Differential Equations In Depth
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# Differential Equations In Depth

An in-depth course on differential equations, covering first/second order ODEs, PDEs and numerical methods, too!
4.7 (41 ratings)
517 students enrolled
Created by Dmitri Nesteruk
Last updated 7/2017
English
Current price: \$10 Original price: \$50 Discount: 80% off
5 hours left at this price!
30-Day Money-Back Guarantee
Includes:
• 3.5 hours on-demand video
• 1 Article
• 1 Supplemental Resource
• Access on mobile and TV
• Certificate of Completion
What Will I Learn?
• Learn how to solve different types of differential equations
• Discover tricks and shortcuts to find solutions quicker
• Find out how to solve equations numerically as well as analytically
• Learn to use MATLAB to solve differential equations
View Curriculum
Requirements
• Good knowledge of calculus (linear algebra, differentiation, integration)
Description

This course has everything you need to learn and understand Differential Equations. This course covers:

• Ordinary differential equations (ODEs)
• Laplace Transform and Fourier Series
• Partial differential equations (PDEs)
• Numeric solutions of differential equations
• Modeling and solving differential equations using MATLAB

This course will continue to evolve and improve based on feedback from the course participants.

Who is the target audience?
• College students
• University students
• Math enthusiasts
Compare to Other Differential Equations Courses
Curriculum For This Course
48 Lectures
03:17:31
+
Introduction to Differential Equations
7 Lectures 19:19

Some information about the course instructor and the structure of the course.

Preview 00:58

A note on the notation (Leibniz, Lagrange, Newton) that is used for the derivatives.

Preview 08:22

A look at the differentiation of compositions of functions.

Chain Rule
03:05

A look at implicitly defined functions and how to differentiate them.

Implicit Differentiation
03:57

Before we learn how to solve differential equations, let's take a look at how to actually make one!

Let's Make a Differential Equation!
00:48

One key characteristic of a differential equation is its order.

Equation Order
00:44

Once you have a solution to a differential equation, verifying a solution is easy: simply substitute the function, together with all necessary derivatives, back into the equation and see if the equality holds.

Verifying Solutions
01:25
+
First-Order Differential Equations
9 Lectures 42:39

A look at the direct integration approach, which helps us solve the simplest differential equations.

Direct Integration
01:48

A look at an approach called separation of variables that helps us separate out the x and y terms to different sides of the equation for subsequent integration.

Separation of Variables
03:42

An explanation of the concept of a homogeneous function of one or more variables. This will be useful for solving homogeneous ODEs.

Preview 03:56

A look at homogeneous equations and how to solve them using the y=vx substitution.

Homogeneous Equations
06:18

A look at linear first-order differential equations and the use of the integrating factor.

Linear Equations
04:32

A look at Bernoulli's equations, which are also first-order but non-linear due to an yn term on the right.

Bernoulli's Equations
09:22

A look at the method of exact equations.

Exact Equations
08:06

A look at MATLAB's support for symbolic differentiation, integration and solving differential equations.

Solving DIfferential Equations in MATLAB
03:08

A summary of all the methods we've seen for solving 1st-order ODEs.

Summary
01:47
+
Second-Order Differential Equations
5 Lectures 12:04

A look at the Reduction of Order technique which helps us turn some higher-order (not necessarily linear) equations into first-order ones.

Reduction of Order
05:28

A look at Second-Order Linear equations with constant coefficients.

Second-Order Linear
02:53

A solution with an auxiliary equation that yields two real roots.

Two Distinct Real Roots
01:15

A solution with an auxiliary equation that yields a single real root.

Single Real Root
01:00

A solution with an auxiliary equation that yields complex roots.

Complex Roots
01:28
+
Laplace Transform
8 Lectures 32:13

An introduction to the idea of transforms and, specifically, the Laplace transform.

Introduction
02:01

A look at a few Laplace transforms of simple functions.

A Few Transforms
02:48

The inverse transform is just as useful as the transform itself!

Inverse Transform
02:36

Laplace transform of first and second derivatives of a function.

Transform of a Derivative
03:56

A look at how to find to find direct and inverse Laplace transforms in MATLAB.

Laplace Transforms in MATLAB
04:58

A look at how to differentiate Laplace transforms.

Differentiating Laplace Transforms
05:56

Finally, leveraging the Laplace transform to simplify solving differential equations.

Solving Differential Equations
04:20

Having differentiated Laplace transforms, how about integrating one?

Integration of a Laplace Transform
05:38
+
Fourier Series
5 Lectures 10:52

Introducing Fourier Series.

Introduction
01:49

A look at how to integrate periodic functions.

Integrals of Periodic Functions
04:09

Introducing the concept of mutually orthogonal functions.

Orthogonality
00:56

Finally, a look at the Fourier Series itself.

Fourier Series
00:57

An explanation of how to calculate the coefficients in the Fourier Series for a particular function f(x).

Fourier Coefficients
03:01
+
Partial Differential Equations
8 Lectures 48:48

A look at what partial derivatives are.

Partial Derivatives
04:30

Ways of actually writing down partial derivatives.

Notation
01:37

A look at the general form of a 2nd-order linear PDE.

Partial Differential Equations
02:01

We solve a pair of differential equations with boundary conditions.

Boundary Conditions
12:27

A look at how to solve PDEs symbolically - in Maple, not MATLAB.

Symbolic Solutions in Maple
06:22

Heat Conduction Equation
04:29

An equation that describes the propagation of waves.

Wave Equation
13:27

A practical example of finding an exact solution to the wave equation.

Wave Equation Example
03:55
+
Numerical Methods
5 Lectures 31:31

Introducing numerical methods.

Introduction
02:14

Our first attempt at finding a numeric solution to differential equations.

Euler's Method
08:51

An attempt to improve upon Euler's method by treating the area under the curve as a trapezoid instead of a rectangle.

Improved Euler's Method
04:00

A significant improvement upon Euler's method, representing the slice between the curves as a parabola.

Runge-Kutta Method
06:56

A look at forward, backward and central difference approximations of first and second derivatives of functions.

Numerical Approximation of Derivaties
09:30
+
End of Course
1 Lecture 00:05
Bonus Lecture: Other Courses at a Discount
00:05