Differential Equations Day 4 -- Intro to Numerical Methods: Euler's Method
- Differential Equations Day 5 -- Newton's Law of Cooling with Numerical Methods
- Differential Equations Day 6 -- Linear Differential Equations
- Differential Equations Day 7 -- Algebraic Newton's Law of Cooling & Programing Euler's Numerical Method
- Euler's Numerical Method Calculator for First Order Differential Equations
- Differential Equations Day 8 -- Exact Differential Equations
- Differential Equations Day 9 -- Revisiting Exact Differential Equations
- Differential Equations Day 10 -- Project 1 -- Newton's Law of Cooling
- Differential Equations Day 11 -- Project 2 -- Logistic Growth
- Differential Equations Day 12 -- Project 3 -- Mixing Models
Second Order Differential Equations
- Differential Equations Day 13 -- Second Order Differential Equations
- Differential Equations Day 14 -- Complex Roots of Homogeneous Constant Coefficient Second Order Differential Equations & Introduction to Systemification
- Differential Equations Day 15 -- Project 4 -- Mechanical Vibrations of Spring Systems
- Differential Equations Day 16 -- Undetermined Coefficients: Solving Non Homogeneous Second Order Constant Coefficient Differential Equations
- Differential Equations Day 17 -- Revisiting Systemification & Euler's Method for Second Order Differential Equations
- Euler's Numerical Method Calculator for Systems or Second Order Differential Equations
- Differential Equations Day 18 -- Runge-Kutta Numerical Method for Systems and Second Order Differential Equations
- Runge Kutta 4 (RK4) Numerical Method Calculator for Systems or Second Order Differential Equations
- Differential Equations Day 19 -- Project 5 -- Pendular Motion
- Developing the Second Order Differential Equation that Models Simple Pendular Motion
- Differential Equations Day 20 -- Laplace Transform for Solving Initial Value Problems
Systems of First Order Differential Equations
- Differential Equations Day 21 -- Introduction to Systems of Differential Equations
- Differential Equations Day 22 -- The Algebraic Theory of Systems of Differential Equations (Real Eigenvalues)
- Phase Plane Sketcher
- Differential Equations Day 23 -- The Algebraic Theory of Systems of Differential Equations (Complex Eigenvalues)
- Differential Equations Day 24 -- Project 6 -- Lotka-Volterra Predator Prey Models
- Chaotic Self-Organizing Behavior in Low-Dimensional Lotka-Volterra Equations
Existence and Uniqueness Theorems
Closing Remarks