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Differential Equations for Engineers

The Hong Kong University of Science and Technology via Coursera

30 Reviews 496 students interested
  • Provider Coursera
  • Cost Free Online Course (Audit)
  • Session Upcoming
  • Language English
  • Certificate Paid Certificate Available
  • Effort 5 hours a week
  • Start Date
  • Duration 4 weeks long
  • Learn more about MOOCs

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Overview

This course is about differential equations, and covers material that all engineers should know. We will learn how to solve first-order equations, and how to solve second-order equations with constant coefficients and also look at some fundamental engineering applications. We will learn about the Laplace transform and series solution methods. Finally, we will learn about systems of linear differential equations, including the very important normal modes problem, and how to solve a partial differential equation using separation of variables. This solution method requires first learning about Fourier series.

After each video, there are problems to solve and I have tried to choose problems that exemplify the main idea of the lecture. I try to give enough problems for students to solidify their understanding of the material, but not so many that students feel overwhelmed. I do encourage students to attempt the given problems, but if they get stuck, full solutions can be found in the lecture notes for the course.

Lecture notes may be downloaded at
http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf

Syllabus

First-Order Differential Equations
-Welcome to the first module! We begin by introducing differential equations and classifying them. We then explain the Euler method for numerically solving a first-order ode. Next, we explain the analytical solution methods for separable and linear first-order odes. An explanation of the theory is followed by illustrative solutions of some simple odes. Finally, we present three real-world examples of first-order odes and their solution: compound interest, terminal velocity of a falling mass, and the resistor-capacitor electrical circuit.

Second-Order Differential Equations
-We begin by generalising the Euler numerical method to a second-order equation. 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 convert the 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 discuss the solutions for these different cases. We then consider the inhomogeneous ode, and the phenomena of resonance, where the forcing frequency is equal to the natural frequency of the oscillator. Finally, some interesting and important applications are discussed.

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 series solution. 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 and Partial Differential Equations
-We solve a coupled system of homogeneous linear first-order differential equations with constant coefficients. This system of odes can be written in matrix form, and we explain how to convert these equations into a standard matrix algebra eigenvalue problem. We then discuss 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. Next, to prepare for a discussion of partial differential equations, we define the Fourier series of a function. Then we derive the well-known one-dimensional diffusion equation, which is a partial differential equation for the time-evolution of the concentration of a dye over one spatial dimension. We proceed to solve this equation for a dye diffusing length-wise within a finite pipe.


Taught by

Jeffrey R. Chasnov

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Reviews for Coursera's Differential Equations for Engineers
4.9 Based on 30 reviews

  • 5 stars 90%
  • 4 stars 10%
  • 3 star 0%
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  • 1
Anonymous
5.0 2 months ago
Anonymous completed this course.
Very interesting the way the teacher it's just not giving any unknown formulas that come from a physics analysis and tackle the, but he reallym directly makes you learn in a very simple way how to truly understand mathemathics while you're learning differential equations in the road, always viewed from a real physics perspective. Covered the most important subjects gave enough material to practice. Excellent and congratulations.
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Anonymous
5.0 a month ago
Anonymous is taking this course right now.
I studied differential equations in college many years ago so this is a review for me, and I am taking it with my wife who is taking it for the first time. Both of us find the course to be excellent. We like that the course is broken into many short modules, each with a review problem immediately following to reinforce the material. We find the videos to be generally clear and easy to understand. The examples are interesting and relevant. Our only challenge is finding enough time to complete each week's work. Although the time estimates are reasonable, we can only spend a couple of hours a week on the course so we will probably need 8-10 weeks to finish this 4 week course. We do appreciate being able to reset our deadlines. I would recommend this course to anyone who needs to learn this material, whether for the first time or as a review.
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Anonymous
5.0 4 months ago
Anonymous completed this course.
It's a fantastic course to learn! The professor has prepared very detailed, informative and easily-understandable notes for the course, and I really enjoy the teaching style! It's very clear and straightforward. The course covers major consequencial part of the differential equation, especially ODE. I've learned a lot through the course.

One little suggestion: maybe the professor can talk more about PDE later in this course. And also, I'm quited interested in the disfussion application and maybe the professor can talk more about the real-life comprehension of those math equations and results.

Thanks so much for professor's efforts! It's really a rewarding course!
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Anonymous
5.0 7 months ago
Anonymous completed this course.
This differential equations course is aimed at engineers and appropriately focuses on physical (and financial) applications. Just enough theory is included to ensure the student can correctly apply the learnings.

The key to success (for me) in this course was to WORK THE PROBLEMS. Learning DE's is not a spectator sport. You've got to sharpen lots of pencils and put in the effort. It will be rewarded. The exercises are well structured and the accompanying e-text is invaluable.

I rated this 5 stars because of how completely I achieved my learning objectives. I will point out that doing so takes approx. twice as long as the time estimates in the syllabus.
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Anonymous
5.0 a month ago
Anonymous completed this course.
In this course, Prof. Chasnov provides an "applications based" approach to differential equations. While the necessary minimum of theory is included, the focus remains on problem solving. As an engineer, I have always approached math as a tool rather than as an end in itself.

