Ace Ordinary Differential Equations in 17 Hours

About Ace Ordinary Differential Equations in 17 Hours

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 :)