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

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: PreliminariesClassification of DEs (type, order, and linearity)Variables SeparableInitial-Value Problems (IVP)Section 3: First-Order ODEs as Mathematical ModelsModel I: Proportional to the Dependent VariableModel II: Proportional to the Difference to a BoundModel III: The Logistic EquationFive Population ModelsModel IV: First-Order Linear ODEApplication: A Mixture ProblemApplication: Series CircuitsApplication: Mathematical Models Describing MotionTorricelli's LawSection 4: First-Order ODEs' Methods of Solution (to be updated)Exact and Non-exact Equations (to be updated)Bernoulli's Equation (to be updated)Solving by Substitutions (to be updated)ODEs with Dependent or Independent Variable Missing (to be updated)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: Series Solutions for Second Order Linear Equations (Available in the complete course)Section 8: 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 successLifetime access to A Complete Guide to First-Order Ordinary Differential EquationHIGHLIGHTS:#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: One problem set at the end of the course (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 :)

Overview

Section 1: Introduction

Lecture 1 Overview

Lecture 2 Welcome and How It Works

Lecture 3 Tips to Maximize Your Learning

Section 2: Preliminaries

Lecture 4 Downloadable Notes

Lecture 5 Overview of Section 2

Lecture 6 Definitions and Terminology

Lecture 7 Verification of a Solution

Lecture 8 Two Special First Order ODEs: Variables Separable

Lecture 9 Initial-Value Problems

Section 3: First-Order ODEs as Mathematical Models

Lecture 10 Downloadable Notes

Lecture 11 Overview of Section 3

Lecture 12 Model I: Proportional to the Dependent Variable

Lecture 13 Applications and Examples of Model I

Lecture 14 Model II: Proportional to the Difference to a Bound

Lecture 15 Applications and Example of Model II

Lecture 16 Model III: The Logistic Equation

Lecture 17 Applications and Example of Model III

Lecture 18 Some Population Models

Lecture 19 Model IV: First-Order Linear ODE

Section 4: Conclusion

Lecture 20 Thank You & Good Luck & Next Step

Lecture 21 BONUS: Let's Keep Learning!

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