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.

This course is part of the Mathematics for Engineers Specialization

**51,118**already enrolled

Offered By

## About this Course

Knowledge of single variable calculus.

### What you will learn

First-order differential equations

Second-order differential equations

The Laplace transform and series solution methods

Systems of differential equations and partial differential equations

Knowledge of single variable calculus.

## Offered by

### The Hong Kong University of Science and Technology

HKUST - A dynamic, international research university, in relentless pursuit of excellence, leading the advance of science and technology, and educating the new generation of front-runners for Asia and the world.

## Syllabus - What you will learn from this course

**5 hours to complete**

## 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.

**5 hours to complete**

**4 hours to complete**

## 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.

**4 hours to complete**

**5 hours to complete**

## 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.

**5 hours to complete**

**4 hours to complete**

## 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.

**4 hours to complete**

## Reviews

- 5 stars88.66%
- 4 stars9.74%
- 3 stars1.20%
- 2 stars0.05%
- 1 star0.32%

### TOP REVIEWS FROM DIFFERENTIAL EQUATIONS FOR ENGINEERS

I don't have a math or engineering background but this course has a great balance of simplicity and challenging problems that I can confidently take to higher level mathematics

The course materials are well prepared and organised. The teaching style is approachable and clear. I have learned a lot from this course. Thank you so much, and wish you all the best Prof. Chasnov!

Excellent course taught by an excellent professor, Dr. Chasnov. Just the right content, just the right pace and practice problems and quiz complemented the course material very well.

The instructor and materials were excellent. The quizzes at the end of each section were non-trivial and it's a great course to jumpstart your ability to work with ODEs and PDEs.

## About the Mathematics for Engineers Specialization

This specialization was developed for engineering students to self-study engineering mathematics. We expect students are already familiar with single variable calculus and computer programming. Students will learn matrix algebra, differential equations, vector calculus and numerical methods. MATLAB programming will be taught. Watch the promotional video!

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