1 


11:02 

What a differential equation is and some terminology. 
2 


12:00 

Introduction to separable differential equations. 
3 


05:37 

Another separable differential equation example. 
4 


09:54 

Chain rule using partial derivatives (not a proof; more intuition). 
5 


10:51 

More intuitive building blocks for exact equations. 
6 


12:09 

First example of solving an exact differential equation. 
7 


08:01 

Some more exact equation examples 
8 


09:59 

One more exact equation example 
9 


10:16 

Using an integrating factor to make a differential equation exact 
10 


08:26 

Now that we've made the equation exact, let's solve it! 
11 


07:21 

Introduction to first order homogenous equations. 
12 


08:22 

Another example of using substitution to solve a first order homogeneous differential equations. 
13 


09:44 

Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients. 
14 


08:28 

Let's find the general solution! 
15 


05:59 

Let's use some initial conditions to solve for the particular solution 
16 


09:10 

Another example with initial conditions! 
17 


10:27 

What happens when the characteristic equations has complex roots?! 
18 


10:23 

What happens when the characteristic equation has complex roots? 
19 


10:12 

Lets do an example with initial conditions! 
20 


11:58 

What happens when the characteristic equation only has 1 repeated root? 
21 


08:52 

An example where we use initial conditions to solve a repeatedroots differential equation. 
22 


10:11 

Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations. 
23 


11:00 

Another example using undetermined coefficients. 
24 


08:09 

Another example where the nonhomogeneous part is a polynomial 
25 


05:54 

Putting it all together! 
26 


08:01 

Introduction to the Laplace Transform 
27 


07:34 

Laplace transform of e^at 
28 


10:44 

Laplace Transform of sin(at) (part 1) 
29 


09:13 

Part 2 of getting the Laplace transform of sin(at) 
30 


11:36 

Useful properties of the Laplace Transform 
31 


09:45 

Laplace transform of cosine and polynomials! 
32 


10:51 

Using the Laplace Transform to solve an equation we already knew how to solve. 
33 


10:46 

Second part of using the Laplace Transform to solve a differential equation. 
34 


11:17 

A grab bag of things to know about the Laplace Transform. 
35 


18:48 

Solving a nonhomogeneous differential equation using the Laplace Transform 
36 


09:06 

Determining the Laplace Transform of t 
37 


10:16 

Laplace Transform of t^n: L{t^n} 
38 


24:15 

Introduction to the unit step function and its Laplace Transform 
39 


19:15 

Using our toolkit to take some inverse Laplace Transforms 
40 


19:12 

Hairy differential equation involving a step function that we use the Laplace Transform to solve. 
41 


17:48 

Introduction to the Dirac Delta Function 
42 


12:13 

Figuring out the Laplace Transform of the Dirac Delta Function 
43 


18:59 

Introduction to the Convolution 
44 


13:46 

Understanding how the product of the Transforms of two functions relates to their convolution. 
45 


12:14 

Using the Convolution Theorem to solve an initial value problem 
Full curriculum
