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Uedu Open / Differential Equations
18.03SC

Differential Equations

Prof. Arthur Mattuck, Prof. Haynes Miller, Dr. Jeremy Orloff, Dr. John Lewis | Fall 2011
Science & Math Mathematics Differential Equations Linear Algebra
前往原始課程
CC BY-NC-SA 4.0
課程簡介

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 the equations and techniques most useful in science and engineering.

Course Format

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

  • Lecture Videos by Professor Arthur Mattuck.
  • Course Notes on every topic.
  • Practice Problems with Solutions.
  • Problem Solving Videos taught by experienced MIT Recitation Instructors.
  • Problem Sets to do on your own with Solutions to check your answers against when you’re done.
  • A selection of Interactive Java® Demonstrations called Mathlets to illustrate key concepts.
  • A full set of Exams with Solutions, including practice exams to help you prepare.

Content Development

Haynes Miller 
Jeremy Orloff 
Dr. John Lewis 
Arthur Mattuck

課程資訊
來源MIT 開放式課程
科系Mathematics
語言English
影片數72
課程影片 (72)
1
Separable Equations | MIT 18.03SC Differential Equations, Fall 2011
Separable Equations | MIT 18.03SC Differential Equations, Fall 2011
2
Exploration of the Amplitude and Phase: First Order Applet
Exploration of the Amplitude and Phase: First Order Applet
3
Lec 1 | MIT 18.03 Differential Equations, Spring 2006
Lec 1 | MIT 18.03 Differential Equations, Spring 2006
4
Exploration of the Isoclines Applet
Exploration of the Isoclines Applet
5
Direction Fields | MIT 18.03SC Differential Equations, Fall 2011
Direction Fields | MIT 18.03SC Differential Equations, Fall 2011
6
Lec 2 | MIT 18.03 Differential Equations, Spring 2006
Lec 2 | MIT 18.03 Differential Equations, Spring 2006
7
Exploration of the Euler's Method Applet
Exploration of the Euler's Method Applet
8
Euler's Method | MIT 18.03SC Differential Equations, Fall 2011
Euler's Method | MIT 18.03SC Differential Equations, Fall 2011
9
Lec 3 | MIT 18.03 Differential Equations, Spring 2006
Lec 3 | MIT 18.03 Differential Equations, Spring 2006
10
Linear Equations | MIT 18.03SC Differential Equations, Fall 2011
Linear Equations | MIT 18.03SC Differential Equations, Fall 2011
11
Solutions of First-order Linear Equations | MIT 18.03SC Differential Equations, Fall 2011
Solutions of First-order Linear Equations | MIT 18.03SC Differential Equations, Fall 2011
12
Lec 6 | MIT 18.03 Differential Equations, Spring 2006
Lec 6 | MIT 18.03 Differential Equations, Spring 2006
13
Complex Numbers and Euler's Formula | MIT 18.03SC Differential Equations, Fall 2011
Complex Numbers and Euler's Formula | MIT 18.03SC Differential Equations, Fall 2011
14
Lec 8 | MIT 18.03 Differential Equations, Spring 2006
Lec 8 | MIT 18.03 Differential Equations, Spring 2006
15
Sinusoidal Functions | MIT 18.03SC Differential Equations, Fall 2011
Sinusoidal Functions | MIT 18.03SC Differential Equations, Fall 2011
16
Lec 7 | MIT 18.03 Differential Equations, Spring 2006
Lec 7 | MIT 18.03 Differential Equations, Spring 2006
17
First-order Constant Coefficient Linear ODE's | MIT 18.03SC Differential Equations, Fall 2011
First-order Constant Coefficient Linear ODE's | MIT 18.03SC Differential Equations, Fall 2011
18
Sinusoidal Inputs | MIT 18.03SC Differential Equations, Fall 2011
Sinusoidal Inputs | MIT 18.03SC Differential Equations, Fall 2011
19
Lec 5 | MIT 18.03 Differential Equations, Spring 2006
