# Differential Equations

Topics covered in a first year course in differential equations.
• Lectures 45
• Video 9 Hours
• Skill level all level
• Languages English
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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

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

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