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Online Course

Differential Equations for Engineers

The Hong Kong University of Science and Technology via Coursera

Overview

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

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

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Reviews

4.9 rating, based on 205 reviews

Start your review of Differential Equations for Engineers

  • 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

    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

    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.
  • Anonymous

    Anonymous completed this course.

    It is a good course to learn different techniques to solve a variety of differential equations. 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. If it is your first time at differential equations after high school, I will definitely recommend it.
  • 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.
  • Anonymous

    Anonymous completed this course.

    This course is modeled nicely and taught effectively making more interested. In each video Reviewing that topic covered was more attracted me. I have learnt many things from this course. Modelling using Heaviside was more interesting. SIR model given on CORONA was very interesting make us to thing on the current pandemic . Overall it was very nice and informative Learning .
  • Anonymous

    Anonymous completed this course.

    The course throws light on the applications of ODE which is not often discussed in class for students. 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

    Anonymous completed this course.

    Excellent course. Practice quize at the end of each session helps a lot to attempt the final quiz. Supplementary video’s are also useful. Prof. Jeffery R Chasnov’s explanation, everything is very clear.
  • Anonymous
    Mr. Jeffrey Chasnoff made an excelent course and use as exaples comon engeneering

    problems; The quality of the slides and excercices are very good; Tank Cousera an Mr.

    Chasnoff for what you did.
  • Anonymous

    Anonymous completed this course.

    Excellent Course Teacher. Thank you Sir
    Excellent Course Teacher. Thank you Sir
    Excellent Course Teacher. Thank you Sir
    Excellent Course Teacher. Thank you Sir
  • 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...
  • Anonymous

    Anonymous completed this course.

    Good course for beigners, but it didn't contain every-thing which was in my syllabus for differential equations. The modelling of Differential equations and how to solve them is perfectly explained. But it doesn't includes Exact Linear Differential Equations,...
  • Anonymous

    Anonymous completed this course.

    This is an amazing course indeed. The Professor was so amicable and taught nicely. Last week was little bit difficult to me but I overcame the situation. Through the course, I came to know a lot of new things like laplace transform, dirac delta function, solving process of heaviside step function, system of differential equations solving method using matrix algebra, fourier series etc. Which of them was not taught by our teachers during ODE course. In the lecture videos, writing on the transparent screen attracted me most. The lecture note pdf was well arranged. Practise quiz and graded quiz made worth of learning.
    Heartiest thanks to Professor for making this course wonderful. Finally, it was a remarkable course on Coursera.
  • Anonymous
    This course is very well designed, and it is very well complemented by the teaching style of Prof. Jeffrey Chasnov. It is perfect for beginners as well as those who have studied these concepts long back and want to brush up their knowledge of differential equations. This course not only explains the analytical methods to solve some standard form of differential equations but also discuss the numerical methods approach as well as geometric interpretation of the differential equations as well. Anyone can use this course to get an easy idea about the differential equations and can easily follow the slightly advanced level books like "Ordinary and Partial Differential Equations" by M. D. Raisinghania, etc.
  • 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!
  • 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.
  • Anonymous

    Anonymous completed this course.

    Illuminatin introductory course, well-structured, with sufficient detail and illustrative examples, however, it could be challenging as it presumes a lot of background knowledge on the part of the student and I often had to look up certain topics on brilliant and khan academy. The fourier series part on solving partial differential equations could use a little more explanation and more detailed examples, futhermore, reading materials could a little more detailed in the derivation of equations, as explanations often skip logical steps that the author presumes the students understand. Full derivation would be a lot clearer and wouldn't add time to the videos.
  • Arun Kumar Chatterjee
    I am very impressed,and I have learnt a lot from this course. Particularly the solution to a system of equations by Matrix method involving eigen values and eigen vectors was something absolutely new to me. I had learnt how to find the inverse of a 3 by 3 matrix by using the Cayley- Hamilton theorem.

    It would be very unfair if I did not mention about the very cool approach of Prof. Jeff Chasnov,our Course Professor. The consciously student friendly approach is highly appreciated. And his meticulous efforts to summarise each lecture at the end is commendable. I am a teacher myself and I have learnt how to be cool and soft spoken. Goodluck Professor Chasnov!
  • 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.

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