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Browse materialsMIT 18.03SC · Unit IV: First-order Systems

Differential Equations — Unit IV: First-order Systems

Subjects: Algebra · Linear Algebra · Mathematics

Art: Anonymous painter,15th century, Westerner and Arab practicing geometry 15th century manuscript, 15th… · Public domain

About this course

Source: MIT OpenCourseWare 18.03SC Differential Equations, Fall 2011, Prof. Arthur Mattuck, Prof. Haynes Miller, Dr. Jeremy Orloff, Dr. John Lewis — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: this unit's sessions in MIT's listing order. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 22, 2026. How RedLectern is built.

Instructors: Prof. Arthur Mattuck, Prof. Haynes Miller, Dr. Jeremy Orloff, Dr. John Lewis
Term: Fall 2011
Level: Undergraduate
What's inside: 30 videos · 1 solution · 84 other files
Materials open: Videos here · files on MIT OCW

Other versions of this course

18.03SC · Fall 2011 · Study here (this version)
18.03 · Spring 2010 · Study here

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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Linear Systems

22 files

Matrix Methods

14 files

Phase Portraits

14 files

Matrix Exponentials

15 files

Nonlinear Systems

Linearization

9 files

Differential Equations — Unit IV: First-order Systems

Materials by section

Linear Systems

Matrix Methods

Phase Portraits

Matrix Exponentials

Nonlinear Systems

Linearization

Limit Cycles and Chaos

Introduction to Systems

Autonomous Systems: Solutions are Parametrized Curves

Linear Systems of Equations

Matrix Methods Introduction, First Example

Matrix Systems: General Terminology

Complex Eigenvalues: Example

Three Chamber Mixing Example: Repeated Roots

Linear Systems: Matrix Methods

Linear Systems: Complex Roots

Sketching Solutions

More Sketching Solutions

Trace-Determinant Diagram

Phase Portraits

Theory of Systems

Fundamental Matrices

The Matrix Exponential I

The Matrix Exponential II

Example: Solving a System with the Matrix Exponential

Calculating the Exponential Matrix

Variation of Parameters

Matrix Exponentials

Decoupling

The Relation Between Nonlinear Systems and First-order ODE's

The Nonlinear Pendulum

Example: Predator-Prey and Volterra's Principle

Linearization

Limit Cycles

Existence of Limit Cycles

Non-existence of Limit Cycles

A Story about Limit Cycles