Numerical Methods for Engineers from Coursera

This course covers the most important numerical methods that an engineer should know, including root finding, matrix algebra, integration and interpolation, ordinary and partial differential equations. We learn how to use MATLAB to solve numerical problems, and access to MATLAB online and the MATLAB grader is given to all students who enroll.

We assume students are already familiar with the basics of matrix algebra, differential equations, and vector calculus. They should have a working knowledge of a programming language, and be willing to learn MATLAB.

The course contains 74 short lecture videos and MATLAB demonstrations. After each lecture or demonstration, there are problems to solve or programs to write. The course is organized into six weeks, and at the end of each week, there is an assessed quiz and a longer programming project.

Download the lecture notes from the link

https://www.math.hkust.edu.hk/~machas/numerical-methods-for-engineers.pdf

And watch the promotional video from the link

https://youtu.be/qFJGMBDfFMY

What's inside

Syllabus

Scientific Computing

MATLAB is a high-level programming language extensively utilized by engineers for numerical computation and visualization. We will learn the basics of MATLAB: how real numbers are represented in double precision; how to perform arithmetic with MATLAB; how to use scripts and functions; how to represent vectors and matrices; how to draw line plots; and how to use logical variables, conditional statements, for loops and while loops. For your programming project, you will write a MATLAB code to compute the bifurcation diagram for the logistic map.

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what should give you pause

and possible dealbreakers

Teaches core scientific computing tools and foundations

Develops critical engineering numerical analysis skills

Arms learners with the coding skills to solve engineering problems

Taught by an instructor recognized for their work in computational fluid dynamics

Develops a strong foundation for learners with little to no technical background

Requires students have basic proficiency in matrix algebra, differential equations, and vector calculus

Reviews summary

Practical numerical methods with matlab

According to students, this course provides a well-structured and comprehensive introduction to numerical methods, with a particular strength in its practical application. Learners consistently praise the clear and engaging instructor and the effective integration of MATLAB through numerous hands-on demonstrations and programming projects. These projects are frequently cited as challenging yet immensely rewarding, significantly reinforcing theoretical concepts. While many find the pacing just right, some learners with less extensive mathematical backgrounds advise that a strong prior understanding of core math concepts is beneficial, as certain topics can be quite fast-paced or brief. The downloadable lecture notes are a highly valuable companion.

Downloadable notes are an excellent and helpful resource.

"I found the lecture notes downloadable from the link to be an excellent companion."

"The lecture notes linked were a lifesaver."

"The downloadable lecture notes are a huge plus."

Programming projects are demanding but highly rewarding.

"The programming projects, especially the Lorenz equations and Bessel function problems, were challenging yet immensely rewarding."

"The final programming projects were definitely the highlight, forcing deep engagement with the material."

"The weekly projects were challenging but incredibly valuable."

"The projects were very demanding, and I felt I needed more guidance to complete them successfully."

Instructor explains complex topics clearly and concisely.

"This course is incredibly well-structured and the lectures are clear and concise."

"The instructor does a great job explaining difficult concepts."

"Instructor's teaching style is clear and engaging."

Excellent hands-on application through demos and projects.

"The integration of MATLAB is superb, making complex numerical methods accessible through practical examples."

"The MATLAB demos were super helpful, and I learned a lot about how to apply these methods in a practical setting."

"The hands-on MATLAB projects were the best part and really helped me understand the practical implementation."

"The way MATLAB was integrated made everything click."

Some topics in lecture videos felt too brief.

"I sometimes found the lecture videos a bit too brief, especially for the more advanced topics like PDEs."

"The lectures felt rushed and I struggled to follow along without constantly pausing and re-reading."

Requires a strong mathematical background, can be fast-paced.

"The assumed prerequisites felt a bit understated; you really need a strong math background."

"I struggled to follow along without constantly pausing and re-reading. The level of assumed prior knowledge seemed higher than advertised..."

"I agree with others that a stronger mathematical background is beneficial, as the pace can be quick in some areas."

"While the MATLAB demos were somewhat useful, the lectures felt rushed and I struggled to follow along..."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Numerical Methods for Engineers with these activities:

Join a study group for the course

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Collaborate with fellow students, discuss the course material, and work on assignments together to enhance understanding.

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Reach out to classmates and form a study group.
Set regular meeting times and stick to them.
Take turns leading discussions and presenting concepts.

Compile a collection of MATLAB resources

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Gather and organize useful MATLAB resources such as tutorials, documentation, and code snippets for easy reference and future use.

Browse courses on MATLAB

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Search for resources online.
Bookmark or download relevant materials.
Create a central repository, such as a folder or online document.

Explore MATLAB documentation and online resources

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Familiarize yourself with the MATLAB environment and its capabilities by exploring the official documentation and searching for helpful tutorials on the web.

Browse courses on MATLAB

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Read the MATLAB documentation on relevant topics.
Search for tutorials on topics you encounter while working on course assignments or projects.

Four other activities

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Attend a MATLAB workshop or webinar

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Engage with experts and learn from practical demonstrations and hands-on activities in a MATLAB workshop or webinar.

Browse courses on MATLAB

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Check for upcoming MATLAB workshops or webinars.
Register and attend the event.
Participate actively and ask questions for clarification.

Solve MATLAB programming problems

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Practice MATLAB programming skills by solving problems and completing drills to build proficiency.

Browse courses on MATLAB

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Find online MATLAB exercises or tutorials.
Work through the problems, debugging and refining code as needed.

Build a MATLAB function for root finding

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Develop a deeper understanding of root finding by creating a custom MATLAB function that implements one of the root-finding methods covered in the course.

Browse courses on MATLAB

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Review the theory and implementation of the chosen method.
Write the MATLAB code for the function.
Test the function with various inputs and compare results to expected values.

Write a MATLAB script to solve a system of nonlinear differential equations using Newton's method

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Apply the concepts learned in class to a practical problem by creating a MATLAB script that solves a system of nonlinear differential equations using Newton's method.

Browse courses on MATLAB

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Formulate the system of equations.
Implement Newton's method in MATLAB.
Write a script that combines the system of equations and the Newton's method implementation.
Test the script with various initial conditions.
Plot the solutions and analyze the results.

Career center

Learners who complete Numerical Methods for Engineers will develop knowledge and skills that may be useful to these careers:

Data Scientist

Learn the most important numerical methods that an engineer should know, such as root finding, matrix algebra, integration and interpolation, and ordinary and partial differential equations.

See salaries and explore the career path for Data Scientist

Data Analyst

Learn how to use MATLAB to solve numerical problems.

See salaries and explore the career path for Data Analyst

Software Engineer

Learn the basics of MATLAB, including how real numbers are represented in double precision and how to represent vectors and matrices.

See salaries and explore the career path for Software Engineer

Financial Analyst

Learn how to compute definite integrals using quadrature and how to interpolate function values at intermediate sample points.

See salaries and explore the career path for Financial Analyst

Actuary

Learn how to solve systems of nonlinear differential equations using Newton's method.