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Lecture 1 | 11:02 | ||
What a differential equation is and some terminology. | |||
Lecture 2 | 12:00 | ||
Introduction to separable differential equations. | |||
Lecture 3 | 05:37 | ||
Another separable differential equation example. | |||
Lecture 4 | 09:54 | ||
Chain rule using partial derivatives (not a proof; more intuition). | |||
Lecture 5 | 10:51 | ||
More intuitive building blocks for exact equations. | |||
Lecture 6 | 12:09 | ||
First example of solving an exact differential equation. | |||
Lecture 7 | 08:01 | ||
Some more exact equation examples | |||
Lecture 8 | 09:59 | ||
One more exact equation example | |||
Lecture 9 | 10:16 | ||
Using an integrating factor to make a differential equation exact | |||
Lecture 10 | 08:26 | ||
Now that we've made the equation exact, let's solve it! | |||
Lecture 11 | 07:21 | ||
Introduction to first order homogenous equations. | |||
Lecture 12 | 08:22 | ||
Another example of using substitution to solve a first order homogeneous differential equations. | |||
Lecture 13 | 09:44 | ||
Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients. | |||
Lecture 14 | 08:28 | ||
Let's find the general solution! | |||
Lecture 15 | 05:59 | ||
Let's use some initial conditions to solve for the particular solution | |||
Lecture 16 | 09:10 | ||
Another example with initial conditions! | |||
Lecture 17 | 10:27 | ||
What happens when the characteristic equations has complex roots?! | |||
Lecture 18 | 10:23 | ||
What happens when the characteristic equation has complex roots? | |||
Lecture 19 | 10:12 | ||
Lets do an example with initial conditions! | |||
Lecture 20 | 11:58 | ||
What happens when the characteristic equation only has 1 repeated root? | |||
Lecture 21 | 08:52 | ||
An example where we use initial conditions to solve a repeated-roots differential equation. | |||
Lecture 22 | 10:11 | ||
Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations. | |||
Lecture 23 | 11:00 | ||
Another example using undetermined coefficients. | |||
Lecture 24 | 08:09 | ||
Another example where the nonhomogeneous part is a polynomial | |||
Lecture 25 | 05:54 | ||
Putting it all together! | |||
Lecture 26 | 08:01 | ||
Introduction to the Laplace Transform | |||
Lecture 27 | 07:34 | ||
Laplace transform of e^at | |||
Lecture 28 | 10:44 | ||
Laplace Transform of sin(at) (part 1) | |||
Lecture 29 | 09:13 | ||
Part 2 of getting the Laplace transform of sin(at) | |||
Lecture 30 | 11:36 | ||
Useful properties of the Laplace Transform | |||
Lecture 31 | 09:45 | ||
Laplace transform of cosine and polynomials! | |||
Lecture 32 | 10:51 | ||
Using the Laplace Transform to solve an equation we already knew how to solve. | |||
Lecture 33 | 10:46 | ||
Second part of using the Laplace Transform to solve a differential equation. | |||
Lecture 34 | 11:17 | ||
A grab bag of things to know about the Laplace Transform. | |||
Lecture 35 | 18:48 | ||
Solving a non-homogeneous differential equation using the Laplace Transform | |||
Lecture 36 | 09:06 | ||
Determining the Laplace Transform of t | |||
Lecture 37 | 10:16 | ||
Laplace Transform of t^n: L{t^n} | |||
Lecture 38 | 24:15 | ||
Introduction to the unit step function and its Laplace Transform | |||
Lecture 39 | 19:15 | ||
Using our toolkit to take some inverse Laplace Transforms | |||
Lecture 40 | 19:12 | ||
Hairy differential equation involving a step function that we use the Laplace Transform to solve. | |||
Lecture 41 | 17:48 | ||
Introduction to the Dirac Delta Function | |||
Lecture 42 | 12:13 | ||
Figuring out the Laplace Transform of the Dirac Delta Function | |||
Lecture 43 | 18:59 | ||
Introduction to the Convolution | |||
Lecture 44 | 13:46 | ||
Understanding how the product of the Transforms of two functions relates to their convolution. | |||
Lecture 45 | 12:14 | ||
Using the Convolution Theorem to solve an initial value problem |
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