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An in-depth course on differential equations, covering first/second order ODEs, PDEs and numerical methods, too!

330 students enrolled

Current price: $10
Original price: $50
Discount:
80% off

30-Day Money-Back Guarantee

- 3.5 hours on-demand video
- 1 Supplemental Resource
- Full lifetime access
- 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

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

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Curriculum For This Course

Expand All 47 Lectures
Collapse All 47 Lectures
03:17:26

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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

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–

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 *y ^{n}* 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

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–

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

About the Instructor

Quant Finance • Algotrading • Software/Hardware Engineering

Dmitri Nesteruk is a developer, speaker and podcaster. His interests lie in software development and integration practices in the areas of computation, quantitative finance and algorithmic trading. His technological interests include C#, F# and C++ programming as well high-performance computing using technologies such as CUDA. He has been a C# MVP since 2009.

Dmitri is a graduate of University of Southampton (B.Sc. Computer Science) where he currently holds a position as a Visiting Researcher. He is also an instructor on an online intro-level Quantitative Finance course, and has also made online video courses on CUDA, MATLAB, D, the Boost libraries and other topics.

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