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Learn Differential Equations
Rating: 4.0 out of 5(21 ratings)
841 students

Learn Differential Equations

An Advanced Course in Differential Equations and Laplace Transform
Created byAD Chauhdry
Last updated 9/2021
English

What you'll learn

  • students will learn differential equations (OD+PD), they find the way how to solve differential equations
  • Order and degree of differential equations
  • Solutions of first order differential equations by various methods
  • Solutions of higher order differential equations by various methods
  • Laplace Transform and it's application
  • Bundles of Examples and Exercises
  • Step by step learning of each and every concept

Course content

2 sections40 lectures4h 48m total length
  • Homogeneous differential equation8:44
  • separating variables2:32

    Learn to solve a first order differential equation by separating variables, integrating both sides, and obtaining the solution y = C e^{-x^2/2} with the constant of integration.

  • separable first order differential equation3:28
  • Homogeneous Differential Equation 24:31

    Learn how to solve homogeneous differential equations by substituting y = v x, separating variables, and deriving the general solution y = x(ln x + C).

  • integrating factor lecture7:05

    Apply the integrating factor to turn a non-exact differential equation into an exact one and solve by integration; verify exactness via partial derivatives.

  • Exact differential Equation6:12

    Explore exact differential equations of the form M dx + N dy = 0. Test exactness with M_y and N_x, then integrate to relate x and y.

  • Exact differential Equation 24:10

    Verify exactness of a differential equation in the form M dx + N dy by comparing partial derivatives, and solve the exact equation by finding a potential function.

  • Integrating Factors3:39
  • Integrating Factors 27:05
  • Integrating Factors 30:28

    Check whether a differential equation is exact, apply an integrating factor to make it exact, and then find the solution.

  • Linear Differential Equation 15:06

    Learn to solve linear first-order differential equations using the integrating factor method. Multiply through by the integrating factor, then integrate to find the solution.

  • Linear Differential Equation 23:28

    Explore first-order linear differential equations, compare methods, and find their general solution, as introduced in the lecture and course on differential equations.

  • Orthogonal Trajectories6:35
  • Orthogonal Trajectories 26:12
  • Clairaut's Equation7:33

    Explore Clairaut's equation and its two solutions: the general solution and the singular solution, and learn how to derive the general solution and identify the singular one.

  • Solution of homogeneous higher order differential equation5:00
  • Solution of homogeneous higher order differential equation example 12:32
  • Solution of homogeneous higher order differential equation example 22:06

    Solve a homogeneous third-order differential equation by forming the cubic equation from the problem, identify roots such as x = -1, and set up the solution.

  • Solution of nonhomogeneous higher order differential equation example 18:20

    Solve higher-order nonhomogeneous differential equations by first finding the complementary (homogeneous) solutions via the characteristic equation, then determine particular solutions, and finally form the general solution.

  • Solution of nonhomogeneous higher order differential equation example 29:17

    Learn to solve a second-order nonhomogeneous differential equation by first finding the complementary (homogeneous) solution from the characteristic equation, then determine a particular solution to obtain the full general solution.

  • Solution of nonhomogeneous higher order differential equation example 310:56
  • Definition of Laplace Transform1:51
  • Laplace Transform Lecture 22:34

    Learn the Laplace transform and apply its definition to evaluate improper limits as infinity, determining when the limit yields a finite value.

  • Laplace Transform Lecture 34:40
  • Laplace Transform Lecture 47:54

    Explore the definition of the Laplace transform and apply limits, L'Hôpital's rule, and partial fraction techniques to derive the transform.

  • Laplace Transformation Lecture 55:44

    Explore the Laplace transform of sine and cosine using the definition from zero to infinity, derive the s-domain expressions, and compare the real and imaginary parts.

Requirements

  • Intermediate

Description

  • <A step-by-step explanation of more than 5-hour video lessons on Differential Equations>

  • <Instant reply to your questions asked during lessons>

  • <Weekly live talks on Differential Equations. You can raise your questions in a live session as well>

  • <Helping materials like notes, examples, and exercises>

  • <Solution of quizzes and assignments>

What if I told you that there is a concept of Differential Equations, that is so universal in everything that we do, that it is almost a must to at least know what it is, if not be proficient in using it? Would you believe me? Furthermore, what if I added that this concept is most commonly associated with Differential Equations, but can be found in economics, technology development, and so on? How about now? Well, such a concept does exist, and it is called differential equations which are vastly used in Differential Equations. In this Differential Equations: Differential Equations course, we will be figuring out and solving differential equations - read on if I’ve caught your interest.

