MIT 18.03SC Differential Equations, Fall 2011
MIT 18.03SC Differential Equations, Fall 2011
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Lectures, recitations, and demonstrations covering topics related to differential equations.
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 firstorder 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 Nonlinear autonomous systems: critical point analysis and phase plane diagrams.
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Course Outline
Chapter 1: MIT 18.03SC Differential Equations, Fall 2011

Lesson 1Separable Equations  MIT 1…07:19

Lesson 2Exploration of the Amplitud…08:06

Lesson 3Lec 1  MIT 18.03 Different…48:55

Lesson 4Exploration of the Isocline…10:59

Lesson 5Direction Fields  MIT 18.0…11:09

Lesson 6Lec 2  MIT 18.03 Different…50:43

Lesson 7Exploration of the Euler's …06:37

Lesson 8Euler's Method  MIT 18.03S…10:17

Lesson 9Lec 3  MIT 18.03 Different…50:22

Lesson 10Linear Equations  MIT 18.0…10:42

Lesson 11Solutions of Firstorder Li…08:56

Lesson 12Lec 6  MIT 18.03 Different…45:26

Lesson 13Complex Numbers and Euler's…11:30

Lesson 14Lec 8  MIT 18.03 Different…50:35

Lesson 15Sinusoidal Functions  MIT …15:04

Lesson 16Lec 7  MIT 18.03 Different…41:10

Lesson 17Firstorder Constant Coeffi…13:19

Lesson 18Sinusoidal Inputs  MIT 18.…13:47

Lesson 19Lec 5  MIT 18.03 Different…45:44

Lesson 20Exploration of the Phase Li…08:54

Lesson 21Lec 9  MIT 18.03 Different…49:58

Lesson 22Autonomous Equations and Ph…11:45

Lesson 23Homogeneous Constant Coeffi…11:29

Lesson 24Homogeneous Constant Coeffi…09:16

Lesson 25Lec 10  MIT 18.03 Differen…46:23

Lesson 26Exploration of the Damped V…06:19

Lesson 27Damped Harmonic Oscillators…09:30

Lesson 28Lec 11  MIT 18.03 Differen…50:31

Lesson 29Lec 12  MIT 18.03 Differen…46:24

Lesson 30Lec 13  MIT 18.03 Differen…47:54

Lesson 31Forced Oscillations  MIT 1…13:07

Lesson 32Gain and Phase Lag  MIT 18…10:40

Lesson 33Undetermined Coefficients …10:42

Lesson 34Lec 14  MIT 18.03 Differen…44:25

Lesson 35Pure Resonance  MIT 18.03S…11:18

Lesson 36Exploration of the Amplitud…11:49

Lesson 37Frequency Response  MIT 18…14:45

Lesson 38Lec 15  MIT 18.03 Differen…49:31

Lesson 39Lec 16  MIT 18.03 Differen…49:28

Lesson 40Computing Fourier Series  …14:42

Lesson 41Exploration of the Fourier …10:02

Lesson 42Manipulating Fourier Series…14:30

Lesson 43Lec 17  MIT 18.03 Differen…45:44

Lesson 44Linear ODE's with Periodic …11:14

Lesson 45Step and Delta Functions  …09:24

Lesson 46Unit Step and Impulse Respo…13:02

Lesson 47Lec 21  MIT 18.03 Differen…44:19

Lesson 48Exploration of the Convolut…06:46

Lesson 49Convolution and Green's For…09:58

Lesson 50Lec 19  MIT 18.03 Differen…47:38

Lesson 51Lec 20  MIT 18.03 Differen…51:05

Lesson 52Laplace Transform: Basics …09:09

Lesson 53Partial Fractions and Lapla…12:30

Lesson 54Laplace: Solving ODE's  MI…11:25

Lesson 55Pole Diagrams  MIT 18.03SC…10:33

Lesson 56Lec 24  MIT 18.03 Differen…47:02

Lesson 57Linear Systems of Equations…06:34

Lesson 58Lec 25  MIT 18.03 Differen…49:05

Lesson 59Lec 26  MIT 18.03 Differen…46:36

Lesson 60Linear Systems: Complex Roo…11:49

Lesson 61Linear Systems: Matrix Meth…08:01

Lesson 62Lec 27  MIT 18.03 Differen…50:25

Lesson 63Phase Portraits  MIT 18.03…12:14

Lesson 64TraceDeterminant Diagram …18:56

Lesson 65Lec 28  MIT 18.03 Differen…46:52

Lesson 66Lec 29  MIT 18.03 Differen…48:51

Lesson 67Matrix Exponentials  MIT 1…11:55

Lesson 68Lec 30  MIT 18.03 Differen…47:05

Lesson 69Lec 33  MIT 18.03 Differen…50:09

Lesson 70Lec 31  MIT 18.03 Differen…47:09

Lesson 71Linearization  MIT 18.03SC…15:55

Lesson 72Lec 32  MIT 18.03 Differen…45:52
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