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Mathematics for Engineers: The Capstone Course
  • Level Professional
  • Duration 10 hours
  • Course by The Hong Kong University of Science and Technology
  • Offered by

About

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

Modules

Welcome to Mathematics for Engineers: The Capstone Course

    • 1 Videos
    • 2 Readings
    • 1 Plugin
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1 Videos

  • Course Overview

2 Readings

  • Welcome and Course Information
  • MATLAB Online

Introduction to Week One

    • 1 Videos
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1 Videos

  • Week One Introduction

Governing Equations

    • 2 Videos
    • 4 Readings
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2 Videos

  • Navier-Stokes Equations | Lecture 1
  • Vorticity Equation | Lecture 2

4 Readings

  • Plane Couette Flow
  • Channel Flow
  • Pipe Flow
  • Vector Identities

Flow Geometry

    • 4 Videos
    • 8 Readings
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4 Videos

  • Geometry of the Flow | Lecture 3
  • Two-dimensional Flow | Lecture 4
  • Stream Function | Lecture 5
  • Streamlines | Lecture 6

8 Readings

  • Flow Boundaries
  • Curl of the Vorticity-Velocity Cross Product
  • Scalar Vorticity in Cartesian Coordinates
  • Scalar Vorticity Equation in Cartesian Coordinates
  • Stream Function in Cartesian Coordinates
  • Scalar Vorticity in terms of the Stream Function in Cartesian Coordinates
  • Stream Function as a Vector Potential
  • Streamlines in Cartesian Coordinates

Nondimensionalization and Coordinates

    • 2 Videos
    • 2 Readings
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2 Videos

  • Reynolds Number | Lecture 7
  • Log-polar Coordinates | Lecture 8

2 Readings

  • Stream Function Equation when Re = 0
  • Steady Flow Equations

Quiz

    • 1 Assignment
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1 Assignment

  • Week One Assessment

Introduction to Week Two

    • 1 Videos
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1 Videos

  • Week Two Introduction

Iterative Method

    • 2 Videos
    • 2 Readings
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2 Videos

  • Finite Difference Method | Lecture 9
  • Iteration Equations | Lecture 10

2 Readings

  • Even and Odd Functions
  • SOR Equations

Boundary Conditions

    • 3 Videos
    • 3 Readings
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3 Videos

  • Free-stream Boundary Conditions | Lecture 11
  • Cylinder Boundary Conditions | Lecture 12
  • Summary of the Boundary Conditions | Lecture 13

3 Readings

  • Vorticity Free-Stream Boundary Condition
  • Test the Cylinder Boundary Condition
  • Starting SOR with zero vorticity

Programming Assignment: Steady Flow at Re = 10

    • 2 Videos
    • 1 Readings
    • 1 ExternalTool
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1 External Tool

  • Steady Flow at Re = 10

2 Videos

  • MATLAB Program (Steady) (Part A) | Lecture 14
  • MATLAB Program (Steady) (Part B) | Lecture 15

1 Readings

  • Reference solution to "Steady Flow at Re = 10"

Introduction to Week Three

    • 1 Videos
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1 Videos

  • Week Three Introduction

Difference Equations

    • 5 Videos
    • 5 Readings
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5 Videos

  • Periodic Boundary Conditions | Lecture 16
  • Finite Difference Equations | Lecture 17
  • Stream Function Computation | Lecture 18
  • Stream Function Boundary Conditions | Lecture 19
  • Vorticity Computation | Lecture 20

5 Readings

  • Ghost Points
  • Vorticity Finite Difference Equation
  • MATLAB Coding of Right-Hand Side
  • Three-by-Three Grid
  • Computational Time

Programming Assignment: Unsteady Flow at Re = 60

    • 2 Videos
    • 1 Readings
    • 1 ExternalTool
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1 External Tool

  • Unsteady Flow at Re = 60

2 Videos

  • MATLAB Program (Unsteady) (Part A) | Lecture 21
  • MATLAB Program (Unsteady) (Part B) | Lecture 22

1 Readings

  • Reference Solution to "Unsteady Flow at Re = 60"

Farewell

    • 1 Videos
    • 2 Readings
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1 Videos

  • Concluding Remarks

2 Readings

  • Please Rate this Course
  • Acknowledgements

Auto Summary

"Mathematics for Engineers: The Capstone Course" is an advanced professional course by Coursera, focusing on computational fluid dynamics. Ideal for those with a background in matrix algebra, differential equations, vector calculus, and MATLAB programming, this course offers 22 video lectures, detailed notes, and practical assignments. With a duration of 600 minutes, it provides comprehensive access to MATLAB tools, culminating in a capstone project on fluid flow around a cylinder.

Jeffrey R. Chasnov
Instructor

Jeffrey R. Chasnov