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Back to Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python

Learner Reviews & Feedback for Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python by Ludwig-Maximilians-Universität München (LMU)

4.7
stars
351 ratings

About the Course

Interested in learning how to solve partial differential equations with numerical methods and how to turn them into python codes? This course provides you with a basic introduction how to apply methods like the finite-difference method, the pseudospectral method, the linear and spectral element method to the 1D (or 2D) scalar wave equation. The mathematical derivation of the computational algorithm is accompanied by python codes embedded in Jupyter notebooks. In a unique setup you can see how the mathematical equations are transformed to a computer code and the results visualized. The emphasis is on illustrating the fundamental mathematical ingredients of the various numerical methods (e.g., Taylor series, Fourier series, differentiation, function interpolation, numerical integration) and how they compare. You will be provided with strategies how to ensure your solutions are correct, for example benchmarking with analytical solutions or convergence tests. The mathematical aspects are complemented by a basic introduction to wave physics, discretization, meshes, parallel programming, computing models. The course targets anyone who aims at developing or using numerical methods applied to partial differential equations and is seeking a practical introduction at a basic level. The methodologies discussed are widely used in natural sciences, engineering, as well as economics and other fields....

Top reviews

EL

Dec 20, 2021

Would have like more "empty" cells in notebooks for trying to establish loop one self and then having a "correct" output to aim for. Maybe followed by a solution cell with a correct implementation.

MF

Nov 26, 2019

A fascinating teaching technique, delivering quality content with a well-thought quizzes system! It' hard to find better courses in the domain of Finite Difference and Spectral Element methods

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26 - 50 of 128 Reviews for Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python

By Luben C G

Jan 7, 2023

This is an excellent course. Many important concepts of four important numerical methods (finite difference, spectral, finite element, and spectral element) are fully explained and worked out for leading with hyperbolic partial differential equations, and others. The Python programs are very interesting and can be used for solving other problems and understanding the presented material.

By afaq a

Jul 7, 2023

One of the plus point of this course is the exhaustiveness of codding examples, which allow students to explore the simulation from both mathematical and physical standpoint. The lectures, though concince and clear, but apparently lacked some depth. This, however, I believe is amply compensated by the coding examples provided. Overall, it is a well-organized and delivered course.

By Phillip Y

Jul 13, 2019

Incredibly good jupyter notebooks. Very good balance between theory and application. I would have liked to learn about more differential equation than the elastic wave equations and how the methods learned in this course can be applied to other pdes. But then again... "waves" is in the title of the course, so it's not too surprising that waves are the focus of the lecture.

By Muhammad B S

Aug 15, 2019

One of the best things about this course is the professor's elegant and lucid explanation of difficult concepts of numerical methods during his scintillating lectures. He is actually aware of his field very well. And the integration of properly commented Jupyter notebooks justified it's name as to "A practical introduction......". Thanks, Professor!!

By Carlos O

Dec 13, 2020

I truly enjoyed the course. It was well-structured, clear and there was a good combination between mathematical derivations and practical aspects using Python. I don't work with wave propagation, but had the interest of exploring numerical methods in Python to solve PDE. Mission accomplished! Especial thanks to Prof. Heiner Igel

By Daniel S W

May 8, 2019

This course has been an eye opener for me in computational seismology. The concepts and content have been presented in a simple to understand and implement manner. The Jupiter notebooks inclusion in the course were very invaluable. This is a great introduction to seismology. Thank you so much Prof. Igel.

By Agastya

Jun 10, 2019

Learnt a lot from this course. Very well structured. Some knowledge of seismology, numerical computation is useful. Even otherwise, Prof.Igel does a great job delivering the core concepts of seismic simulation. Would highly recommend to anyone who is interested in numerical modeling of wave propagation.

By Frank D

Jan 7, 2022

Initially I didn't like the course. During months the course was waiting for me to revise my opinion. Ultimately, after finishing the course I feel that I have learnt quite a lot. It has refreshed a lot of stuff that I had forgotten and I learnt also plenty of new stuff.

