Differential Equations

Topics covered in a first year course in differential equations.
Instructed by The Khan Academy
  • Lectures 45
  • Video 9 Hours
  • Skill level all level
  • Languages English
  • Includes Lifetime access
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Course Description

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

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  • Over 45 lectures and 8.5 hours of content!

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Curriculum

11:02
What a differential equation is and some terminology.
12:00
Introduction to separable differential equations.
05:37
Another separable differential equation example.
09:54
Chain rule using partial derivatives (not a proof; more intuition).
10:51
More intuitive building blocks for exact equations.
12:09
First example of solving an exact differential equation.
08:01
Some more exact equation examples
09:59
One more exact equation example
10:16
Using an integrating factor to make a differential equation exact
08:26
Now that we've made the equation exact, let's solve it!
07:21
Introduction to first order homogenous equations.
08:22
Another example of using substitution to solve a first order homogeneous differential equations.
09:44
Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients.
08:28
Let's find the general solution!
05:59
Let's use some initial conditions to solve for the particular solution
09:10
Another example with initial conditions!
10:27
What happens when the characteristic equations has complex roots?!
10:23
What happens when the characteristic equation has complex roots?
10:12
Lets do an example with initial conditions!
11:58
What happens when the characteristic equation only has 1 repeated root?
08:52
An example where we use initial conditions to solve a repeated-roots differential equation.
10:11
Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations.
11:00
Another example using undetermined coefficients.
08:09
Another example where the nonhomogeneous part is a polynomial
05:54
Putting it all together!
08:01
Introduction to the Laplace Transform
07:34
Laplace transform of e^at
10:44
Laplace Transform of sin(at) (part 1)
09:13
Part 2 of getting the Laplace transform of sin(at)
11:36
Useful properties of the Laplace Transform
09:45
Laplace transform of cosine and polynomials!
10:51
Using the Laplace Transform to solve an equation we already knew how to solve.
10:46
Second part of using the Laplace Transform to solve a differential equation.
11:17
A grab bag of things to know about the Laplace Transform.
18:48
Solving a non-homogeneous differential equation using the Laplace Transform
09:06
Determining the Laplace Transform of t
10:16
Laplace Transform of t^n: L{t^n}
24:15
Introduction to the unit step function and its Laplace Transform
19:15
Using our toolkit to take some inverse Laplace Transforms
19:12
Hairy differential equation involving a step function that we use the Laplace Transform to solve.
17:48
Introduction to the Dirac Delta Function
12:13
Figuring out the Laplace Transform of the Dirac Delta Function
18:59
Introduction to the Convolution
13:46
Understanding how the product of the Transforms of two functions relates to their convolution.
12:14
Using the Convolution Theorem to solve an initial value problem

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