I particularly appreciated the many real world examples of how to apply the lecture material. A caution to prospective students - - you won't get much out of this by simply watching the lectures. You MUST do the problem sets to really benefit. It is worth the investment.
Was this review helpful to you? Yes
Anonymous
5.0 4 months ago
Anonymous completed this course.
The course is very useful in particular for understanding how different maths skills are related and how important to use differential equation to see the dynamics of any system. The course helps visualize and structuralize all the maths thinking and problem solving skills needed for modelling and problem solving via the very clear presentation by Prof. Jeff and very logical structured and designed course framework. Looking forward to other courses that will be thought by Prof. Jeff in the future.
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Anonymous
5.0 a month ago
Anonymous completed this course.
I completed and have cert. This course is very well organized. The course encourage me to go further in Phyasics for my life-long study. During I taking this course I built study site in Korean.

http://math-mass-goodkook.blogspot.com/search/label/%EC%9D%B4%EA%B3%BC%EC%83%9D%EC%9D%84+%EC%9C%84%ED%95%9C+%EB%AF%B8%EB%B6%84+%EB%B0%A9%EC%A0%95%EC%8B%9D

Thanks Prof. Chasnov for providing great course.

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Anonymous
5.0 a month ago
Anonymous completed this course.
Professor Jeff does a great job! The course is challenging, no doubt, but I really enjoyed it. I took DiffEQ many years ago, but at that time, it was just a hurdle to complete my coursework. Over the years, I really wanted to learn it for its own sake, it is a beautiful topic in Math. I mean, without the pressure of a degree looming. Jeff's course was the perfect experience for me.
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Anonymous
5.0 a month ago
Anonymous completed this course.
I have tried and failed many times to take a differential equation class, but now I actually completed this class. Thank you Prof. Chasnov for creating this course. It is presented very logically, with prerequisites included to understand the rest of the materials, math derivations, as well as real life examples. I'd even encourage you to read the accompanying book.
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Gaetano P
5.0 7 months ago
by Gaetano completed this course, spending 4 hours a week on it and found the course difficulty to be medium.
I took other courses on DEs both on coursera and edx platforms by MIT, Boston University and other universities and i have to say that this course is one of the best. Really well teached with essential theory and practice. Homework and final module tests are really challenging. Prof.Chasnov's teaching is really clear and understandable.
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Anonymous
5.0 a month ago
Anonymous completed this course.
i studied international business but love deep learning a lot. I get stuck with different type of differential equation and this course give me a more clear understanding, which improve my knowledge about derivatives a lot. I like how the instructor teaches in an intuitive ways. I like how he end the video :)
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Kasun P
5.0 a month ago
Kasun is taking this course right now.
The course is amazingly good with plenty of explanations and real world exampes. I have never been good and confident at differential equations, but now, here I am, solving problems thrown and me easily and confidently. Thank you so much for this course. I can't wait till you air your course on vector calculus
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Anonymous
5.0 3 weeks ago
Anonymous completed this course.
In spite of the complexity of the subject, the lessons are well presented making to be relatively easy to follow and finish the course. The examples presented for application, each type of differential equation, to the solution of real life problems, makes the course very interesting.
Was this review helpful to you? Yes
Anonymous
4.0 a month ago
Anonymous completed this course.
It's an excellent course for students looking to either learn differential equations from scratch or for undergraduates looking to brush up their basics. Professor Jeff Chasnov is really convincing and professional... all in all it makes for a great learning experience!
Was this review helpful to you? Yes
Anonymous
5.0 a month ago
Anonymous completed this course.
The course was designed very well and had just the right amount of difficulty. Amazing professor! He made topics clear and made sure there is enough practice problems for students to do. Practice Quiz was a good idea that other courses should also look at.
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Anonymous
5.0 6 months ago
Anonymous is taking this course right now.
This course is the best course on differential equations I have taken so far. It is very informative and interactive. The instructor is very active and this is very helpful to have him clear doubts. The course is very well designed and covers almost all topics.
Was this review helpful to you? Yes
Anonymous
4.0 5 months ago
Anonymous completed this course.
The class was pretty tough, but it wasn't too bad. The video were okay, but the explanations could have been more thorough. Some of the practice problems for the quizzes were pretty hard compared to the examples done by the professor.
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Robert B
5.0 a month ago
Robert completed this course.
The lectures are clear and to the point. Better, the course comes with a very well done companion textbook. As a learner that prefers the written to the spoken word, the textbook is more important and useful than the lectures.
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Anonymous
5.0 4 months ago
Anonymous completed this course.
This course is a little hard for me since I never learned about this aspect things before. But it's ok. Professor gives so meaningful and understandable information to me. I learned so many things.
Was this review helpful to you? Yes
Anonymous
5.0 a month ago
Anonymous is taking this course right now.
i study agri-food engineering and i found this course very helpful while studying heat transfer and material transfer. i also have to ackowledge that professor Jeff Chasnof has a great pedagogy!

Was this review helpful to you? Yes
  • 1

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