Topics covered in a first year course in differential equations.
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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.
Over 45 lectures and 8.5 hours of content!
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CURRICULUM
1
Introduction to differential equations
11:02
What a differential equation is and some terminology.
2
Separable Differential Equations
12:00
Introduction to separable differential equations.
3
Separable differential equations 2
05:37
Another separable differential equation example.
4
Exact Equations Intuition 1 (proofy)
09:54
Chain rule using partial derivatives (not a proof; more intuition).
5
Exact Equations Intuition 2 (proofy)
10:51
More intuitive building blocks for exact equations.
6
Exact Equations Example 1
12:09
First example of solving an exact differential equation.
7
Exact Equations Example 2
08:01
Some more exact equation examples
8
Exact Equations Example 3
09:59
One more exact equation example
9
Integrating factors 1
10:16
Using an integrating factor to make a differential equation exact
10
Integrating factors 2
08:26
Now that we've made the equation exact, let's solve it!
11
First order homegenous equations
07:21
Introduction to first order homogenous equations.
12
First order homogenous equations 2
08:22
Another example of using substitution to solve a first order homogeneous differential equations.
13
2nd Order Linear Homogeneous Differential Equations 1
09:44
Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients.
14
2nd Order Linear Homogeneous Differential Equations 2
08:28
Let's find the general solution!
15
2nd Order Linear Homogeneous Differential Equations 3
05:59
Let's use some initial conditions to solve for the particular solution
16
2nd Order Linear Homogeneous Differential Equations 4
09:10
Another example with initial conditions!
17
Complex roots of the characteristic equations 1
10:27
What happens when the characteristic equations has complex roots?!
18
Complex roots of the characteristic equations 2
10:23
What happens when the characteristic equation has complex roots?
19
Complex roots of the characteristic equations 3
10:12
Lets do an example with initial conditions!
20
Repeated roots of the characteristic equation
11:58
What happens when the characteristic equation only has 1 repeated root?
21
Repeated roots of the characterisitic equations part 2
08:52
An example where we use initial conditions to solve a repeated-roots differential equation.
22
Undetermined Coefficients 1
10:11
Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations.
23
Undetermined Coefficients 2
11:00
Another example using undetermined coefficients.
24
Undetermined Coefficients 3
08:09
Another example where the nonhomogeneous part is a polynomial
25
Undetermined Coefficients 4
05:54
Putting it all together!
26
Laplace Transform 1
08:01
Introduction to the Laplace Transform
27
Laplace Transform 2
07:34
Laplace transform of e^at
28
Laplace Transform 3 (L{sin(at)})
10:44
Laplace Transform of sin(at) (part 1)
29
Laplace Transform 4
09:13
Part 2 of getting the Laplace transform of sin(at)
30
Laplace Transform 5
11:36
Useful properties of the Laplace Transform
31
Laplace Transform 6
09:45
Laplace transform of cosine and polynomials!
32
Laplace Transform to solve an equation
10:51
Using the Laplace Transform to solve an equation we already knew how to solve.
33
Laplace Transform solves an equation 2
10:46
Second part of using the Laplace Transform to solve a differential equation.
34
More Laplace Transform tools
11:17
A grab bag of things to know about the Laplace Transform.
35
Using the Laplace Transform to solve a nonhomogenous eq
18:48
Solving a non-homogeneous differential equation using the Laplace Transform
36
Laplace Transform of : L{t}
09:06
Determining the Laplace Transform of t
37
Laplace Transform of t^n: L{t^n}
10:16
Laplace Transform of t^n: L{t^n}
38
Laplace Transform of the Unit Step Function
24:15
Introduction to the unit step function and its Laplace Transform
39
Inverse Laplace Examples
19:15
Using our toolkit to take some inverse Laplace Transforms
40
Laplace/Step Function Differential Equation
19:12
Hairy differential equation involving a step function that we use the Laplace Transform to solve.
41
Dirac Delta Function
17:48
Introduction to the Dirac Delta Function
42
Laplace Transform of the Dirac Delta Function
12:13
Figuring out the Laplace Transform of the Dirac Delta Function
43
Introduction to the Convolution
18:59
Introduction to the Convolution
44
The Convolution and the Laplace Transform
13:46
Understanding how the product of the Transforms of two functions relates to their convolution.
45
Using the Convolution Theorem to Solve an Initial Value Prob
12:14
Using the Convolution Theorem to solve an initial value problem