Lec 5 | MIT 18.03 Differential Equations, Spring 2006
20
Exploration of the Phase Lines Applet
Exploration of the Phase Lines Applet
21
Lec 9 | MIT 18.03 Differential Equations, Spring 2006
Lec 9 | MIT 18.03 Differential Equations, Spring 2006
22
Autonomous Equations and Phase Lines | MIT 18.03SC Differential Equations, Fall 2011
Autonomous Equations and Phase Lines | MIT 18.03SC Differential Equations, Fall 2011
23
Homogeneous Constant Coefficient Equations: Any Roots | MIT 18.03SC Differential Equations
Homogeneous Constant Coefficient Equations: Any Roots | MIT 18.03SC Differential Equations
24
Homogeneous Constant Coefficient Equations: Real Roots | MIT 18.03SC Differential Equations
Homogeneous Constant Coefficient Equations: Real Roots | MIT 18.03SC Differential Equations
25
Lec 10 | MIT 18.03 Differential Equations, Spring 2006
Lec 10 | MIT 18.03 Differential Equations, Spring 2006
26
Exploration of the Damped Vibrations Applet
Exploration of the Damped Vibrations Applet
27
Damped Harmonic Oscillators | MIT 18.03SC Differential Equations, Fall 2011
Damped Harmonic Oscillators | MIT 18.03SC Differential Equations, Fall 2011
28
Lec 11 | MIT 18.03 Differential Equations, Spring 2006
Lec 11 | MIT 18.03 Differential Equations, Spring 2006
29
Lec 12 | MIT 18.03 Differential Equations, Spring 2006
Lec 12 | MIT 18.03 Differential Equations, Spring 2006
30
Lec 13 | MIT 18.03 Differential Equations, Spring 2006
Lec 13 | MIT 18.03 Differential Equations, Spring 2006
31
Forced Oscillations | MIT 18.03SC Differential Equations, Fall 2011
Forced Oscillations | MIT 18.03SC Differential Equations, Fall 2011
32
Gain and Phase Lag | MIT 18.03SC Differential Equations, Fall 2011
Gain and Phase Lag | MIT 18.03SC Differential Equations, Fall 2011
33
Undetermined Coefficients | MIT 18.03SC Differential Equations, Fall 2011
Undetermined Coefficients | MIT 18.03SC Differential Equations, Fall 2011
34
Lec 14 | MIT 18.03 Differential Equations, Spring 2006
Lec 14 | MIT 18.03 Differential Equations, Spring 2006
35
Pure Resonance | MIT 18.03SC Differential Equations, Fall 2011
Pure Resonance | MIT 18.03SC Differential Equations, Fall 2011
36
Exploration of the Amplitude and Phase: Second Order II Applet
Exploration of the Amplitude and Phase: Second Order II Applet
37
Frequency Response | MIT 18.03SC Differential Equations, Fall 2011
Frequency Response | MIT 18.03SC Differential Equations, Fall 2011
38
Lec 15 | MIT 18.03 Differential Equations, Spring 2006
Lec 15 | MIT 18.03 Differential Equations, Spring 2006
39
Lec 16 | MIT 18.03 Differential Equations, Spring 2006
Lec 16 | MIT 18.03 Differential Equations, Spring 2006
40
Computing Fourier Series | MIT 18.03SC Differential Equations, Fall 2011
Computing Fourier Series | MIT 18.03SC Differential Equations, Fall 2011
41
Exploration of the Fourier Coefficient Applet
Exploration of the Fourier Coefficient Applet
42
Manipulating Fourier Series | MIT 18.03SC Differential Equations, Fall 2011
Manipulating Fourier Series | MIT 18.03SC Differential Equations, Fall 2011
43
Lec 17 | MIT 18.03 Differential Equations, Spring 2006
Lec 17 | MIT 18.03 Differential Equations, Spring 2006
44
Linear ODE's with Periodic Input | MIT 18.03SC Differential Equations, Fall 2011
Linear ODE's with Periodic Input | MIT 18.03SC Differential Equations, Fall 2011
45
Step and Delta Functions | MIT 18.03SC Differential Equations, Fall 2011
Step and Delta Functions | MIT 18.03SC Differential Equations, Fall 2011
46
