MIT 18.03 Differential Equations - Spring 2006

MIT 18.03 Differential Equations - Spring 2006

67 Lectures · Feb 5, 2003

About

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.

Course Homepage 18.03 Differential Equations Spring 2006

Course features at MIT OpenCourseWare page:

*Syllabus *Calendar *Readings *Lecture Notes *Recitations *Assignment *Exams *Tools *Download Course Materials

Complete MIT OCW video collection at MIT OpenCourseWare - VideoLectures.NET

Related categories

Uploaded videos:

video-img
48:55

Lecture 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves

Arthur Mattuck

Jan 19, 2009

 Â· 

52726 Views

Lecture
video-img
50:45

Lecture 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations

Arthur Mattuck

Jan 19, 2009

 Â· 

21375 Views

Lecture
video-img
50:22

Lecture 3: Solving First-order Linear ODE's; Steady-state and Transient Solution...

Arthur Mattuck

Jan 19, 2009

 Â· 

18305 Views

Lecture
video-img
50:13

Lecture 4: First-order Substitution Methods: Bernouilli and Homogeneous ODE's

Arthur Mattuck

Jan 19, 2009

 Â· 

13542 Views

Lecture
video-img
45:46

Lecture 5: First-order Autonomous ODE's: Qualitative Methods, Applications

Arthur Mattuck

Jan 19, 2009

 Â· 

10462 Views

Lecture
video-img
45:28

Lecture 6: Complex Numbers and Complex Exponentials

Arthur Mattuck

Jan 19, 2009

 Â· 

15614 Views

Lecture
video-img
41:09

Lecture 7: First-order Linear with Constant Coefficients: Behavior of Solutions,...

Arthur Mattuck

Jan 19, 2009

 Â· 

10361 Views

Lecture
video-img
50:36

Lecture 8: Continuation; Applications to Temperature, Mixing, RC-circuit, Decay...

Arthur Mattuck

Jan 19, 2009

 Â· 

8057 Views

Lecture
video-img
50:00

Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients: The Thr...

Arthur Mattuck

Jan 19, 2009

 Â· 

10170 Views

Lecture
video-img
46:24

Lecture 10: Continuation: Complex Characteristic Roots; Undamped and Damped Osci...

Arthur Mattuck

Jan 19, 2009

 Â· 

8325 Views

Lecture
video-img
50:31

Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superpositi...

Arthur Mattuck

Jan 19, 2009

 Â· 

8121 Views

Lecture
video-img
46:24

Lecture 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Crit...

Arthur Mattuck

Jan 19, 2009

 Â· 

7534 Views

Lecture
video-img
47:55

Lecture 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Fo...

Arthur Mattuck

Jan 19, 2009

 Â· 

8130 Views

Lecture
video-img
44:26

Lecture 14: Interpretation of the Exceptional Case: Resonance

Arthur Mattuck

Jan 19, 2009

 Â· 

7144 Views

Lecture
video-img
49:31

Lecture 15: Introduction to Fourier Series; Basic Formulas for Period 2(pi)

Arthur Mattuck

Jan 19, 2009

 Â· 

25841 Views

Lecture
video-img
49:29

Lecture 16: Continuation: More General Periods; Even and Odd Functions; Periodic...

Arthur Mattuck

Jan 19, 2009

 Â· 

9415 Views

Lecture
video-img
45:46

Lecture 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hea...

Arthur Mattuck

Jan 19, 2009

 Â· 

8273 Views

Lecture
video-img
47:40

Lecture 19: Introduction to the Laplace Transform; Basic Formulas

Arthur Mattuck

Jan 19, 2009

 Â· 

36777 Views

Lecture
video-img
51:07

Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE...

Arthur Mattuck

Jan 19, 2009

 Â· 

14771 Views

Lecture
video-img
44:19

Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Appli...

Arthur Mattuck

Jan 19, 2009

 Â· 

15291 Views

Lecture
video-img
44:08

Lecture 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs

Arthur Mattuck

Jan 19, 2009

 Â· 

10919 Views

Lecture
video-img
44:55

Lecture 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer F...

Arthur Mattuck

Jan 19, 2009

 Â· 

10484 Views

Lecture
video-img
47:04

Lecture 24: Introduction to First-order Systems of ODE's; Solution by Eliminatio...

Arthur Mattuck

Jan 19, 2009

 Â· 

7312 Views

Lecture
video-img
49:06

Lecture 25: Homogeneous Linear Systems with Constant Coefficients: Solution via ...

Arthur Mattuck

Jan 19, 2009

 Â· 

9858 Views

Lecture
video-img
46:37

Lecture 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues

Arthur Mattuck

Jan 19, 2009

 Â· 

7377 Views

Lecture
video-img
50:27

Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant C...

Arthur Mattuck

Jan 19, 2009

 Â· 

7338 Views

Lecture
video-img
46:53

Lecture 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix...

Arthur Mattuck

Jan 19, 2009

 Â· 

7468 Views

Lecture
video-img
48:53

Lecture 29: Matrix Exponentials; Application to Solving Systems

Arthur Mattuck

Jan 19, 2009

 Â· 

6268 Views

Lecture
video-img
47:06

Lecture 30: Decoupling Linear Systems with Constant Coefficients

Arthur Mattuck

Jan 19, 2009

 Â· 

6761 Views

Lecture
video-img
47:11

Lecture 31: Non-linear Autonomous Systems: Finding the Critical Points and Sketc...

