Ace Ordinary Differential Equations in 17 Hours (The Complete Course)

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 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

• 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

• Reduction of Order

• Homogeneous Linear ODE with Constant Coefficients

• Homogeneous Cauchy-Euler Equation

• Undetermined Coefficients

• Variation of Parameters

• Green's Function

Section 6: Laplace Transforms

• Gamma Function

• 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

• Complementary Function, Particular Solution, and General Solution

• Superposition Principle

• Homogeneous Linear Systems with Constant Coefficients

• Undetermined Coefficients

• Variation of Parameters

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)

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: Five problem sets at the end of each section (with solutions!) for you to do more practice.

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

See you inside the course!

- Gina :)