Course 11 · College

Diff. Equations

Differential equations and dynamical systems — modeling the real world.

Overview

What this course covers.

Differential Equations is the study of equations involving derivatives and how they model change in science, engineering, and economics. Students learn to solve, analyze, and interpret both ordinary differential equations and systems — with an emphasis on qualitative understanding and real-world applications.

PrerequisitesCalculus III and Linear Algebra (or concurrent enrollment in Linear Algebra).

Curriculum

Topics & units.

Unit 1

First-Order ODEs

›Separable equations
›Linear first-order equations (integrating factor)
›Exact equations
›Modeling: growth, decay, mixing problems

Unit 2

Second-Order ODEs

›Homogeneous equations with constant coefficients
›Undetermined coefficients & variation of parameters
›Spring-mass and RLC circuit models
›Resonance and damping

Unit 3

Systems of ODEs

›Converting to first-order systems
›Eigenvalue method for linear systems
›Phase portraits & stability analysis
›Qualitative behavior of nonlinear systems

Unit 4

Laplace Transforms & Series

›Laplace transform and inverse
›Step functions and impulse inputs
›Power series solutions
›Frobenius method (intro)

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