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# Differential Equations for Engineers

12 Reviews 66 students interested
Found in
• 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

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## Overview

#### Class Central Tips

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.

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

## Reviews for Coursera's Differential Equations for Engineers 4.8 Based on 12 reviews

• 5 stars 83%
• 4 stars 17%
• 3 star 0%
• 2 star 0%
• 1 star 0%

Did you take this course? Share your experience with other students.

• 1
Anonymous
5.0 2 months ago
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
5.0 5 months ago
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
5.0 2 months ago
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.
Anonymous
5.0 2 weeks ago
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.
Gaetano P
5.0 5 months ago
by 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.
Anonymous
5.0 4 months ago
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.
Anonymous
4.0 3 months ago
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.
Anonymous
5.0 2 months ago
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.
Michael O
5.0 5 months ago
completed this course.
This is a very good course, well structured and well explained. It requires a lot of work from the student and it is essential that you work out all the problems and quizzes along the way.
Anonymous
4.0 2 months ago
completed this course.
This course is very useful to implement the applications of differential and difference equations. Its very to useful to understand through lecture videos. Thank you .
Anonymous
5.0 2 months ago
completed this course.
Thanks for explaining every concept with applications in detailed manner. All concepts are clear because os so many applications in every topic what have discussed.
Anonymous
5.0 3 weeks ago
completed this course.
This is a very interesting and useful course. I've learned a lot about differential equations and I really enjoyed the process.