By Iván L J

Feb 13, 2021

It's a very useful course to remember or to study for first time numerical methods and implement them on python. I think it is a little short but all the information is of a very high level and the professor made a really good job with the videos and the forums.

By Andrey M S d S d L

Apr 7, 2019

It was the greatest course that I have taken online because it asks you the main ideas through the video, so I only needed to take feel notes on the calculations. I finished it in 9 days and I will definitely recommend to my friends from my former university.

By Hubert L

Nov 6, 2022

I am a french student interested in numerical resolution. This course was great. The mix between maths, physics and informatics was perfect.

I will search a course about the topics wich were not treated (boundary conditions, 2D for finite-element scheme ...)

By David

Feb 8, 2020

Really good professor, good balance between pure maths/physics and its applications in the computational world! As a 'just graduated' physicist, I feel like it was a nice boost in my knowledge because, besides everything, we always learn something new.

By Victor M

Nov 3, 2019

Five stars? Yes!!! Because this is a great course. The instructor is in top of his game. I have learnt and understood things I did not understand since 4 years I started learning them. I suggest the instructor give tutorials on 2D methods as well.

By ASHISH C

Apr 9, 2019

Had a great time learning the concepts of numerical methods and how to apply them using python. This course gave an insight into many real world problems and how their solution can be approached using numerical techniques.

Thank you very much sir.

By vishnu s

Jul 25, 2020

Such an amazing Instructor, hats of to you sir. It was such a nice experience to do this course, the lecture videos are very lucid and I am really happy to learn a wide variety of numerical methods along with the ability to code it in python.

By Tejas j

Oct 24, 2021

This was a great introduction to numerical methods! Prof. Heiner Igel did a fantastic job of making the course the right balance between approachable and rigorous. The python labs were insightful and great learning tools. Highly recommended!

By Mohammad

Aug 4, 2020

One of the best online courses I've ever had. It helped me to learn concepts of numerical analysis in the area of wave propagation , dynamics and seismology , special thanks to Dr.Heiner Igel and Coursera for this state-of-the-art course !

By Doreen B

Jun 9, 2019

Very clear explanations, and visually striking. Python parts well thought out- both in their content, accompanying videos and notebook implementation. Of all the courses I have taken online, this makes the best use of the medium.

By Sergio Z

Mar 25, 2021

A great course, substantial, rigorous, and highly enjoyable. A well-balanced mix of theory and practice, leading to the spectral element method in 1D. Nice Python implementations, an excellent presenter, highly recommended !!

By Jose H

May 25, 2020

A highly recommended course to enter in the basics of numerical simulation. Good explanations, clear Python codes and Prof. Igel always ready to answer the questions. Hope to see the next part (discontinuous Galerkin) soon.

By Дмитрий М

May 25, 2019

Very good course as an introduction into methods used in solving wave equation numerically. As for me, there were too little maths, especially in the last weeks. Probably it's right, because not everyone is good at it.

By Esteban F G L

Dec 24, 2019

An impressive and compelling lecture. meaningful introduction to different sort of numerical methods that could help to solve different real problems, it is really notewhorthy that is very dynamic and entertaining.

By Le L

Jul 8, 2019

I really enjoyed this course. Professor Igel has done an great job putting all this material together. All concepts are very well explained . The python notebooks are well documented and completes.the theory.

Thanks!

By Malcolm W

Jun 24, 2019

I really enjoyed this course. Concepts are explained simply and the Jupyter notebooks are a lot of fun to play with. One criticism is the few typos found in the course, but they are quite minor. Thanks!

By JOSE M A E

Oct 22, 2023

Interesting condensate introduction to modern methods to solve numerically the elastic wave equation. To highlight the pedagogical qualification of Prof. Igel which clearly explains complex concepts