Differential Equations for Engineers

The Hong Kong University of Science and Technology via Coursera

Go to class Write review

Details

Go to class

Provider

Coursera
Pricing

Free Online Course (Audit)
Languages

English
Certificate

Paid Certificate Available
Duration & workload

6 weeks long, 27 hours worth of material
Sessions
Level

Beginner
Subtitles

Arabic, French, Portuguese, Italian, German, Russian, English, Spanish

Found in

Part of

Mathematics for Engineers

Overview

Class Central Tips

This course is all about differential equations. Both basic theory and applications are taught. In the first five weeks we will learn about ordinary differential equations, and in the final week, partial differential equations.

The course contains 56 short lecture videos, with a few problems to solve after each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of six weeks in the course, and at the end of each week there is an assessed quiz.

Download the lecture notes:
http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf

Watch the promotional video:
https://youtu.be/eSty7oo09ZI

Syllabus

First-Order Differential Equations

A differential equation is an equation for a function with one or more of its derivatives. We introduce differential equations and classify them. We then learn about the Euler method for numerically solving a first-order ordinary differential equation (ode). Then we learn analytical methods for solving separable and linear first-order odes. An explanation of the theory is followed by illustrative solutions of some simple odes. Finally, we learn about three real-world examples of first-order odes: compound interest, terminal velocity of a falling mass, and the resistor-capacitor electrical circuit.

Homogeneous Linear Differential Equations

We generalize the Euler numerical method to a second-order ode. We then develop two theoretical concepts used for linear equations: the principle of superposition, and the Wronskian. Armed with these concepts, we can find analytical solutions to a homogeneous second-order ode with constant coefficients. We make use of an exponential ansatz, and transform the constant-coefficient ode to a quadratic equation called the characteristic equation of the ode. The characteristic equation may have real or complex roots and we learn solution methods for the different cases.

Inhomogeneous Linear Differential Equations

We now add an inhomogeneous term to the constant-coefficient ode. The inhomogeneous term may be an exponential, a sine or cosine, or a polynomial. We also study the phenomena of resonance, when the forcing frequency is equal to the natural frequency of the oscillator. Finally, we learn about three important applications: the RLC electrical circuit, a mass on a spring, and the pendulum.

The Laplace Transform and Series Solution Methods

We present two new analytical solution methods for solving linear odes. The first is the Laplace transform method, which is used to solve the constant-coefficient ode with a discontinuous or impulsive inhomogeneous term. The Laplace transform is a good vehicle in general for introducing sophisticated integral transform techniques within an easily understandable context. We also discuss the series solution of a linear ode. Although we do not go deeply here, an introduction to this technique may be useful to students that encounter it again in more advanced courses.

Systems of Differential Equations

We learn how to solve a coupled system of homogeneous first-order differential equations with constant coefficients. This system of odes can be written in matrix form, and we learn how to convert these equations into a standard matrix algebra eigenvalue problem. The two-dimensional solutions are visualized using phase portraits. We then learn about the important application of coupled harmonic oscillators and the calculation of normal modes. The normal modes are those motions for which the individual masses that make up the system oscillate with the same frequency.

Partial Differential Equations

To learn how to solve a partial differential equation (pde), we first define a Fourier series. We then derive the one-dimensional diffusion equation, which is a pde for the diffusion of a dye in a pipe. We proceed to solve this pde using the method of separation of variables.

Taught by

Jeffrey R. Chasnov

Charts

#1 in Subjects / Mathematics
#1 in Subjects / Engineering

Reviews

4.9 rating, based on 282 Class Central reviews

4.9 rating at Coursera based on 1910 ratings

Start your review of Differential Equations for Engineers

Soumya Acharya @strmclk

Great course, great overall coverage of topics, application-based examples aplenty. The instructor is really great at what he teaches. Worth the time and effort, especially if you are looking to simply learn/refresh your knowledge about DEs. Very satisfied overall with the learning; and there are other courses in an extension of this one that will be useful too (PDEs and numerical methods (the instructor is an author of a book on the latter that I've extensively used), for example.

As a pre-final year undergrad, I found it basic yet rigorous and ended up happily learning quite a few tricks I didn't initially set out to as part of my goals.
Anonymous

Dear Prof Jeff Chasnov: How are u? I am an alumni of HKUST with Master in Telecom , however, I took B. SC in electronic engineering dated back in 1974 and as I missed the intense study of Matrix algebra, Vector calculus as well as Differential equations...

Dear Prof Jeff Chasnov:
How are u?
I am an alumni of HKUST with Master in Telecom , however, I took B. SC in electronic engineering dated back in 1974 and as I missed the intense study of Matrix algebra, Vector calculus as well as Differential equations since then, I always trying to make up the study for the past 48 years but not able to find ad hoc classes in HK covering all such math course and also heavy work schedule is the limiting factor! I retired by end of 2019 and then I found your three courses by reading nearly some 160+ video plus notes and I must salute to your passion and detail layout plus tedious/vivid explanation of the concept and illustration!
Very much grateful to your commitment and hard work!
Best,
Tony Ngai (Msc of telecom - HKUST)
Maria Eduarda De Sousa Pinheiro @Mahpinheiro

Bom, com esse curso básico de 6 semanas eu espero compreender, e me apaixonar mais pela engenharia, pois quando eu for realmente fazer a faculdade eu gostaria de está bem preparada.
Anavheoba Abraham Ogenakohgie

Anavheoba Abraham Ogenakohgie completed this course.

Professor Jeff chaznov really did a good job in taking this course (Differential equation for engineers) At first when he started he went back to basic calculus and was nurturing us like babies(for the first three weeks of the course) and I appreciate...

