A Complete Guide to 1st-Order Ordinary Differential Equation

Construct and solve real-life examples using first-order ordinary differential equations

What you'll learn
- Identify a differential equation's type, order, and linearity
- Verify solutions to differential equations
- Find the solution to a first-order ODE by separation of variables
- Use initial conditions to solve initial-value problems
- Construct differential equations as mathematical models
- Understand and solve different population models
- Construct and solve mixture problems using first-order linear ODE
- Construct and solve differential equations related to series circuits
- Construct and solve differential equations as mathematical models describing motion
- Understand and apply Torricelli's Law
- Solve a homogeneous first-order equation
- Solve an exact first-order equation
- Make a non-extract equation exact by multiplying an integrating factor
- Identify a Bernoulli's equation and find the solution of the DE using substitution
- Solve a first-order ODE by substitution

Requirements
- Calculus 3 (Multivariable Calculus)
- Linear Algebra

Description
HOW THIS COURSE WORK:

Differential Equations (DE) are equations that contain derivatives of one or more dependent variables with respect to one or more independent variables. DEs have many real-life applications. For example, population dynamics, continuous compound interest, series circuits, motion of a particle, and more.

This course, A Complete Guide to First-Order Ordinary Differential Equation, includes the first two sections of my complete course on ODE, including video, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:

Section 2: Preliminaries

Classification of DEs (type, order, and linearity)

Variables Separable

Initial-Value Problems (IVP)

Section 3: First-Order ODEs as Mathematical Models

Model I: Proportional to the Dependent Variable

Model II: Proportional to the Difference to a Bound

Model III: The Logistic Equation

Five Population Models

Model IV: First-Order Linear ODE

Application: A Mixture Problem

Application: Series Circuits

Application: Mathematical Models Describing Motion

Torricelli's Law

Section 4: First-Order ODEs' Methods of Solution

Variables Separable

First-Order Linear ODE

Homogeneous First-Order ODE

Exact First-Order Equation

Making an Equation Exact by an Integrating Factor

Bernoulli's Equation

Solving by Substitutions

Section 5: Second Order Equations and Linear Equations of Higher Order (Available in the complete course)

Section 6: Laplace Transforms (Available in the complete course)

Section 7: Linear Systems of ODEs (Available in the complete course)

CONTENT YOU WILL GET INSIDE EACH SECTION:

Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.

Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).

Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again.

THINGS THAT ARE INCLUDED IN THE COURSE:

An instructor who truly cares about your success

Lifetime access to A Complete Guide to First-Order Ordinary Differential Equation

HIGHLIGHTS:

#1:Downloadable lectures so you can watch the videos whenever and wherever you are.

#2:Downloadable lecture notes so you can review the lectures without having a device to watch/listen.

#3:Two problem sets at the end of Sections 3 and 4 (with solutions!) for you to do more practice.

#4:Step-by-step guide to help you solve problems.

See you inside the course!

- Gina Chou :)

Who this course is for:
- Anyone who has completed Calculus 3 and wants to learn more applications of calculus
- Current ODE students who are looking for extra help outside school
- Anyone who is not in the science stream but wants to study calculus for fun
More Info