Differential Equations (MIT 18.03) - Video lectures 2003
Arthur Mattuck

@article{,
title= {Differential Equations (MIT 18.03) - Video lectures 2003},
journal= {},
author= {Arthur Mattuck},
year= {2003},
url= {http://ocw.mit.edu/18-03S06},
abstract= {The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on linear differential equations and their applications in science and engineering.

**Main course URL:** http://ocw.mit.edu/18-03S06

---

**Prerequisites:**
* Multivariable Calculus (MIT 18.02) - [Video lectures](https://academictorrents.com/details/81d27851df2879ed1307c8d60980d2b8af19264b) and [Worked examples](https://academictorrents.com/details/28a30bdd9a6859622e87e04ffb9eb4a9810bdf77)

**Related materials:**
* [Differential Equations (MIT 18.03) - Worked examples 2011](https://academictorrents.com/edit/6c3432a82526a1f25ca0edc4e9f09254da66aeb2)
* [Differential Equations (MIT 18.03) - Supplementary notes 2010](https://academictorrents.com/details/1d3ced525d5c5bfbcaa71e176c371c373e4122dc)
* [Notes on Diffy Qs: Differential Equations for Engineers - Textbook, edition 6.11, 2026](https://academictorrents.com/details/7bacfc3ee249d6506c16ed1df2bbb19d825eb665)

---

**Table of contents:**

* Unit I: First Order Differential Equations
  * Lecture 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves
  * Lecture 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations
  * Lecture 3: Solving First-order Linear ODE's (Ordinary Differential Equations); Steady-state and Transient Solutions
  * Lecture 4: First-order Substitution Methods: Bernoulli and Homogeneous ODE's
  * Lecture 5: First-order Autonomous ODE's: Qualitative Methods, Aplications
  * Lecture 6: Complex Numbers and Complex Exponentials
  * Lecture 7: First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods
  * Lecture 8: Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models


* Unit II: Second Order Constant Coefficient Linear Equations
  * Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases
  * Lecture 10: Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations
  * Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians
  * Lecture 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODEs
  * Lecture 13: Finding Particular Solutions to Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials
  * Lecture 14: Interpretation of the Exceptional Case: Resonance


* Unit III: Fourier Series and Laplace Transform
  * Lecture 15: Introduction to Fourier Series; Basic Formulas for Period 2π.
  * Lecture 16: Continuation: More General Periods; Even and Odd Functions;  Periodic Extension
  * Lecture 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds
  * Lecture 19: Introduction to the Laplace Transform; Basic Formulas
  * Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's
  * Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems
  * Lecture 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs
  * Lecture 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions


* Unit IV: First-order Systems
  * Lecture 24: Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System.
  * Lecture 25: Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case)
  * Lecture 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues
  * Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
  * Lecture 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters
  * Lecture 29: Matrix Exponentials; Application to Solving Systems
  * Lecture 30: Decoupling Linear Systems with Constant Coefficients
  * Lecture 31: Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum
  * Lecture 32: Limit Cycles: Existence and Non-existence Criteria
  * Lecture 33: Relation Between Non-linear Systems and First-order ODEs; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle

---

This content hosted at the Internet Archive at https://archive.org/details/MIT18.03S06
Files may have changed, which prevents torrents from downloading correctly or completely; please check for an updated torrent at https://archive.org/download/MIT18.03S06/MIT18.03S06_archive.torrent
Note: retrieval usually requires a client that supports webseeding (GetRight style).
Note: many Internet Archive torrents contain a 'pad file' directory. This directory and the files within it may be erased once retrieval completes.
Note: the file MIT18.03S06_meta.xml contains metadata about this torrent's contents.},
keywords= {Math, Maths, mathematics, calculus},
terms= {https://ocw.mit.edu/terms},
license= {http://creativecommons.org/licenses/by-nc-sa/3.0/us/},
superseded= {}
}