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Jeffrey R. Chasnov
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.
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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.
Read more
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
Register for this course and see more details by visiting:
OpenCourser.com/course/6ss2e2/mathematics
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What's inside
Syllabus
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.
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Syllabus
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.
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Steady Flows
We formulate the computational fluid dynamics problem of the steady flow around a cylinder. We introduce the finite difference method and derive iteration equations. We derive boundary conditions and discuss the outline of a MATLAB program. Students will write a MATLAB code to compute the stream function at a Reynolds number of ten.
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.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Teaches computational fluid dynamics, a highly relevant skill in aerospace engineering
Builds a strong foundation in computational fluid dynamics for future research or work in this domain
Taught by Dr. Jeffrey R. Chasnov, a respected researcher in the field of computational fluid dynamics
Involves hands-on MATLAB programming assignments, providing practical experience
Assumes prior knowledge in matrix algebra, differential equations, vector calculus, and numerical methods, making it suitable for students with a strong mathematical background
Requires access to MATLAB online and the MATLAB grader, which may incur additional costs for some students
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Activities
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Review concepts in Multivariable Calculus, Differential Equations, and Linear Algebra
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Strengthen your understanding of the mathematical foundations necessary for the course.
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Multivariable Calculus
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Review relevant sections of your textbooks or class notes
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Practice solving problems related to the concepts being reviewed.
Organize lecture notes and assignment solutions
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Create a system for organizing notes and solutions.
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Review the organized materials regularly.
Review 'Fluid Dynamics' by M. Kumar.
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Read chapters 2 through 4
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Solve problems at the end of each chapter
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Follow MATLAB tutorials on solving governing equations for fluid flow
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Gain hands-on experience in MATLAB programming and how to utilize it to derive and solve fluid flow equations.
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MATLAB
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Find relevant MATLAB tutorials
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Follow the tutorials to solve governing equations for fluid flow
Network with professionals in the field of computational fluid dynamics
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Build connections with professionals in the field, gain insights into industry practices, and explore potential career opportunities.
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Attend the events and engage with professionals
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Gain exposure to advanced concepts and techniques in computational fluid dynamics through expert-led workshops.
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Identify relevant computational fluid dynamics workshops
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Register and attend the workshop
Create a computational model of a 2D fluid flow
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Integrate knowledge of governing equations, finite difference method, and matrix methods to create a computational model of a 2D fluid flow.
Browse courses on
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Plan the model geometry and boundary conditions
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Derive the governing equations for the model
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Discretize the governing equations using the finite difference method
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Solve the discretized equations using a matrix method
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Visualize the results of the simulation
Design and implement a computational model to simulate fluid flow
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Combine knowledge of computational fluid dynamics, finite difference method, and matrix methods to build a project that simulates fluid flow.
Browse courses on
Computational Fluid Dynamics
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Plan the project scope and design
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Develop the computational model
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Implement the model in MATLAB or another programming language
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Validate and refine the model
-
Write a report summarizing the project
Review concepts in Multivariable Calculus, Differential Equations, and Linear Algebra
Show steps
Strengthen your understanding of the mathematical foundations necessary for the course.
Browse courses on
Multivariable Calculus
Show steps
Show steps
Show steps
- Review relevant sections of your textbooks or class notes
- Practice solving problems related to the concepts being reviewed.
Organize lecture notes and assignment solutions
Show steps
Gain a better understanding of the course material by organizing and reviewing lecture notes and assignment solutions.
Show steps
Show steps
Show steps
- Create a system for organizing notes and solutions.
- Review the organized materials regularly.
Review 'Fluid Dynamics' by M. Kumar.
Show steps
Get a general overview of fluid dynamics including the concept of viscosity, pressure, and drag force.
View
Mathematical Modeling and Simulation:...
on Amazon
Show steps
Show steps
Show steps
- Read chapters 2 through 4
- Solve problems at the end of each chapter
Five other activities
Expand to see all activities and additional details
Show all eight activities
Follow MATLAB tutorials on solving governing equations for fluid flow
Show steps
Gain hands-on experience in MATLAB programming and how to utilize it to derive and solve fluid flow equations.
