## Differential Equations

1. 1

### What is a differential equation

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What a differential equation is and some terminology.

2. 2

### Separable Differential Equations

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Introduction to separable differential equations.

3. 3

### Separable differential equations 2

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Another separable differential equation example.

4. 4

### Exact Equations Intuition 1 (proofy)

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

5. 5

### Exact Equations Intuition 2 (proofy)

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More intuitive building blocks for exact equations.

6. 6

### Exact Equations Example 1

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First example of solving an exact differential equation.

7. 7

### Exact Equations Example 2

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Some more exact equation examples

8. 8

### Exact Equations Example 3

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One more exact equation example

9. 9

### Integrating factors 1

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Using an integrating factor to make a differential equation exact

10. 10

### Integrating factors 2

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

11. 11

### First order homegenous equations

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Introduction to first order homogenous equations.

12. 12

### First order homogenous equations 2

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

13. 13

### 2nd Order Linear Homogeneous Differential Equations 1

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

14. 14

### 2nd Order Linear Homogeneous Differential Equations 2

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Let's find the general solution!

15. 15

### 2nd Order Linear Homogeneous Differential Equations 3

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

16. 16

### 2nd Order Linear Homogeneous Differential Equations 4

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Another example with initial conditions!

17. 17

### Complex roots of the characteristic equations 1

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What happens when the characteristic equations has complex roots?!

18. 18

### Complex roots of the characteristic equations 2

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What happens when the characteristic equation has complex roots?

19. 19

### Complex roots of the characteristic equations 3

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Lets do an example with initial conditions!

20. 20

### Repeated roots of the characteristic equation

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

21. 21

### Repeated roots of the characterisitic equations part 2

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An example where we use initial conditions to solve a repeated-roots differential equation.

22. 22

### Undetermined Coefficients 1

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

23. 23

### Undetermined Coefficients 2

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Another example using undetermined coefficients.

24. 24

### Undetermined Coefficients 3

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Another example where the nonhomogeneous part is a polynomial

25. 25

### Undetermined Coefficients 4

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Putting it all together!

26. 26

### Laplace Transform 1

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Introduction to the Laplace Transform

27. 27

### Laplace Transform 2

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Laplace transform of e^at

28. 28

### Laplace Transform 3 (L{sin(at)})

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Laplace Transform of sin(at) (part 1)

29. 29

### Laplace Transform 4

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

30. 30

### Laplace Transform 5

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Useful properties of the Laplace Transform

31. 31

### Laplace Transform 6

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Laplace transform of cosine and polynomials!

32. 32

### Laplace Transform to solve an equation

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

33. 33

### Laplace Transform solves an equation 2

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

34. 34

### More Laplace Transform tools

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

35. 35

### Using the Laplace Transform to solve a nonhomogenous eq

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Solving a non-homogeneous differential equation using the Laplace Transform

36. 36

### Laplace Transform of : L{t}

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Determining the Laplace Transform of t

37. 37

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

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

38. 38

### Laplace Transform of the Unit Step Function

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Introduction to the unit step function and its Laplace Transform

39. 39

### Inverse Laplace Examples

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Using our toolkit to take some inverse Laplace Transforms

40. 40

### Laplace/Step Function Differential Equation

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

41. 41

### Dirac Delta Function

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Introduction to the Dirac Delta Function

42. 42

### Laplace Transform of the Dirac Delta Function

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Figuring out the Laplace Transform of the Dirac Delta Function

43. 43

### Introduction to the Convolution

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Introduction to the Convolution

44. 44

### The Convolution and the Laplace Transform

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

45. 45

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