MIT 18.03SC Differential Equations, Fall 2011

Lectures, recitations, and demonstrations covering topics related to differ
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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 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.

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Course Outline

Chapter 1: MIT 18.03SC Differential Equations, Fall 2011

  • Lesson 1
    Separable Equations | MIT 1…
    07:19
  • Lesson 2
    Exploration of the Amplitud…
    08:06
  • Lesson 3
    Lec 1 | MIT 18.03 Different…
    48:55
  • Lesson 4
    Exploration of the Isocline…
    10:59
  • Lesson 5
    Direction Fields | MIT 18.0…
    11:09
  • Lesson 6
    Lec 2 | MIT 18.03 Different…
    50:43
  • Lesson 7
    Exploration of the Euler's …
    06:37
  • Lesson 8
    Euler's Method | MIT 18.03S…
    10:17
  • Lesson 9
    Lec 3 | MIT 18.03 Different…
    50:22
  • Lesson 10
    Linear Equations | MIT 18.0…
    10:42
  • Lesson 11
    Solutions of First-order Li…
    08:56
  • Lesson 12
    Lec 6 | MIT 18.03 Different…
    45:26
  • Lesson 13
    Complex Numbers and Euler's…
    11:30
  • Lesson 14
    Lec 8 | MIT 18.03 Different…
    50:35
  • Lesson 15
    Sinusoidal Functions | MIT …
    15:04
  • Lesson 16
    Lec 7 | MIT 18.03 Different…
    41:10
  • Lesson 17
    First-order Constant Coeffi…
    13:19
  • Lesson 18
    Sinusoidal Inputs | MIT 18.…
    13:47
  • Lesson 19
    Lec 5 | MIT 18.03 Different…
    45:44
  • Lesson 20
    Exploration of the Phase Li…
    08:54
  • Lesson 21
    Lec 9 | MIT 18.03 Different…
    49:58
  • Lesson 22
    Autonomous Equations and Ph…
    11:45
  • Lesson 23
    Homogeneous Constant Coeffi…
    11:29
  • Lesson 24
    Homogeneous Constant Coeffi…
    09:16
  • Lesson 25
    Lec 10 | MIT 18.03 Differen…
    46:23
  • Lesson 26
    Exploration of the Damped V…
    06:19
  • Lesson 27
    Damped Harmonic Oscillators…
    09:30
  • Lesson 28
    Lec 11 | MIT 18.03 Differen…
    50:31
  • Lesson 29
    Lec 12 | MIT 18.03 Differen…
    46:24
  • Lesson 30
    Lec 13 | MIT 18.03 Differen…
    47:54
  • Lesson 31
    Forced Oscillations | MIT 1…
    13:07
  • Lesson 32
    Gain and Phase Lag | MIT 18…
    10:40
  • Lesson 33
    Undetermined Coefficients |…
    10:42
  • Lesson 34
    Lec 14 | MIT 18.03 Differen…
    44:25
  • Lesson 35
    Pure Resonance | MIT 18.03S…
    11:18
  • Lesson 36
    Exploration of the Amplitud…
    11:49
  • Lesson 37
    Frequency Response | MIT 18…
    14:45
  • Lesson 38
    Lec 15 | MIT 18.03 Differen…
    49:31
  • Lesson 39
    Lec 16 | MIT 18.03 Differen…
    49:28
  • Lesson 40
    Computing Fourier Series | …
    14:42
  • Lesson 41
    Exploration of the Fourier …
    10:02
  • Lesson 42
    Manipulating Fourier Series…
    14:30
  • Lesson 43
    Lec 17 | MIT 18.03 Differen…
    45:44
  • Lesson 44
    Linear ODE's with Periodic …
    11:14
  • Lesson 45
    Step and Delta Functions | …
    09:24
  • Lesson 46
    Unit Step and Impulse Respo…
    13:02
  • Lesson 47
    Lec 21 | MIT 18.03 Differen…
    44:19
  • Lesson 48
    Exploration of the Convolut…
    06:46
  • Lesson 49
    Convolution and Green's For…
    09:58
  • Lesson 50
    Lec 19 | MIT 18.03 Differen…
    47:38
  • Lesson 51
    Lec 20 | MIT 18.03 Differen…
    51:05
  • Lesson 52
    Laplace Transform: Basics |…
    09:09
  • Lesson 53
    Partial Fractions and Lapla…
    12:30
  • Lesson 54
    Laplace: Solving ODE's | MI…
    11:25
  • Lesson 55
    Pole Diagrams | MIT 18.03SC…
    10:33
  • Lesson 56
    Lec 24 | MIT 18.03 Differen…
    47:02
  • Lesson 57
    Linear Systems of Equations…
    06:34
  • Lesson 58
    Lec 25 | MIT 18.03 Differen…
    49:05
  • Lesson 59
    Lec 26 | MIT 18.03 Differen…
    46:36
  • Lesson 60
    Linear Systems: Complex Roo…
    11:49
  • Lesson 61
    Linear Systems: Matrix Meth…
    08:01
  • Lesson 62
    Lec 27 | MIT 18.03 Differen…
    50:25
  • Lesson 63
    Phase Portraits | MIT 18.03…
    12:14
  • Lesson 64
    Trace-Determinant Diagram |…
    18:56
  • Lesson 65
    Lec 28 | MIT 18.03 Differen…
    46:52
  • Lesson 66
    Lec 29 | MIT 18.03 Differen…
    48:51
  • Lesson 67
    Matrix Exponentials | MIT 1…
    11:55
  • Lesson 68
    Lec 30 | MIT 18.03 Differen…
    47:05
  • Lesson 69
    Lec 33 | MIT 18.03 Differen…
    50:09
  • Lesson 70
    Lec 31 | MIT 18.03 Differen…
    47:09
  • Lesson 71
    Linearization | MIT 18.03SC…
    15:55
  • Lesson 72
    Lec 32 | MIT 18.03 Differen…
    45:52

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