This course is part of the Mathematics for Engineers Specialization

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stars
10 ratings

Jeffrey R. Chasnov

Top Instructor

1,623 already enrolled

Offered By

Mathematics for Engineers SpecializationThe Hong Kong University of Science and Technology

About this Course

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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.  
Before enrolling, students should have already taken courses in  matrix algebra, differential equations, vector calculus and numerical methods, and be able to program in  MATLAB.  

The course contains 22 short video lectures and a full set of lecture notes.  After each lecture,  there are problems to solve, and at the end of the second and third weeks, there is a substantial MATLAB programming assignment.

Download the lecture notes from the link
https://www.math.hkust.edu.hk/~machas/flow-around-a-cylinder.pdf

Watch the promotional video from the link
https://youtu.be/FlM1de9Sxh0

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Course 5 of 5 in the

Mathematics for Engineers Specialization

Intermediate Level

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

Approx. 9 hours to complete

English

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What you will learn

Computational Fluid Dynamics
Scientific Computing

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 5 of 5 in the

Mathematics for Engineers Specialization

Intermediate Level

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

Approx. 9 hours to complete

English

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Try Coursera for Business

Instructor

Instructor rating

5/5 (6 Ratings)

Jeffrey R. Chasnov
Top Instructor

Professor

Department of Mathematics

172,353 Learners

16 Courses

Offered by

The Hong Kong University of Science and Technology

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Syllabus - What you will learn from this course

Week1

Week 1

4 hours to complete

Governing Equations

We learn the governing equations for the flow around a cylinder. We discuss the Navier-Stokes equations and the continuity equation, and derive a pair of coupled equations for the stream function and scalar vorticity. We nondimensionalize these equations so that they contain only a single dimensionless parameter called the Reynolds number. We then simplify the nondimensional governing equations using log-polar coordinates.

4 hours to complete

10 videos (Total 67 min), 16 readings, 1 quiz

10 videos

16 readings

Welcome and Course Information2mMATLAB Online5mPlane Couette Flow10mChannel Flow10mPipe Flow10mVector Identities10mFlow Boundaries10mCurl of the Vorticity-Velocity Cross Product10mScalar Vorticity in Cartesian Coordinates10mScalar Vorticity Equation in Cartesian Coordinates10mStream Function in Cartesian Coordinates10mScalar Vorticity in terms of the Stream Function in Cartesian Coordinates10mStream Function as a Vector Potential10mStreamlines in Cartesian Coordinates10mStream Function Equation when Re = 010mSteady Flow Equations10m

1 practice exercise

Week One Assessment30m

Week2

Week 2

3 hours to complete

Steady Flows

3 hours to complete

8 videos (Total 63 min), 6 readings, 1 quiz

8 videos

6 readings

Even and Odd Functions5mSOR Equations10mVorticity Free-Stream Boundary Condition10mTest the Cylinder Boundary Condition10mStarting SOR with zero vorticity1mReference solution to "Steady Flow at Re = 10"1m

Week3

Week 3

3 hours to complete

Unsteady Flows

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. We show how to use a MATLAB ODE integrator to solve for the scalar vorticity. Students will write a MATLAB code to compute the time-dependent scalar vorticity at a Reynolds number of sixty.

3 hours to complete

9 videos (Total 50 min), 8 readings, 1 quiz

9 videos

Week Three Introduction 1mPeriodic Boundary Conditions | Lecture 166mFinite Difference Equations | Lecture 176mStream Function Computation | Lecture 187mStream Function Boundary Conditions | Lecture 199mVorticity Computation | Lecture 204mMATLAB Program (Unsteady) (Part A) | Lecture 218mMATLAB Program (Unsteady) (Part B) | Lecture 224mConcluding Remarks1m

8 readings

Ghost Points10mVorticity Finite Difference Equation15mMATLAB Coding of Right-Hand Side10mThree-by-Three Grid10mComputational Time10mReference Solution to "Unsteady Flow at Re = 60"1mPlease Rate this Course1mAcknowledgements

Reviews

4.9

5 reviews

5 stars
90%
4 stars
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TOP REVIEWS FROM MATHEMATICS FOR ENGINEERS: THE CAPSTONE COURSE

by BBSep 5, 2022

It is an excellent course, with some challenging assignments. I learned a lot from this course and would recommend it to anyone interested in fluid dynamics and with some coding knowledge.

by KLMay 5, 2022

I missed the path through the entire program, and wish you all good luck!

View all reviews

About the Mathematics for Engineers Specialization

This specialization was developed for engineering students to self-study engineering mathematics. We expect students to already be familiar with single variable calculus and computer programming. Through this specialization, students will learn matrix algebra, differential equations, vector calculus, numerical methods, and MATLAB programming. This will provide them with the tools to effectively apply mathematics to engineering problems and be well-equipped to pursue a degree in engineering. To get a better understanding of what this specialization has to offer, be sure to watch the Promotional Video!

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I subscribe to this Specialization?
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

More questions? Visit the Learner Help Center.

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Mathematics for Engineers: The Capstone Course

About this Course

What you will learn