Online Course
Differential Equations for Engineers
The Hong Kong University of Science and Technology via Coursera
- Provider Coursera
- Cost Free Online Course (Audit)
- Session In progress
- Language English
- Certificate Paid Certificate Available
- Effort 5 hours a week
- Duration 6 weeks long
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Overview
Class Central Tips
This course is about differential equations and covers material that all engineers should know. 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 is composed of 56 short lecture videos, with a few simple problems to solve following 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.
Lecture notes can be downloaded from
http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf
The course is composed of 56 short lecture videos, with a few simple problems to solve following 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.
Lecture notes can be downloaded from
http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf
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 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 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.
-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 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 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
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- #2 in Subjects / Engineering
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Reviews for Coursera's Differential Equations for Engineers Based on 40 reviews
- 5 stars 93%
- 4 stars 8%
- 3 star 0%
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Anonymous
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
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
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!
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
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.
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
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.
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.
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Anonymous
Anonymous
completed this course.
This course is very useful in my career. I am entering into an MFE program, and since I did not take PDE in my undergraduate, my program set this course as a prerequiste of PDE. This course is very interesting and easy understand. It took me 1 week to complete when I just concentrate on this course and set everything aside. Now I could take some advanced PDE application course in field of finance. Before this course, I really could not understand what is going on in terms like non-linear solver in my finance book. Great adventure!
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Anonymous
Anonymous
completed this course.
For something as abstract as ODEs and PDEs, this course has done a great job in connecting the math, equation solving skills, and the real world applications. I personally enjoyed every lecture video, practice quiz, and graded quiz.
The configuration of the course is very helpful. The introduction of the concepts/skilss, followed by a quick summary in the video, then a practice session before any actual quiz helped me strengthen the material I learnt.
Prof. Chasnov showed great passion about what he teaches!
The configuration of the course is very helpful. The introduction of the concepts/skilss, followed by a quick summary in the video, then a practice session before any actual quiz helped me strengthen the material I learnt.
Prof. Chasnov showed great passion about what he teaches!
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Anonymous
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
Anonymous
completed this course.
This course is an excellent introduction for anyone wants to study Diff Eq. It is clearly elaborated with exact practice problems. All the math techniques you need could be found in the appendix or supplemental videos. This course is highly recommended for any engineering student with a good command of physics as you need to deal with physical problems in the application part. (Though myself is an econ student)
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Anonymous
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.
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
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
Anonymous
completed this course.
I learned about the basic knowledge about the differential equation and the application of engineering, which are both useful for me to prepare my future study. I am not a student major in mathematics. However, the difficulty level of this course is suitable and I can keep learning. The professor always responses students' questions in time and offer valuable advice. Hope this course rank top!!
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Anonymous
Anonymous
completed this course.
In the beginning, this course is easy. After three weeks, the course becomes more challenging. The length of this course is appropriate. If you want to get the certificate as soon as possible, you will need to try your best to learn this course for several hours a day. Hope this course brings a good luck to me and helps me to get an admission of my dream school from the waitlist! See you.
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Anonymous
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
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
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
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
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.
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Anonymous
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!
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Anonymous
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.
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