Unit Step and Impulse Response | MIT 18.03SC Differential Equations, Fall 2011
Unit Step and Impulse Response | MIT 18.03SC Differential Equations, Fall 2011
47
Lec 21 | MIT 18.03 Differential Equations, Spring 2006
Lec 21 | MIT 18.03 Differential Equations, Spring 2006
48
Exploration of the Convolution Accumulation Applet
Exploration of the Convolution Accumulation Applet
49
Convolution and Green's Formula | MIT 18.03SC Differential Equations, Fall 2011
Convolution and Green's Formula | MIT 18.03SC Differential Equations, Fall 2011
50
Lec 19 | MIT 18.03 Differential Equations, Spring 2006
Lec 19 | MIT 18.03 Differential Equations, Spring 2006
51
Lec 20 | MIT 18.03 Differential Equations, Spring 2006
Lec 20 | MIT 18.03 Differential Equations, Spring 2006
52
Laplace Transform: Basics | MIT 18.03SC Differential Equations, Fall 2011
Laplace Transform: Basics | MIT 18.03SC Differential Equations, Fall 2011
53
Partial Fractions and Laplace Inverse | MIT 18.03SC Differential Equations, Fall 2011
Partial Fractions and Laplace Inverse | MIT 18.03SC Differential Equations, Fall 2011
54
Laplace: Solving ODE's | MIT 18.03SC Differential Equations, Fall 2011
Laplace: Solving ODE's | MIT 18.03SC Differential Equations, Fall 2011
55
Pole Diagrams | MIT 18.03SC Differential Equations, Fall 2011
Pole Diagrams | MIT 18.03SC Differential Equations, Fall 2011
56
Lec 24 | MIT 18.03 Differential Equations, Spring 2006
Lec 24 | MIT 18.03 Differential Equations, Spring 2006
57
Linear Systems of Equations | MIT 18.03SC Differential Equations, Fall 2011
Linear Systems of Equations | MIT 18.03SC Differential Equations, Fall 2011
58
Lec 25 | MIT 18.03 Differential Equations, Spring 2006
Lec 25 | MIT 18.03 Differential Equations, Spring 2006
59
Lec 26 | MIT 18.03 Differential Equations, Spring 2006
Lec 26 | MIT 18.03 Differential Equations, Spring 2006
60
Linear Systems: Complex Roots | MIT 18.03SC Differential Equations, Fall 2011
Linear Systems: Complex Roots | MIT 18.03SC Differential Equations, Fall 2011
61
Linear Systems: Matrix Methods | MIT 18.03SC Differential Equations, Fall 2011
Linear Systems: Matrix Methods | MIT 18.03SC Differential Equations, Fall 2011
62
Lec 27 | MIT 18.03 Differential Equations, Spring 2006
Lec 27 | MIT 18.03 Differential Equations, Spring 2006
63
Phase Portraits | MIT 18.03SC Differential Equations, Fall 2011
Phase Portraits | MIT 18.03SC Differential Equations, Fall 2011
64
Trace-Determinant Diagram | MIT 18.03SC Differential Equations, Fall 2011
Trace-Determinant Diagram | MIT 18.03SC Differential Equations, Fall 2011
65
Lec 28 | MIT 18.03 Differential Equations, Spring 2006
Lec 28 | MIT 18.03 Differential Equations, Spring 2006
66
Lec 29 | MIT 18.03 Differential Equations, Spring 2006
Lec 29 | MIT 18.03 Differential Equations, Spring 2006
67
Matrix Exponentials | MIT 18.03SC Differential Equations, Fall 2011
Matrix Exponentials | MIT 18.03SC Differential Equations, Fall 2011
68
Lec 30 | MIT 18.03 Differential Equations, Spring 2006
Lec 30 | MIT 18.03 Differential Equations, Spring 2006
69
Lec 33 | MIT 18.03 Differential Equations, Spring 2006
Lec 33 | MIT 18.03 Differential Equations, Spring 2006
70
Lec 31 | MIT 18.03 Differential Equations, Spring 2006
Lec 31 | MIT 18.03 Differential Equations, Spring 2006
71
Linearization | MIT 18.03SC Differential Equations, Fall 2011
Linearization | MIT 18.03SC Differential Equations, Fall 2011
72
Lec 32 | MIT 18.03 Differential Equations, Spring 2006
Lec 32 | MIT 18.03 Differential Equations, Spring 2006