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### Introduction to Differential Equations

00:11:02Salman KhanWhat a differential equation is and some terminology?

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### Separable Differential Equations

00:12:00Salman KhanIntroduction to separable differential equations.

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### Separable Differential Equations II

00:05:37Salman KhanAnother separable differential equation example.

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### Exact Equations Intuition Part 1 (proofy)

00:09:54Salman KhanChain rule using partial derivatives (not a proof; more intuition).

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### Exact Equations Intuition Part 2 (proofy)

00:10:51Salman KhanMore intuitive building blocks for exact equations.

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### Exact Equations Example 1

00:12:09Salman KhanFirst example of solving an exact differential equation.

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### Integrating Factors 1

00:10:16Salman KhanUsing an integrating factor to make a differential equation exact.

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### First Order Homogeneous (Part 1)

00:07:21Salman KhanIntroduction to first order homogenous equations.

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### First Order Homogeneous (Part 2)

00:08:22Salman KhanAnother example of using substitution to solve a first order homogeneous differential equations.

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### 2nd Order Linear Homogeneous Differential Equations 1

00:09:44Salman KhanIntroduction to 2nd order, linear, homogeneous differential equations with constant coefficients.

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### 2nd Order Linear Homogeneous Differential Equations 2

00:08:28Salman KhanLet's find the general solution!

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### 2nd Order Linear Homogeneous Differential Equations 3

00:05:59Salman KhanLet's use some initial conditions to solve for the particular solution.

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### 2nd Order Linear Homogeneous Differential Equations 4

00:09:10Salman KhanAnother example with initial conditions!

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### Complex Roots of the Characteristic Equations 1

00:10:27Salman KhanWhat happens when the characteristic equations has complex roots?!

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### Complex Roots of the Characteristic Equations 2

00:10:23Salman KhanWhat happens when the characteristic equation has complex roots?

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### Complex Roots of the Characteristic Equations 3

00:10:12Salman KhanLets do an example with initial conditions!

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### Repeated Roots of the Characteristic Part 1

00:11:58Salman KhanWhat happens when the characteristic equation only has 1 repeated root?

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### Repeated Roots of the Characteristic Part 2

00:08:52Salman KhanAn example where we use initial conditions to solve a repeated-roots differential equation.

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### Undetermined Coefficients 1

00:10:11Salman KhanUsing the method of undetermined coefficients to solve nonhomogeneous linear differential equations.

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### Undetermined Coefficients 3

00:08:09Salman KhanAnother example where the nonhomogeneous part is a polynomial.

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### Laplace Transform to Solve an Equation

00:10:51Salman KhanUsing the Laplace Transform to solve an equation we already knew how to solve.

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### Laplace Transform Solves an Equation 2

00:10:46Salman KhanSecond part of using the Laplace Transform to solve a differential equation.

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### More Laplace Transform Tools

00:11:17Salman KhanA grab bag of things to know about the Laplace Transform.

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### Using the Laplace Transform to Solve a Nonhomogeneous Equation

00:18:48Salman KhanSolving a non-homogeneous differential equation using the Laplace Transform.

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### Laplace Transform of the the Unit Step

00:24:15Salman KhanIntroduction to the unit step function and its Laplace Transform.

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### Inverse Laplace Examples

00:19:15Salman KhanUsing our toolkit to take some inverse Laplace Transforms.

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### Laplace/Step Function Differential

00:19:12Salman KhanHairy differential equation involving a step function that we use the Laplace Transform to solve

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### Laplace Transform of the Dirac Delta

00:12:13Salman KhanFiguring out the Laplace Transform of the Dirac Delta Function.

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### The Convolution and the Laplace

00:13:46Salman KhanUnderstanding how the product of the Transforms of two functions relates to their convolution.

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### Using the Convolution Theorem to Solve an Intial Value Prob

00:12:14Salman KhanUsing the Convolution Theorem to solve an initial value problem.

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