Differential Equations In Depth

Focused View

Dmitri Nesteruk

3:17:25

11 View

1 - Introduction to Differential Equations

1 - Course Introduction.mp4

00:58

2 - A Word on Notation.mp4

08:22

3 - Chain Rule.mp4

03:05

4 - Implicit Differentiation.mp4

03:57

5 - Lets Make a Differential Equation.mp4

00:48

6 - Equation Order.mp4

00:44

7 - Verifying Solutions.mp4

01:25

2 - FirstOrder Differential Equations

8 - Direct Integration.mp4

01:48

9 - Separation of Variables.mp4

03:42

10 - Homogeneous Functions.mp4

03:56

11 - Homogeneous Equations.mp4

06:18

12 - Linear Equations.mp4

04:32

13 - Bernoullis Equations.mp4

09:22

14 - Exact Equations.mp4

08:06

15 - Solving DIfferential Equations in MATLAB.mp4

03:08

16 - Summary.mp4

01:47

3 - SecondOrder Differential Equations

17 - Reduction of Order.mp4

05:28

18 - SecondOrder Linear.mp4

02:53

19 - Two Distinct Real Roots.mp4

01:15

20 - Single Real Root.mp4

01:00

21 - Complex Roots.mp4

01:28

4 - Laplace Transform

22 - Introduction.mp4

02:01

23 - A Few Transforms.mp4

02:48

24 - Inverse Transform.mp4

02:36

25 - Transform of a Derivative.mp4

03:56

26 - Laplace Transforms in MATLAB.mp4

04:58

27 - Differentiating Laplace Transforms.mp4

05:55

28 - Solving Differential Equations.mp4

04:20

29 - Integration of a Laplace Transform.mp4

05:38

5 - Fourier Series

30 - Introduction.mp4

01:49

31 - Integrals of Periodic Functions.mp4

04:09

32 - Orthogonality.mp4

00:56

33 - Fourier Series.mp4

00:57

34 - Fourier Coefficients.mp4

03:01

6 - Partial Differential Equations

35 - Partial Derivatives.mp4

04:30

36 - Notation.mp4

01:37

37 - Partial Differential Equations.mp4

02:01

38 - Boundary Conditions.mp4

12:27

39 - Symbolic Solutions in Maple.mp4

06:22

40 - Heat Conduction Equation.mp4

04:29

41 - Wave Equation.mp4

13:27

42 - Wave Equation Example.mp4

03:55

7 - Numerical Methods

43 - Introduction.mp4

02:14

44 - Eulers Method.mp4

08:51

45 - Improved Eulers Method.mp4

04:00

45 - improvedeuler.zip

46 - RungeKutta Method.mp4

06:56

47 - Numerical Approximation of Derivaties.mp4

09:30

8 - End of Course

48 - A Beginners Guide to Numerical Methods in MATLAB.txt

48 - Bonus Lecture Other Courses at a Discount.html

Description

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

What You'll 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

Who is this for?

College students

University students

Math enthusiasts

What You Need to Know?

Good knowledge of calculus (linear algebra, differentiation, integration)

More details

Description
This course has everything you need to learn and understand Differential Equations. Differential equations are a class of equation that involves the use of differentials (derivatives) in their construction. Differential equations are used in many areas of science, particularly in physics, where they are used to model real-world phenomena such as the propagation of waves.
This course covers:Â
Ordinary differential equations (ODEs) - first and second order
Laplace Transform and Fourier Series
Partial differential equations (PDEs) - including common equations such as theÂ WaveÂ Equation and the Heat Conduction Equation
Numeric solutions of differential equations - e.g., Euler's Method, Runge-Kutta
Modeling and solving differential equations using MATLAB and Maple.
Course pre-requisites:
Fundamental understanging of differentiation and integration
Knowledge of common integration operations (integration by parts, integration by substitution)
Basic understanding of numerical computing (required for numerical methods)
Access and basic knowledge of common CAS packages such as MATLAB, Maple, Mathematica, etc.
This course is presented as a series of hand-written lectures where we discuss the relevant topics. IÂ also present approaches to using CASÂ (Computer-aided Algebra Systems) to solving differential equations either analytically or symbolically.
It is recommended that you augment your study of differential equations on this course with a good textbook on differential equations.
This course will continue to evolve and improve based on feedback from the course participants.Â Please leave feedback!
Who this course is for:
College students
University students
Math enthusiasts

User Reviews

Rating

average 0

Total votes0

Focused display

Differential Equations

Dmitri Nesteruk

Instructor's Courses

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

Udemy

View courses Udemy

Students take courses primarily to improve job-related skills.Some courses generate credit toward technical certification. Udemy has made a special effort to attract corporate trainers seeking to create coursework for employees of their company.