Differential Equations

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

Lectures

1. favorites

   Lecture 1 - Introduction to Differential Equations

   What a differential equation is and some terminology?

2. favorites

   Lecture 2 - Separable Differential Equations

   Introduction to separable differential equations.

3. favorites

   Lecture 3 - Separable Differential Equations II

   Another separable differential equation example.

4. favorites

   Lecture 4 - Exact Equations Intuition Part 1 (proofy)

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

5. favorites

   Lecture 5 - Exact Equations Intuition Part 2 (proofy)

   More intuitive building blocks for exact equations.

6. favorites

   Lecture 6 - Exact Equations Example 1

   First example of solving an exact differential equation.

7. favorites

   Lecture 7 - Exact Equations Example 2

   Some more exact equation examples.

8. favorites

   Lecture 8 - Exact Equations Example 3

   One more exact equation example.

9. favorites

   Lecture 9 - Integrating Factors 1

   Using an integrating factor to make a differential equation exact.

10. favorites

    Lecture 10 - Integrating Factors 2

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

11. favorites

    Lecture 11 - First Order Homogeneous

    Introduction to first order homogenous equations.

12. favorites

    Lecture 12 - First Order Homogeneous

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

13. favorites

    Lecture 13 - 2nd Order Linear Homogeneous Differential Equations 1

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

14. favorites

    Lecture 14 - 2nd Order Linear Homogeneous Differential Equations 2

    Let's find the general solution!

15. favorites

    Lecture 15 - 2nd Order Linear Homogeneous Differential Equations 3

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

16. favorites

    Lecture 16 - 2nd Order Linear Homogeneous Differential Equations 4

    Another example with initial conditions!

17. favorites

    Lecture 17 - Complex Roots of the Characteristic Equations 1

    What happens when the characteristic equations has complex roots?!

18. favorites

    Lecture 18 - Complex Roots of the Characteristic Equations 2

    What happens when the characteristic equation has complex roots?

19. favorites

    Lecture 19 - Complex Roots of the Characteristic Equations 3

    Lets do an example with initial conditions!

20. favorites

    Lecture 20 - Repeated Roots of the Characteristic Part 1

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

21. favorites

    Lecture 21 - Repeated Roots of the Characteristic Part 2

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

22. favorites

    Lecture 22 - Undetermined Coefficients 1

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

23. favorites

    Lecture 23 - Undetermined Coefficients 2

    Another example using undetermined coefficients.

24. favorites

    Lecture 24 - Undetermined Coefficients 3

    Another example where the nonhomogeneous part is a polynomial.

25. favorites

    Lecture 25 - Undetermined Coefficients 4

    Putting it all together!

26. favorites

    Lecture 26 - Laplace Transfrom 1

    Introduction to the Laplace Transform.

27. favorites

    Lecture 27 - Laplace Transfrom 2

    Laplace transform of e^at.

28. favorites

    Lecture 28 - Laplace Transfrom 3

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

29. favorites

    Lecture 29 - Laplace Transfrom 4

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

30. favorites

    Lecture 30 - Laplace Transfrom 5

    Useful properties of the Laplace Transform.

31. favorites

    Lecture 31 - Laplace Transfrom 6

    Laplace transform of cosine and polynomials!

32. favorites

    Lecture 32 - Laplace Transform to Solve an Equation

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

33. favorites

    Lecture 33 - Laplace Transform Solves an Equation 2

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

34. favorites

    Lecture 34 - More Laplace Transform Tools

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

35. favorites

    Lecture 35 - Using the Laplace Transform to Solve a Nonhomogeneous Equation

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

36. favorites

    Lecture 36 - Laplace Transform of: L(t)

    Determining the Laplace Transform of t.

37. favorites

    Lecture 37 - Laplace Transform of t^n: L(t^n)

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

38. favorites

    Lecture 38 - Laplace Transform of the the Unit Step

    Introduction to the unit step function and its Laplace Transform.

39. favorites

    Lecture 39 - Inverse Laplace Examples

    Using our toolkit to take some inverse Laplace Transforms.

40. favorites

    Lecture 40 - Laplace/Step Function Differential

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

41. favorites

    Lecture 41 - Dirac Delta Function

    Introduction to the Dirac Delta Function.

42. favorites

    Lecture 42 - Laplace Transform of the Dirac Delta

    Figuring out the Laplace Transform of the Dirac Delta Function.

43. favorites

    Lecture 43 - Introduction to the Convolution

    Introduction to the Convolution.

44. favorites

    Lecture 44 - The Convolution and the Laplace

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

45. favorites

    Lecture 45 - Using the Convolution Theorem to Solve an Intial Value Prob

    Using the Convolution Theorem to solve an initial value problem.