Mathematics for Engineers: The Capstone Course provides a capstone project for students who are completing the Mathematics for Engineers specialization. Students will first learn some basic concepts in computational fluid dynamics, and then apply these concepts to compute the fluid flow around a cylinder. Access to MATLAB online and the MATLAB grader is given to all students who enroll.

Offered By

## About this Course

Knowledge of matrix algebra, differential equations, vector calculus, numerical methods and the MATLAB programming language

### What you will learn

Computational Fluid Dynamics

Scientific Computing

Knowledge of matrix algebra, differential equations, vector calculus, numerical methods and the MATLAB programming language

## 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

**4 hours to complete**

## Governing Equations

This week we learn the governing equations for the flow around a cylinder. We begin with the Navier-Stokes equations and the continuity equation, and derive a pair of coupled equations for the stream function and scalar vorticity. These equations are nondimensionalized and contain only a single dimensionless parameter called the Reynolds number. The governing equations are then simplified using log-polar coordinates.

**4 hours to complete**

**3 hours to complete**

## Steady Flows

In this week, we formulate the computational fluid dynamics problem of the steady flow around a cylinder. We introduce the finite difference method and derive iteration equations. Boundary conditions are derived and the outline of a MATLAB program is discussed. Students will write a program to compute the stream function at a Reynolds number of ten.

**3 hours to complete**

**3 hours to complete**

## Unsteady Flows

In this week, we formulate the computational fluid dynamics problem of the unsteady flow around a cylinder. We introduce periodic boundary conditions in the polar angle and show how to solve for the stream function using matrix methods. The solution for the scalar vorticity will use a MATLAB ode integrator. Students will write code to compute the time-dependent scalar vorticity at a Reynolds number of sixty.

**3 hours to complete**

## 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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