# Differential Equations with the Math Sorcerer

## What you'll learn

- Determining the Type and Order of a Differential Equation
- Determining whether a Differential Equation is Linear or Nonlinear
- Understand the Different Types of Solutions of Differential Equations: one-parameter families, two-parameter families, singular solutions, general solutions
- Understand Initial Value Problems and the Interval of Definition
- How to Solve Separable Differential Equations, First Order Linear, Exact, Homogeneous, Bernoulli, and DE's of the form dy/dx = f(Ax + By + C)
- How to Determine if Functions are Linearly Independent or Dependent using the Definition
- How to Prove Functions are Linearly Independent using the Wronskian
- How to Solve Higher Order Linear Homogeneous Differential Equations with Constant Coefficients
- How to Solve DE's with the Method of Undetermined Coefficients(The Superposition Principle)
- How to Solve DE's with Variation of Parameters
- How to Solve Cauchy-Euler Differential Equations
- How to Compute Laplace Transforms with the Definition
- How to Compute Laplace Transforms and Inverse Laplace Transforms with Tables, Partial Fractions, and Trigonometric Identities
- How to use the First Translation Theorem to Compute Laplace Transforms
- How to use the Derivatives of Transforms Theorems
- How to Solve DE's using Laplace Transforms
- Understand what the Unit Step Function is and use it to Find the Laplace Transform of a Piecewise Function
- Understand what the Dirac Delta Function is
- How to use the Second Translation Theorem to compute Laplace Transforms and Inverse Laplace Transforms
- How to Solve DE's that involve the Dirac Delta Function
- How to Find the Minimum Radius of Convergence
- How to Solve DE's using Power Series

## Requirements

- You should know basic calculus.
- The ability to integrate well helps, but all integration techniques are reviewed in the problems.

## Description

**This is a complete college level course in Differential Equations with TONS of examples.**

***** In order to get the most out of the course you should know Calculus *****

**Basically just,**

**1) Watch the videos, and try to follow along. Try to do the problems before I do them if you can. If you can't, no big deal:)**

**2) After each section there is short assignment(with solutions). **

**3) Repeat!**

**If you finish even 50% of this course you will know A LOT of Differential Equations and more importantly just a lot of really solid mathematics.**

**Differential Equations is an awesome class not just because of the differential equations but because of all of the other key math techniques you learn in the process.**

**I hope you enjoy watching these videos and working through these problems as much as I have:)**

## Who this course is for:

- Students who want to learn Differential Equations.
- Students who plan to take Differential Equations.
- Students currently taking Differential Equations.

## Course content

- Preview04:08
- 07:17Linear Versus Nonlinear Differential Equations
- 00:03Assignment 1 with Solutions
- 01:52More Examples of Linear versus Nonlinear Differential Equations
- 10:52Solutions to Differential Equations
- 04:52Initial Value Problems
- 08:04An Initial Value Problem and Finding the Interval of Definition: Key Example!
- 00:03Assignment 2 with Solutions

## Instructor

I was born on a small unnamed Island in the Pacific Ocean inhabited mostly by natives who practiced mathematics on a daily basis.

My mother was a witch who specialized in Calculus and my father was a warlock who was well versed in the dark arts of Algebra.

As I grew older so did my thirst for knowledge, and so I set out on a long voyage to improve my mathematical skills. I traveled the world for years and learned a great deal of mathematics, but it wasn't until I met that raging Hobbit that my true powers started to show.

I am here today to share my magical powers with you.

Come join on me on this journey as we explore the world of mathematics together.