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 WORKifferential 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
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
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