Professor Jeff chaznov really did a good job in taking this course (Differential equation for engineers)
At first when he started he went back to basic calculus and was nurturing us like babies(for the first three weeks of the course) and I appreciate that a lot. It was easy at first in the first three weeks but it became complex due to the introduction of Laplace transform,Heaviside's step function,Airy's expansion it was really fun cause I learnt a lot and I would love to know more.
This course was really challenging it made me think outside the Box,and I appreciate prof for tutoring this course like this.
I can boast now that there is nothing in calculus that I don't have knowledge of,because of the way this course was treated. I'm still in college but I believe this course will prove very useful in the future.
Thank you very much Jeff chaznov
It was worth it cause u changed lives
Anonymous

This class has a very beautiful and practical topic. Professor Chasnov's mastery of the subject along with his beautiful teaching method will make you interested to. Also, the presence of numerous practical examples in this course will help you if the application of abstract mathematical concepts in your life is unclear. Many thanks to the teacher!
Anonymous

It's very helpful for the students to learn more topics in a short time .i learned so many things and different topics through this course.i would thank to the professor who is taught easily and understand of all the topics. It's very useful for the students who wants to do PhD in math.
Anonymous

Excellent explanation and step-by-step detailed problem-solving videos with lecture notes. Easy-to-understand content. Great for those who want to have a gentle preview of differential equations. Genuinely nice to have exercises that include answers which have detailed explanations.
Anonymous

Anonymous completed this course.

very good course. easily able to understand all the concepts. the way of teaching is also very good. videos are short and simple. but contains good content. teacher knowledge is very nice it's an excellent course which really improved my skills. good...

very good course. easily able to understand all the concepts. the way of teaching is also very good.
videos are short and simple. but contains good content. teacher knowledge is very nice
it's an excellent course which really improved my skills. good work by the team. all videos and material are really helpful and informative.thanks to the team. am thank full for coursers that create this cite .this is very good and leaning cites for everyone.one of the best courses I have taken by far. Everything from the videos to assignments is amazing and informative. It has helped me tremendously. I encourage everyone to take it. Coursera has contained more attraction, interaction, and Effective knowledge. I really enjoyed the course & also I updated my knowledge through COURSERA. ThanksThe course is good and very helpful. I felt the synthesis essay part needs a little work in terms of explanation, with some more detailing and specifications of the essay. The assignment strategies and evaluations during the videos is another strength which makes it very helpful. Topics for assignments can include wider areas or can be given choice to the participants to explore different areas to increase knowledge. The knowledge sharing or questioning sections had very vague responses from participants and not related to course,no new knowledge or point of views were shared, so din't find that section appropriate and worthy. Peer reviews just involved reviewing on the basis of format and not what was learnt from the course and were the essays structures based on the course specifications. Some documents were not accessible and the reporting or problem-solving part needs improvement. Overall, the course shared many pointers of academic writing which were significant and research focused which is what makes it effective.
Anonymous

Very interesting course, clear and understandable explanations accompanied me the whole time. The only thing that might put you off is the presence of physics in this course, but don't be intimidated)
Anonymous

Thank you so much prof. The course content is intense, which is exactly what I was looking for!!!! I will definitely recommend the course to anyone wishing to improve maths knowledge.
Anonymous

All important topics been covered. The structure of topics is well designed with exercises. Quiz is good. Sometimes the quiz' task could be solved indirectly in case you know the topic.
Anonymous

Prof. Jeff had provided clear explanation with examples, exercises and solutions. He also provided videos to cover knowledge that is needed for the course. Keep up the good work!
Anonymous

Great course, perfect for any math-related majors like myself who seeks the knowledge on how to solve differential equations and apply them to real life scenarios and situations.
Anonymous

I loved this course. The content is perfectly paced; the problems between videos are sized just perfectly so that I can learn the content bit-by-bit.
PURVI RASTOGI

very good teach to us by mr. jess sir
i learned a lot in this course
for example:-
physics, applied mathematichs, formulas, gravity, and many more
Anonymous

This course is very helpful for anyone who wants to remember or learn. I've found several new interpretation and interesting problems
Anonymous

It is a magnificent course, Dr. Jeffrey's lessons are excellent, I have learned concepts that I did not understand, thank you, Dr. Jeffrey
Anonymous

This is an amazing course. It's not much difficult, so I think anyone can solve the problems involved in the practices and quizzes.
Anonymous

Anonymous completed this course.

THIS COURSE IS VERY HELPFUL TO ME TO UNDERSTAND DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS.I GOT MORE INFORMATION REGARDING APPLICATIONS OF DIFFERENTIAL EQUATIONS LIKE PHASE PORTRAITS ,PHYSICAL APPLICATIONS,FOURIER SERIES,COMPOUND INTEREST,RC CIRCUITS,TERMINAL VELOCITY,EULERS METHOD,R.K METHODS,LAPLACE TRANSFORMS,DIRAC DELTA FUNCTIONS,HEAVISIDE STEP FUNCTIONS,EIGEN VALUES,EIGEN VECTORS,COUPLED OSCILLATIONS,DIFFUSION EQUATIONS AND LOT MORE.THIS COURSE IS AMAZING.I THINK ANYONE CAN ACQUIRE MORE KNOWLEDGE BY TAKING THIS COURSE.I AM VERY HAPPY THAT I HAVE SUCCESSFULLY COMPLETED THE COURSE.I WOULD LIKE TO THANK PROFESSOR JEFF R.CHASNOV
Anonymous

This course is very helpful to me to understand differential equations and their applications.Further, we also get surprising results in this course specially in the Fourier Series section which may seem interesting to all. I feel it is a good introduction but if you want to practice more, you may want to search for another course. I found that the number of problems given to solve were just sufficient but I could have fancied more problems to practice.

This approach will and has brought more interest for me in the subject as I am seeing the applications visually also. Thank you professor.