
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 repeatedroots 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 nonhomogeneous 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 
Full curriculum
