Intro To Differential Equation

Your Guide For Learning First Order Differential Equations, And Second Order Differential Equations

What you'll learn

• Learn Ordinary Differential Equation
• Learn Initial Value Problems
• Learn Separable Equations
• Learn First Order Linear Differential Equation
• Learn Solving Exact ODE
• Learn Homogeneous Differential Equation
• Learn Bernoulli Differential Equation
• Learn Second Order Differential Equation
• Learn, Real, Distinct Roots
• Learn Complex Roots
• Learn Wronskian
• Learn Second Order Repeated Roots

Requirements

Calculus 2

Description

This is a lower-level introduction to differential equation course. This course is broken into 6 sections:

1) Intro to differential equations, 2) First order differential equations, 3) Second order differential equations, 4) Series solution, 5) Laplace transform. First, we will go over definitions and terminology, we will go over the difference between linear non linear equations. Then storm into initial value problems, go over the difference between first order DE, second order DE, ordinary differential equations, classify ODE by order and linearity.

The first thing we will go over is define a differential equation. A differential equation is an equation containing the derivatives of one or more dependent variables with respect to one or more independent variables(equation involving some unknown function and one or more of its derivatives). In a differential equation the solution is always going to be an equation. There are two types of differential equations: ordinary differential equation, partial differential equation. Also a differential equation can be linear or nonlinear.

First Order Differential Equations:

1. Direction fields
2. Separable equations
3. Euler's method
4. First order linear differential equation
5. Solving exact ODE's
6. Homogeneous Differential Equation
7. Bernoulli differential equation
8. Linear and nonlinear models
9. Predator prey models and electrical newtworks

Second Order Differential Equations

1. Distinct real roots
2. Complex roots
3. Repeated roots
4. Wronskian
5. Undetermined coefficients
6. Differential operators
7. Variation of parameters
8. Cauchy euler equation
9. Mechanical vibrations

Series Solutions

1. Power series
2. Series Solutions

Laplace Transform

1. Laplace transform overview
2. Inverse laplace transforms
3. Initial value problems with laplace transforms
4. Translation theorems of laplace transforms

Systems Of Differential Equations

1. Homogeneous linear systems
2. Phase plane portraits

Who this course is for:

Pre Med Major, All Engineer Major, And Math Major