This course is all about differential equations and covers both theory and applications. In the first five weeks, students will learn about ordinary differential equations, while the sixth week is an introduction to partial differential equations.
The course includes 56 concise lecture videos, with a few problems to solve after each lecture. After each major topic, there is a short practice quiz. At the end of each week, there is an assessed quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes.
Download the lecture notes from the link
https://www.math.hkust.edu.hk/~machas/differential-equations-for-engineers.pdf
Watch the promotional video from the link
https://youtu.be/eSty7oo09ZI
Differential Equations for Engineers
The Hong Kong University of Science and Technology via Coursera
Overview
Syllabus
- First-Order Differential Equations
- A differential equation is an equation for a function with one or more of its derivatives. We introduce different types of differential equations and how to classify them. We then discuss the Euler method for numerically solving a first-order ordinary differential equation (ODE). We learn analytical methods for solving separable and linear first-order ODEs, with an explanation of the theory followed by illustrative solutions of some simple ODEs. Finally, we explore three real-world examples of first-order ODEs: compound interest, the 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. Using 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 second-order polynomial 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 introduce the solution of a linear ODE by a series solution. Although we do not go deeply into it here, an introduction to this technique may be useful to students who 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 then visualized using phase portraits. We next 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. We then apply the theory to solve a system of two coupled harmonic oscillators, and use the normal modes to analyze the motion of the system.
- 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 describing the diffusion of a dye in a pipe. We then proceed to solve this PDE using the method of separation of variables. This involves dividing the PDE into two ordinary differential equations (ODEs), which can then be solved using the standard techniques of solving ODEs. We then use the solutions of these two ODEs, and our definition of a Fourier series, to recover the solution of the original PDE.
Taught by
Jeffrey R. Chasnov
Tags
Related Courses
Related articles
Reviews
4.9 rating, based on 346 Class Central reviews
4.9 rating at Coursera based on 2119 ratings
-
Very easy to learn and fabulous technique of teaching for Differential Equations. I hope the instructor "Jeff Chasnov" will start the courses on Complex Variables, Co-ordinate Geometry, Probability and Statistics. It will be great pleasure for me if he will start these courses.
-
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. -
"Differential Equations for Engineers" by HKUST on Coursera is an excellent course for anyone looking to strengthen their understanding of differential equations, particularly from an engineering perspective. The instructors break down complex topics into manageable lessons, covering everything from basic concepts to advanced applications, with clear explanations and plenty of examples. The course structure is intuitive, with quizzes and assignments that reinforce key concepts and encourage active learning. I especially appreciated the focus on real-world engineering applications, making it highly relevant for practical use. A solid choice for both students and professionals wanting to build foundational skills in differential equations.
-
A nice introduction to DE, but not the same as taking it in a face-to-face class obviously. You only get out of a course what you put into it and without larger homework sets, you just don't get a large amount out. Of course, if you took the class face-to-face, along with larger homework sets, you'd have interactions with other students and office-hours with the professor. I don't think you could make it better by just making the homework sets larger.
Two things are nice, though, compared to an average coursea course. I took this course independently, but (1) the instructor replied to a question within 24 hours, so he is still monitoring the course and (2) the course pings you if you don't do one assignment a week. -
Engineers can take advantage of a thorough and organized introduction to differential equations in the "Differential Equations for Engineers" Coursera course. In order to guarantee that students develop a solid foundation, the course covers a wide range of crucial topics, from fundamental ideas to more complex applications. Clear and captivating lectures are enhanced with real-world application examples from the actual world. The information is successfully reinforced by the problem sets and quizzes, which facilitates understanding of difficult ideas. All things considered, anyone wishing to expand on their knowledge of differential equations in an engineering setting should take this course.
-
I very much enjoyed the course, which was a review for me (of classes taken 4 decades ago). I thought the course is well organized and the prof. delivered well prepared lectures. The review at the end of each lecture is good, but perhaps a bit long for some shorter lectures. I bought the book which was easier than referencing an online doc for me. I took the class because of my course work in engineering mechanics. It is unfortunate that not all students for this class have access to Matlab/simulink, as I think those tools could compliment the course content.
-
Overall, "Differential Equations for Engineers" is an excellent course for anyone looking to grasp this fundamental topic. The combination of comprehensive content, expert instruction, and supportive community makes it a standout option. I highly recommend it to students, professionals, and anyone interested in enhancing their mathematical skills. Whether you're new to differential equations or seeking to refresh your knowledge, this course is well worth the investment! But to be honest, I didn't understand anyhing
-
Prof. Jeff Chasnov explained vivid and step by step the concept and types of differential equations. Various applications for modelling real life physical problems by differential equations are also stated in detail procedures. I've also learned several useful techniques to solve first order ODE, second order ODE, knowledge of Laplace transform, series solution method, and some PDEs. This is a great course, and I would like to recommend it to all want to learn differential equations.
-
"Differential Equations for Engineers" was an exceptional course that surpassed my expectations. The instructor's expertise and passion for the subject created an engaging learning environment. The course incorporated real-world applications, deepening my understanding and appreciation for differential equations. The assignments were challenging yet fair, promoting critical thinking. The course materials were well-organized, with multimedia tools enhancing the learning experience. I highly recommend this course to anyone looking to master differential equations and uncover the beauty and practicality of this mathematical field.
-
Great class! I really like the use of the available textbook (Lecture and Quizzes covered in videos written by him!) and the quizzes with the workings of the solution at the end of the textbook. I could study it offline and come back online to finish it. There aren't any curveballs. Extremely organized and digestible. I truly enjoyed learning from Jeff Chasnov, he was succinct and thorough.
-
This class about differential equations is probably one of the most interested that I have ever seen. Everything is explained in an understandable way. It has helped me remember some notions I learnt a few years ago. Furthermore, I have learnt many other mathematical calculations and formulae. If you want to improve your knowledge, do not hesitate.
-
Fantastic course! Clear, engaging lessons with practical applications. The instructor explains concepts well, making it easy to follow and understand. The course offers valuable insights and real-world examples that help you apply what you've learned. Highly recommended for anyone looking to gain useful skills quickly and effectively!
-
very refined and useful courses， in university, what I learn is starting from the proof, I try to remember every proof but finally I could not write any of them by myself without the textbook. This courses give us a simple outline about which equation is used for which purpose, so we can easily know what we are learning
-
This course was so informative and useful for me. During this course, I have learned a lot of new things, new formulas, more detailed information about each topic, everything was clear and understandable. Also, passing some test was useful for us to check our ability and understanding of how we understanding these topics.
-
Very nice course. And those beautiful equations and methods. I learned a lot. And for me the best lectures are "Complex conjugate roots", "Laplace transform, Dirac delta function" and "Series solution method". Week 6 was difficult, however it was worth it to solve pdes. I'd like to recommend this course to everyone.
-
Очень классный;курс выполняйте внимательно, и обращайте внимания на- формулы которые даётся в лекции, и видио уроков очень помогает, очень интересно и полезные курсы
-
I really enjoyed this course. It provides a comprehensive introduction to all the key topics in differential equations while also including real-life applications that deepen understanding and make the subject more engaging.
-
I find this course very interesting and entertaining. In addition to calm and measured explanations of differential equations, this course was remembered in clear language. Thank you for such an interesting lesson!
-
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 equat…
-
Nur Hidayat MuhammadI've got a good lesson from the course. It reminds when I was still in my undergraduate taking ODE class. The course materials are so good, easy to understand and not too much theory