Arthur Mattuck

Jan 19, 2009

 Â· 

9320 Views

Lecture
video-img
45:53

Lecture 32: Limit Cycles: Existence and Non-existence Criteria

Arthur Mattuck

Jan 19, 2009

 Â· 

16434 Views

Lecture
video-img
50:09

Lecture 33: Relation Between Non-linear Systems and First-order ODE's; Structura...

Arthur Mattuck

Jan 19, 2009

 Â· 

7633 Views

Lecture

Unit I: First Order Differential Equations

video-img
07:18

Separable Equations

Lydia Bourouiba

Mar 05, 2013

 Â· 

6150 Views

Lecture
video-img
11:08

Direction Fields

David Shirokoff

Mar 05, 2013

 Â· 

3120 Views

Lecture
video-img
10:16

Euler's Method

David Shirokoff

Mar 05, 2013

 Â· 

3028 Views

Lecture
video-img
10:41

Linear Equations

David Shirokoff

Mar 05, 2013

 Â· 

2635 Views

Lecture
video-img
08:56

Solutions of First Order Linear Equations

Lydia Bourouiba

Mar 05, 2013

 Â· 

4201 Views

Lecture
video-img
11:30

Complex Numbers and Euler's Formula

Lydia Bourouiba

Mar 05, 2013

 Â· 

3286 Views

Lecture
video-img
15:03

Sinusoidal Functions

David Shirokoff

Mar 05, 2013

 Â· 

2248 Views

Lecture
video-img
13:18

First Order Constant Coefficient Linear ODE's

David Shirokoff

Mar 05, 2013

 Â· 

2405 Views

Lecture
video-img
13:46

Sinusoidal Inputs

Lydia Bourouiba

Mar 05, 2013

 Â· 

2539 Views

Lecture
video-img
11:44

Autonomous Equations and Phase Lines

David Shirokoff

Mar 05, 2013

 Â· 

2407 Views

Lecture

Unit II: Second Order Constant Coefficient Linear Equations

video-img
09:15

Homogeneous Constant Coefficient Equations: Real Roots

David Shirokoff

Mar 05, 2013

 Â· 

2532 Views

Lecture
video-img
11:28

Homogeneous Constant Coefficient Equations: Any Roots

Lydia Bourouiba

Mar 05, 2013

 Â· 

3076 Views

Lecture
video-img
13:06

Forced Oscillations

David Shirokoff

Mar 05, 2013

 Â· 

2299 Views

Lecture
video-img
10:39

Gain and Phase Lag

David Shirokoff

Mar 05, 2013

 Â· 

2321 Views

Lecture
video-img
10:42

Undetermined Coefficients

David Shirokoff

Mar 05, 2013

 Â· 

2447 Views

Lecture
video-img
11:17

Pure Resonance

Lydia Bourouiba

Mar 05, 2013

 Â· 

3314 Views

Lecture
video-img
14:44

Frequency Response

David Shirokoff

Mar 05, 2013

 Â· 

2272 Views

Lecture

Unit III: Fourier Series and Laplace Transform

video-img
14:41

Computing Fourier Series

David Shirokoff

Mar 05, 2013

 Â· 

2781 Views

Lecture
video-img
14:29

Manipulating Fourier Series

David Shirokoff

Mar 05, 2013

 Â· 

2384 Views

Lecture
video-img
11:14

Linear ODE's with Periodic Input

David Shirokoff

Mar 05, 2013

 Â· 

2389 Views

Lecture
video-img
09:57

Convolution and Green's Formula

David Shirokoff

Mar 05, 2013

 Â· 

2601 Views

Lecture
video-img
12:29

Partial Fractions and Laplace Inverse

David Shirokoff

Mar 05, 2013

 Â· 

2546 Views

Lecture
video-img
09:08

Laplace Transform: Basics

Lydia Bourouiba

Mar 05, 2013

 Â· 

8319 Views

Lecture
video-img
09:23

Step and Delta Functions: Integration and Generalized Derivatives

Lydia Bourouiba

Mar 05, 2013

 Â· 

3176 Views

Lecture
video-img
13:01

Unit Step and Impulse Response

Lydia Bourouiba

Mar 05, 2013

 Â· 

3021 Views

Lecture
video-img
10:32

Pole Diagrams

Lydia Bourouiba

Mar 05, 2013

 Â· 

2555 Views

Lecture

IV: First-order Systems

video-img
08:00

Linear Systems: Matrix Methods

Lydia Bourouiba

Mar 05, 2013

 Â· 

3301 Views

Lecture
video-img
11:54

Matrix Exponentials

Lydia Bourouiba

Mar 05, 2013

 Â· 

2492 Views

Lecture
video-img
12:13

Phase Portraits

Lydia Bourouiba

Mar 05, 2013

 Â· 

2745 Views

Lecture
video-img
15:54

Linearization

Lydia Bourouiba

Mar 05, 2013

 Â· 

2727 Views

Lecture
video-img
09:29

Damped Harmonic Oscillators

Lydia Bourouiba

Mar 05, 2013

 Â· 

2876 Views

Lecture
video-img
18:55

Trace-Determinant Diagram

Lydia Bourouiba

Mar 05, 2013

 Â· 

2693 Views

Lecture
video-img
11:48

Linear Systems: Complex Roots

Lydia Bourouiba

Mar 05, 2013

 Â· 

2851 Views

Lecture
video-img
06:33

Linear Systems of Equations

Lydia Bourouiba

Mar 05, 2013

 Â· 

8055 Views

Lecture
video-img
11:24

Laplace: Solving ODE's

David Shirokoff

Mar 05, 2013

 Â· 

2978 Views

Lecture