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# Differential Equations 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.

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

## Reviews

4.9 rating, based on 267 reviews

Start your review of Differential Equations for Engineers

• 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...
• 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.
• 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.
• Anonymous
My quiz scores started with three full marks in a row, decayed gradually, and ended with just scraping through the pass line. hahaha. Professor Chesnov is definitely very detailed with the lectures and all the interesting yet troublesome "chores". I would...
• Anonymous
The course is quite helpful for university students, especially engineering students. The lecture videos are separated into several parts allowing students to learn step by step. the quizzes can also recall the knowledge in the previous videos to ensure we are on the right track. Besides, the exam at the end of every week helps to check how much have we learned; it also gives us the opportunity to utilize what we learned into reality. The course is over all well-structured and easy to catch up. This is a great course for beginners and it is even better with the help of the course book.
• 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.
• Anonymous
Well organised and delivered course. The small doses of methods or topics were given in very manageable paces. I was amazed with the way some progressive complex equations were broken down to allow a ‘student’ to use knowledge gained in previous lessons of the course. Once I finished one lesson could not wait for the next one. I am going to register to another course of the same instructor.
• 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...
• Anonymous
Very good course for learning the basics of differential equations. I was happy to see that it covered not just the math, but the engineering perspective well, all the way up to diffusion equations (partial differential equations). Warning: If you need to take a math test on differential equations, this class leaves much out and you'll need to learn more after completing this course.
• Anonymous
I enjoyed a lot with this course.
It is teached clearly and it is easy to understand.
I did not know anything about Laplace transform or Fourier series but now I have a clear idea about then.
Same test were a bit hard for me and I had to rewiued and think but I could solve then.

In summary an excelente course and a Great teacher.

From Spain a 62 year old….. congratulations
• Anonymous
I love this course. Professor Chasnov explains everything very succinctly and gives an intuition for it as well. As a hobbyist I took this course because I wanted to feel more comfortable reading scientific papers and this course indeed gave me a solid step forward in that direction. If you don't know much about differential equations I 100% recommend this!
• Anonymous
I enjoyed very much all the course. I learned a lot of new skills. Great comprehensive materials and very great professor , who is concise, clear, very effective. .I am glad to finish the third course by professor Chasnov . I can’t be thankful enough for his courses.
• Anonymous
This course mainly teaches about ordinary differential equations and partial differential equations in the last week. The instructor provides some interesting concrete examples for us to practice the techniques we have learned and better understand the odes and pdes.
• Jose
A very good course. The professor is very clear and you can learn very quickly. The structure of the course is well conformed for a course in engineering , without a great burden of mathematical formalisms , only the just for understanding the subject .
• Anonymous
One of the best online courses ! There is all you need to learn : a complete and well made pdf document small exercices after each notions to uderstand them; and the best, video of the teacher writting the equations on a transparent board.
• 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...
• Anonymous
Very nice course design by the professor. such a nice experience to learn this course. The students learn differential equations for engineers and understand the application.
• Anonymous

Anonymous completed this course.

I am very proud about to complete this amazing and interested course,I felt very happy for enhanced my knowledge through this this wonderful platform
• Anonymous
G​reat & very well organized course! Congratulations. As a retired professor I appreciate the effort to produce a course of this quality very much
• Anonymous
I believed this course is really helpful, however the last few classes were a bit difficult, but I believed I was able to get through them.

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