What’s the Point in Solving Differential Equations?

If math is the last thing in this world that you would associate with the word “fun”, you’re probably not very excited to hear that ordinary differential equations can be found almost everywhere and anywhere in our daily lives. To add to that, in a lot of career opportunity-offering places, it’s actually very important to know the processes of solving differential equations, be it the homogeneous differential equations or other ones. But why is this concept so important? What’s the use of knowing the difference between separable differential equations and ordinary ones? Well, the differences are actually quite prominent.

To put it painstakingly simply, ordinary differential equations are mathematical equations that are used to relate functions to their derivatives. The functions usually represent some sort of a physical quantity, while the derivatives stand for rates of change. The equation is used to define the relationship between these two. As you can probably imagine, these types of relationships are extremely common in all fields of life (biology, chemistry, economics) - that’s why it’s very important to know the methods of solving differential equations - homogeneous differential equations, separable differential equations and everything in between.

Why This Course?

OK, so I have proved to you that knowing the methods of solving differential equations is important - but why should you learn this information from me? Why not choose another guide? Well, I have been teaching mathematics in a university for the past 15 years - I’ve published a lot of successful manuscripts, and have countless years of experience in solving differential equations. I say all of this not to boast of my achievements - I say this so that you could understand my guarantee of quality of this course. Once you choose to take this tutorial, you can be sure that you will receive only the highest quality of information.

Additionally to that, you can be sure that, once you finish this differential equations course, you will have a much broader and deeper understanding of the concept of differential equations (provided you put in the work, of course). I will teach you how to solve differential equations step-by-step. You do not need any prior experience in the field to start learning from this course - we will take things from the top, so you will have the opportunity to either learn everything or revise it, depending on your previous skills. Don’t miss out on this opportunity - enroll today and learn all of the different methods of solving differential equations!

This course covers all areas related to engineering, physics, economics, applied chemistry, bio-mathematics, medicals sciences, cost and management, banking and finance, commerce and business, technologies and so many others fields.

  • Due to its vast applications in each field of life, it is most arising and hot topic in today world. It describes the physical behavior of objects and their rate of change concerning special circumstances.

  • I have described the different features and solution of ordinary and partial differential equations along with Laplace transform.

  • The course has its worth concerning its application and being taught in every field.

  • Degree and order of a differential equation

  • Separating the variables and various examples along with detail

  • Solutions of homogeneous and non homogeneous first order differential equations

  • Solutions of exact differential equations

  • Solutions of non exactly differential equations

  • Integrating Factor

  • Solutions of first order differential equations by orthogonal trajectories

  • Solutions of first order linear differential equations

  • Solutions of Higher order differential equations

  • Laplace transform and it's application

  • Derivatives

  • Functions of several variables

  • nth order derivatives

MONEY BACK GUARANTEE

It is not like that I have wasted the time anywhere in the course. I am giving you the genuine course contents presentations. So I promise you that you will not waste your money. Also Udemy has 30 day money back guarantee and if you feel that the course is not like that you were looking, then you can take your money back.

WHAT PEOPLE ASK ABOUT MY COURSES

Here are some review about my courses by the students.

1- Brava Man: Superb course!!

The instructor is very knowledgeable and presents the Quantum Physics concepts in a detailed and methodical way.

We walked through aspects like doing research and implementation via examples that we can follow in addition, to actual mathematical problems we are presented to solve .

2- Manokaran Masikova: This is a good course to learn about quantum mechanics from basic and he explained with example to understand the concept.

3- Dr B Baskaran: very nice to participate in the course and very much interesting and useful also.

4- Mashrur Bhuiyan: Well currently i am an Engineering student and i forgot the basics of my calculus . but this course helped me to get a good understanding of differentiation and integration. Overall all of the teaching method is good.

5- Kaleem Ul Haq: Really a great explanations and each step have explain well. I am enjoying this course. He is familiar instructor in calculus. I have seen many lectures of this instructor before taking this course.

                                           

                                                                    HOPE YOU WILL JOIN ME IN THIS COURSE


                                                                                                                                                                                          AD CHAUHDRY

Who this course is for:

  • Intermediate level student