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The Hong Kong University of Science and Technology

Differential Equations for Engineers

The Hong Kong University of Science and Technology via Coursera

Overview

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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

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

Reviews

4.9 rating, based on 317 Class Central reviews

4.9 rating at Coursera based on 2023 ratings

Start your review of Differential Equations for Engineers

  • Anonymous
    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.
  • 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.
  • 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.
  • 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.
  • Anonymous
    "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.
  • Anonymous
    Really good review of differential equations which I took in college. I haven't used most of this math for a long time and had to do some refreshers on items; however, Jeff teaches in a good manner and the reviews/problems/quizzes are excellent to help learn the topic.
  • Anonymous
    Even if you have already had this class at college, I think this course is a must if you didn't understand some of the topics, it is all explained really well, the book they provide is of great help if you get stuck at something.
  • Anonymous
    The course was very helpful for me, because it contains all material which I need to study. Explanations of the lecturer is clear and easy to understand. Thank you for a such valuable knowledge on differential equations course
  • Anonymous
    The course was very helpful for me, because it contains all material which I need to study. Explanations of the lecturer is clear and easy to understand. Thank you for a such valuable knowledge on differential equations course
  • 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 equat…
  • Anonymous
    VERY INFORMATIVE COURSE AND THE TEACHER IS EXCELLENT

    GET TO KNOW WIDER APPLICATIONS OF DIFFERENTAL EQUATIONS AND PARTIAL DIFFERENTIAL EQUATIONS AND LEARN MODELLING DIFFERENTIAL EQUATIONS IN DIFFERENT SITUATIONS
  • Anonymous
    This course was very interesting. I could remember and learn some new methods about the resolutions for differential equations for engineers. Thanks for "Coursera" for the opportunity.
  • Anonymous
    The course covers basic to advanced topics on differential equations. I thoroughly enjoyed the course, and I'd recommend this course to anyone who's interest in the subject.
  • Anonymous
    A very informative course. I studied Linear Algebra and ODEs in second semester and as my interview days are near I took this course and am not regretting it a bit.
  • Anonymous
    This course helps in understanding how to approach solving various problems of physics by modeling into mathematical equtions and solving them.
  • Anonymous
    A well-structured course that introduces the concepts of differential equations with a focus on applications to engineering problems.
  • Anonymous
    Chasnov is an excellent instructor with extra interesting details and applications of the theory. Totally recommend it.
  • Anonymous
    Really understandable and easy to learn the concepts and it was an awesome experience to bea part of this course
  • Anonymous
    I had some knowledge of Integrals and Derivatives but the content of this course was completely new to me and so, I have learnt a lot. Everything is very well explained. At the end, the last week was a bit difficult because it's a lot of information to remember and to review. I fully recommend this course and I give it five stars. A big "thanks you" to the excellent teacher. Now, I need some rest before going to the next course.
  • Anavheoba Abraham Ogenakohgie
    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 apprecia…
  • Anonymous
    This is an amazing course, I've discovered maths is fun especially if its taught well, I found the instructor to be amazing and even though I struggled in the latter part of the course his style of teaching was extremely engaging. I'll be looking at other course taught by this instructor as I continue on my maths journey

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