Browse courses on
MATLAB
Show steps
Show steps
Show steps
- Find relevant MATLAB tutorials
- Follow the tutorials to solve governing equations for fluid flow
Network with professionals in the field of computational fluid dynamics
Show steps
Build connections with professionals in the field, gain insights into industry practices, and explore potential career opportunities.
Browse courses on
Computational Fluid Dynamics
Show steps
Show steps
Show steps
- Attend the events and engage with professionals
- Identify relevant networking events
Attend a computational fluid dynamics workshop
Show steps
Gain exposure to advanced concepts and techniques in computational fluid dynamics through expert-led workshops.
Browse courses on
Computational Fluid Dynamics
Show steps
Show steps
Show steps
- Identify relevant computational fluid dynamics workshops
- Register and attend the workshop
Create a computational model of a 2D fluid flow
Show steps
Integrate knowledge of governing equations, finite difference method, and matrix methods to create a computational model of a 2D fluid flow.
Browse courses on
Computational Fluid Dynamics
Show steps
Show steps
Show steps
- Plan the model geometry and boundary conditions
- Derive the governing equations for the model
- Discretize the governing equations using the finite difference method
- Solve the discretized equations using a matrix method
- Visualize the results of the simulation
Design and implement a computational model to simulate fluid flow
Show steps
Combine knowledge of computational fluid dynamics, finite difference method, and matrix methods to build a project that simulates fluid flow.
Browse courses on
Computational Fluid Dynamics
Show steps
Show steps
Show steps
- Plan the project scope and design
- Develop the computational model
- Implement the model in MATLAB or another programming language
- Validate and refine the model
- Write a report summarizing the project
Career center
Learners who complete Mathematics for Engineers: The Capstone Course will develop knowledge and skills
that may be useful to these careers:
Computational Fluid Dynamics Engineer
Computational Fluid Dynamics Engineer
Computational Fluid Dynamics Engineers use computers to simulate and analyze the flow of fluids. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course would be particularly helpful for Computational Fluid Dynamics Engineers who want to develop or use computational fluid dynamics models to solve real-world problems.
Aerospace Engineer
Aerospace Engineer
Aerospace Engineers design, develop, test, and operate aircraft, spacecraft, and related systems. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which is essential for understanding and predicting the flow of fluids around aircraft and spacecraft. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course would be particularly helpful for Aerospace Engineers who want to develop or use computational fluid dynamics models to design or analyze aircraft or spacecraft.
Mechanical Engineer
Mechanical Engineer
Mechanical Engineers design, develop, test, and operate mechanical systems, such as engines, turbines, and robots. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which is essential for understanding and predicting the flow of fluids around mechanical systems. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course would be particularly helpful for Mechanical Engineers who want to develop or use computational fluid dynamics models to design or analyze mechanical systems.
Civil Engineer
Civil Engineer
Civil Engineers design, build, and maintain infrastructure, such as bridges, buildings, and roads. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which is essential for understanding and predicting the flow of fluids around civil engineering structures. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course would be particularly helpful for Civil Engineers who want to develop or use computational fluid dynamics models to design or analyze civil engineering structures.
Chemical Engineer
Chemical Engineer
Chemical Engineers design, develop, and operate chemical plants and processes. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which is essential for understanding and predicting the flow of fluids in chemical plants and processes. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course would be particularly helpful for Chemical Engineers who want to develop or use computational fluid dynamics models to design or analyze chemical plants and processes.
Petroleum Engineer
Petroleum Engineer
Petroleum Engineers design, develop, and operate oil and gas wells. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which is essential for understanding and predicting the flow of fluids in oil and gas wells. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course would be particularly helpful for Petroleum Engineers who want to develop or use computational fluid dynamics models to design or analyze oil and gas wells.
Nuclear Engineer
Nuclear Engineer
Nuclear Engineers design, develop, and operate nuclear power plants and other nuclear facilities. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which is essential for understanding and predicting the flow of fluids in nuclear power plants and other nuclear facilities. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course would be particularly helpful for Nuclear Engineers who want to develop or use computational fluid dynamics models to design or analyze nuclear power plants and other nuclear facilities.
Materials Scientist
Materials Scientist
Materials Scientists research and develop new materials and improve existing materials. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which is essential for understanding and predicting the flow of fluids through materials. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course may be helpful for Materials Scientists who want to develop or use computational fluid dynamics models to research or develop new materials.
