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Course

# Differential Equations

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus before starting here.

Home > Mathematics > Calculus > Differential Equations Lectures:
• ### Introduction to Differential Equations

00:11:02Salman Khan

What a differential equation is and some terminology?

• ### Separable Differential Equations

00:12:00Salman Khan

Introduction to separable differential equations.

• ### Separable Differential Equations II

00:05:37Salman Khan

Another separable differential equation example.

• ### Exact Equations Intuition Part 1 (proofy)

00:09:54Salman Khan

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

• ### Exact Equations Intuition Part 2 (proofy)

00:10:51Salman Khan

More intuitive building blocks for exact equations.

• ### Exact Equations Example 1

00:12:09Salman Khan

First example of solving an exact differential equation.

• ### Exact Equations Example 2

00:08:01Salman Khan

Some more exact equation examples.

• ### Exact Equations Example 3

00:09:59Salman Khan

One more exact equation example.

• ### Integrating Factors 1

00:10:16Salman Khan

Using an integrating factor to make a differential equation exact.

• ### Integrating Factors 2

00:08:26Salman Khan

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

• ### First Order Homogeneous (Part 1)

00:07:21Salman Khan

Introduction to first order homogenous equations.

• ### First Order Homogeneous (Part 2)

00:08:22Salman Khan

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

• ### 2nd Order Linear Homogeneous Differential Equations 1

00:09:44Salman Khan

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

• ### 2nd Order Linear Homogeneous Differential Equations 2

00:08:28Salman Khan

Let's find the general solution!

• ### 2nd Order Linear Homogeneous Differential Equations 3

00:05:59Salman Khan

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

• ### 2nd Order Linear Homogeneous Differential Equations 4

00:09:10Salman Khan

Another example with initial conditions!

• ### Complex Roots of the Characteristic Equations 1

00:10:27Salman Khan

What happens when the characteristic equations has complex roots?!

• ### Complex Roots of the Characteristic Equations 2

00:10:23Salman Khan

What happens when the characteristic equation has complex roots?

• ### Complex Roots of the Characteristic Equations 3

00:10:12Salman Khan

Lets do an example with initial conditions!

• ### Repeated Roots of the Characteristic Part 1

00:11:58Salman Khan

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

• ### Repeated Roots of the Characteristic Part 2

00:08:52Salman Khan

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

• ### Undetermined Coefficients 1

00:10:11Salman Khan

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

• ### Undetermined Coefficients 2

00:11:00Salman Khan

Another example using undetermined coefficients.

• ### Undetermined Coefficients 3

00:08:09Salman Khan

Another example where the nonhomogeneous part is a polynomial.

• ### Undetermined Coefficients 4

00:05:54Salman Khan

Putting it all together!

• ### Laplace Transfrom 1

00:08:01Salman Khan

Introduction to the Laplace Transform.

• ### Laplace Transfrom 2

00:07:34Salman Khan

Laplace transform of e^at.

• ### Laplace Transfrom 3

00:10:44Salman Khan

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

• ### Laplace Transfrom 4

00:09:13Salman Khan

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

• ### Laplace Transfrom 5

00:11:36Salman Khan

Useful properties of the Laplace Transform.

• ### Laplace Transform 6

00:09:45Salman Khan

Laplace transform of cosine and polynomials!

• ### Laplace Transform to Solve an Equation

00:10:51Salman Khan

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

• ### Laplace Transform Solves an Equation 2

00:10:46Salman Khan

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

• ### More Laplace Transform Tools

00:11:17Salman Khan

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

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

00:18:48Salman Khan

Solving a non-homogeneous differential equation using the Laplace Transform.

• ### Laplace Transform of: L(t)

00:09:06Salman Khan

Determining the Laplace Transform of t.

• ### Laplace Transform of t^n: L(t^n)

00:10:16Salman Khan

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

• ### Laplace Transform of the the Unit Step

00:24:15Salman Khan

Introduction to the unit step function and its Laplace Transform.

• ### Inverse Laplace Examples

00:19:15Salman Khan

Using our toolkit to take some inverse Laplace Transforms.

• ### Laplace/Step Function Differential

00:19:12Salman Khan

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

• ### Dirac Delta Function

00:17:48Salman Khan

Introduction to the Dirac Delta Function.

• ### Laplace Transform of the Dirac Delta

00:12:13Salman Khan

Figuring out the Laplace Transform of the Dirac Delta Function.

• ### Introduction to the Convolution

00:18:59Salman Khan

Introduction to the Convolution.

• ### The Convolution and the Laplace

00:13:46Salman Khan

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

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

00:12:14Salman Khan

Using the Convolution Theorem to solve an initial value problem.