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Construct and solve real-life examples using ordinary differential equations
Updated on Sep, 2026
Teaching and Academics , Math, Calculus
Duration - 16.5 hours
Training 5 or more people ?
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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, Ace Ordinary Differential Equations in 17 Hours, is intended to introduce students to construct and solve real-life problems involving the rate of change of some quantity. The course includes video, notes from the 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)
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
Section 4: First-Order ODEs' Methods of Solution
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
Second-Order with Dependent or Independent Variable Missing
Initial-Value Problem and Boundary-Value Problem
Homogeneous vs. Nonhomogeneous DEs
Complementary Function, Particular Solution, and General Solution
Superposition Principle
Linear Independence of Functions
Homogeneous Linear ODE with Constant Coefficients
Homogeneous Cauchy-Euler Equation
Undetermined Coefficients
Variation of Parameters
Section 6: Laplace Transforms
Transforms of Some Basic Functions
Transforms of Derivatives
Transforms of Integrals
Derivatives of Transforms
Integrals of Transforms
Transform of a Periodic Function
Transform of the Dirac Delta Function
First Translation Theorem (Translation on the s-axis)
Second Translation Theorem (Translation on the t-axis)
Convolution Theorem and Its Applications
Section 7: Linear Systems of ODEs
Homogeneous vs. Nonhomogeneous Linear Systems
Homogeneous Linear Systems with Constant Coefficients
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 before moving on to the next section.
THINGS THAT ARE INCLUDED IN THE COURSE:
An instructor who truly cares about your success
Lifetime access to Ace Ordinary Differential Equations in 17 Hours (The Complete Course)
Downloadable lectures so you can watch the videos whenever and wherever you are.
Downloadable lecture notes so you can review the lectures without having a device to watch/listen.
Five problem sets at the end of each section (with solutions!) for you to do more practice.
Step-by-step guide to help you solve problems.
See you inside the course!
Check out the detailed breakdown of what’s inside the course
During my undergraduate years, I always looked forward to exams because I was well-prepared and found them rewarding. I know this isn’t the case for everyone, so I'm here to share my knowledge and help make your university journey a bit easier!
I earned my BSc in Atmospheric Science and Physics, with a minor in Mathematics, from McGill University in 2018. I then completed my MSc in 2019 and my PhD in 2024, both in Physics at the University of Toronto. My research focuses on the impact of wind observations on global predictability, Arctic climate, and weather processes.
Since my second year of undergrad, I’ve gained extensive tutoring experience, working with students at Liberty Tutoring, supporting high school and university students through SUS Peer Tutoring and Saturday Programs, and working with private students both in person and online. I also served as a teaching assistant for math and physics courses at both the undergraduate and graduate levels from 2017 to 2024.
I look forward to seeing you in class!
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