Bioengineer
Bioengineer
Bioengineers design, develop, and operate medical devices and other biological systems. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which is essential for understanding and predicting the flow of fluids in biological systems. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course may be helpful for Bioengineers who want to develop or use computational fluid dynamics models to design or analyze medical devices or other biological systems.
Environmental Engineer
Environmental Engineer
Environmental Engineers design, develop, and operate systems to protect the environment. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which is essential for understanding and predicting the flow of fluids in the environment. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course may be helpful for Environmental Engineers who want to develop or use computational fluid dynamics models to design or analyze environmental systems.
Data Scientist
Data Scientist
Data Scientists collect, analyze, and interpret data to solve real-world problems. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which can be used to solve a variety of real-world problems. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course may be helpful for Data Scientists who want to use computational fluid dynamics to solve real-world problems.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software applications. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which can be used to develop software applications for a variety of industries. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course may be helpful for Software Engineers who want to use computational fluid dynamics to develop software applications.
Financial Analyst
Financial Analyst
Financial Analysts provide investment advice to individuals and organizations. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which can be used to analyze financial data. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course may be helpful for Financial Analysts who want to use computational fluid dynamics to analyze financial data.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical techniques to solve problems in a variety of industries. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which can be used to solve a variety of problems in operations research. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course may be helpful for Operations Research Analysts who want to use computational fluid dynamics to solve problems in operations research.
Actuary
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty. This course provides a strong foundation in the governing equations and numerical methods used in computational fluid dynamics, which can be used to assess risk and uncertainty in a variety of industries. It also provides hands-on experience with MATLAB, which is a widely-used software package for computational fluid dynamics. This course may be helpful for Actuaries who want to use computational fluid dynamics to assess risk and uncertainty.
For more career information including salaries, visit:
OpenCourser.com/course/6ss2e2/mathematics
Reading list
We've selected nine books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Mathematics for Engineers: The Capstone Course.
This comprehensive textbook provides a detailed introduction to the fundamental principles of computational fluid dynamics. It covers a wide range of topics, from the basics of fluid mechanics to advanced numerical methods. valuable resource for students and practitioners of CFD.
Provides a clear and concise introduction to the finite volume method for solving fluid dynamics problems. It valuable resource for students and practitioners of CFD.
Provides a comprehensive introduction to viscous fluid flow. It covers a wide range of topics, from the basics of fluid mechanics to advanced topics such as boundary layer theory. This book valuable resource for students and practitioners of fluid mechanics.
Save
This textbook provides a clear and concise introduction to fluid mechanics. It valuable resource for students and practitioners of fluid mechanics.
This textbook provides a comprehensive introduction to fluid mechanics. It valuable resource for students and practitioners of fluid mechanics.
This textbook provides a clear and concise introduction to fluid dynamics. It valuable resource for students and practitioners of fluid mechanics.
Save
This textbook provides a comprehensive introduction to fluid dynamics. It valuable resource for students and practitioners of fluid mechanics.
This textbook provides a clear and concise introduction to computational fluid dynamics. It valuable resource for students and practitioners of CFD.
This textbook provides a comprehensive introduction to fluid dynamics. It valuable resource for students and practitioners of fluid mechanics.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/6ss2e2/mathematics
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Effort
3 weeks of study, 8 hours/week
Level
Intermediate
Via
Coursera
Institution
The Hong Kong University of Science and Technology
Instructor
Jeffrey R. Chasnov
Language
English
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This course belongs to a
collection
called
Mathematics for Engineers. It's comprised of five courses:
- Matrix Algebra for Engineers
- Mathematics for Engineers: The Capstone Course (viewing)
- Differential Equations for Engineers
- Vector Calculus for Engineers
- Numerical Methods for Engineers
Good to know
Teaches computational fluid dynamics, a highly relevant skill in aerospace engineering
Builds a strong foundation in computational fluid dynamics for future research or work in this domain
Taught by Dr. Jeffrey R. Chasnov, a respected researcher in the field of computational fluid dynamics
Involves hands-on MATLAB programming assignments, providing practical experience
Assumes prior knowledge in matrix algebra, differential equations, vector calculus, and numerical methods, making it suitable for students with a strong mathematical background
Requires access to MATLAB online and the MATLAB grader, which may incur additional costs for some students
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