Differential Equations - Complete Review Course | Online Crash Course

This will be important for anyone studying differential equations. It includes all four major topics that should appear in an undergraduate level differential equation course. Here below are the timestamps with direct link to the relevant lectures. List of typos are given at the end.

Topics line up
Part 1 - First Order Differential Equations
1) Intro 0:00 https://youtu.be/YHxBaOttKCU
a) Verifying solutions 6:04
2) Four fundamental equations 29:26 https://youtu.be/5pPqCsoxCAg
3) Classifying differential equations 33:14 https://youtu.be/FnJvoDC9YLY
4) Basic Integration 47:52 https://youtu.be/RoGAe-RS_9Y
a) Table of common integrals 1:02:06 https://youtu.be/deFbVR5uGNk
5) Separation of variable method 1:02:08 https://youtu.be/2PSqkauhzN4
6) Integration factor method 1:12:13 https://youtu.be/ggRo6G7iAzM
7) Direct substitution method 1:29:38 https://youtu.be/1pUYQsOR2bI
8) Homogeneous equation 1:38:40 https://youtu.be/5hUB6HRTAOU
9) Bernoulli's equation 1:49:03 https://youtu.be/3KnDQUY9mKs
10) Exact equation 2:02:29 https://youtu.be/WJJKZHuzq64
11) Almost-exact equation 2:21:13 https://youtu.be/tOdlvZpdako
All-In-One review 2:32:20 https://youtu.be/Eqi7mTCmr6M
12) Numerical Methods 2:32:56 https://youtu.be/HWuanyR-5R0
13) Euler's method 2:34:20
14) Runge-Kutta method 2:46:12
15) Directional fields 2:50:54 https://youtu.be/mswRlRmE1CI
16) Existence & Uniqueness Thm 3:00:58 https://youtu.be/Ago6DCYtYoY
17) Autonomous equation 3:08:28 https://youtu.be/PGcb-6JYgkI

Part 2 - Second Order Differential Equations
18) 2nd Order Linear Differential Eq. 3:18:09 https://youtu.be/At7wz7P84Y8
a) Linear Independence 3:39:09
b) Form of the General Solution 3:44:14
19) Reduction of Order Method 3:57:25 https://youtu.be/AL3bHEsXcYo
a) Reduction of Order formula 4:19:23
20) Constant Coefficient Diff. Eq 4:28:12 https://youtu.be/S24Y5BTZJtw
a) Complex Numbers Review 4:28:11 https://youtu.be/oxBI9hQuW48
21) Cauchy-Euler Diff. Equation 4:55:44 https://youtu.be/i09piUdnO9U
22) Higher Order Constant Coefficient Eq 5:15:56 https://youtu.be/-dqVyI6XpHY
23) Non-homogeneous Diff. Eq 5:33:42
24) Undetermined Coefficient Method 5:39:24 https://youtu.be/n1TldVpXp48
25) Variation of Parameters Method 6:14:52 https://youtu.be/8wy4badZXUw
a) Formula for VP method 6:33:57

Part 3 - Series, Laplace Transforms & Systems
26) Series Solution Method 6:40:22 https://youtu.be/7unqSjn_knM
a) SeeSaw method for series https://youtu.be/_ylM-Fv36lA
27) Laplace transform method 7:22:28
a) Find Laplace transform 7:25:33 https://youtu.be/jLh1nyGcFMk
b) Inverse Laplace transform 7:37:9 https://youtu.be/GOle3ZCgNCA
c) Cover-Up Method https://youtu.be/NS-KgLwTmok
d) Solving Diff. Equations 7:59:47 https://youtu.be/wFzdCtBfKnM
e) Convolution method 8:13:30 https://youtu.be/T4pQTGzGFa0
f) Heaviside function 8:28:55 https://youtu.be/l82ScRxQWNI
g) Dirac Delta function 8:50:12 https://youtu.be/FgSk_6JeYv0
28) System of equations 9:04:08
a) Elimination method 9:06:44 https://youtu.be/1tCwpNHWX5I
b) Laplace transform method 9:22:23 https://youtu.be/1tCwpNHWX5I
c) Eigenvectors method 9:32:47 https://youtu.be/xlM3QKBJY6E
d) Shortcut method for 2 x 2 https://youtu.be/2rAu-52Lo88
e) Shortcut method for 3 x 3 (repeat) https://youtu.be/HNDrTLuBYjs
f) Shortcut method for 3 x 3 https://youtu.be/NjOUAJlR534
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List of typos
at 21:28, it should be dy/dt = ky
at 22:38, it should be dy/dt = -ky
at 4:38:50. The equation has -3 in it, not +3.
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Important Derivatives Review (All topics) https://youtu.be/0ljuv5NWiuk

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I hope you learn something new. Thank you for watching.

#Mathematics #DifferentialEquations #Review

Видео Differential Equations - Complete Review Course | Online Crash Course канала The Math Tutor