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.

## About this Course

Knowledge of single variable calculus.

### Skills you will gain

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**

**15 videos**

**12 readings**

**6 practice exercises**

**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**

**11 videos**

**11 readings**

**3 practice exercises**

**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**

**12 videos**

**9 readings**

**4 practice exercises**

**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**

**11 videos**

**10 readings**

**4 practice exercises**

## Reviews

### TOP REVIEWS FROM DIFFERENTIAL EQUATIONS FOR ENGINEERS

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!

Very good course if you want to start using differential equations without any rigorous details. Thanks to professor`s explanation everything is very clear. Good basis to continue to dive deeper.

Best course. have explained the theoratical and practical aspects of differential equations and at the same time covered a substantial chunk of the subject in a very easy and didactic manner.

I think this course is very suitable for any curious mind. You can learn very important and necessary concepts with this course. The courses taught by Professor Dr. Chasnov are excellent.

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