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

4.8

36 classificações

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14 avaliações

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....

Mar 14, 2019

Well thought out. The material is ordered logically and easy to follow. This online course compliments the book from which it is based on.

Apr 09, 2019

This is a great course for intro to numerical course with additional bonus on python code, although a little bit too fast pace.

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By James S

•May 13, 2019

A great course for anyone interested in numerical methods applied to the wave equation. Clear and engaging lectures.

By tom w

•May 01, 2019

This is an excellent course. Professor Igel did an excellent job putting this material together. His intimate familiarity and comfort with the material is certainly key to the clear explanation of concepts he provides.The subject material was something I should have learned at a younger age. Those planning to pursue a career in Geophysics will benefit greatly from this course. Many topics are covered in the course, the use of Green's functions is clarified, finite difference methods are derived and illustrated using Taylor series expansions, pseudospectral methods are developed... It was nice to return to uses of Chebyhev polynmials, Lagrange and Legendre polynomials and get a better grasp of their use. The psudospectral section was particularly fascinating since geophysicists routinely use Fourier transforms in their analysis and the applications to simulation provide new insights into their use.There is much to be gained through the course. I suspect it is at an intermediate level and serves as a good foundation for more advanced study. The Jupyter notebooks were excellent and provide an excellent resource for further study and application. They also serve as excellent examples of Python coding of various finite difference and finite element simulations along with applications going beyond this course.

By Agastya

•Jun 11, 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 rasheed a

•Jun 10, 2019

This is a great course! It has the perfect amount of theory and practice of seismic wave propagation. I had a lot of fun experimenting with the Python codes and converting them to MATLAB. Thank you for the effort you put into its development, Dr. Igel. Moving forward, I wonder if you planned to develop a similar course for the inverse problem.

By Doreen B

•Jun 09, 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 Nguyen D T

•May 26, 2019

A nice course for learning numerical methods. Though it requires a little advanced calculus but python codes are clear and understandable.

By Melnitskii D S

•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 daniel w

•May 08, 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 Niels C N

•Apr 13, 2019

Heiner Igel is an excellent teacher and he stops Just before the real complications begin as he should at this introduction level. The format of the course is such that Heiner Igel explains to the viewer while hand-written equations and drawings appear absolutely synchronized in the background. Then there are programming exercises where you can run simulations in Python (using Jupyter Notebooks). The programs are well-structured and easy to follow and manipulate to test out the theories. Super well prepared - it has clearly taken a very long time to put this course together. The explanations are detailed enough to get a good feel for the numerical methods and their implementations, but not such that everything is painstakingly derived mathematically. Overall a good introduction to numerical methods without too many complications, but you do get a feel for how complicated it could quickly become.

By Yitao H

•Apr 09, 2019

This is a great course for intro to numerical course with additional bonus on python code, although a little bit too fast pace.

By ANKUR W

•Apr 09, 2019

GOOD

By ASHISH C

•Apr 09, 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 Andrey M S d S d L

•Apr 07, 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 Vivek K G

•Apr 02, 2019

The course was highly enlightening. Go to learn a great deal from the course. Thanks to coursera !!

By Souvik M

•Mar 28, 2019

GREAT COURSE

By Noah L

•Mar 14, 2019

Well thought out. The material is ordered logically and easy to follow. This online course compliments the book from which it is based on.

By New D

•Feb 25, 2019

I already know that I will learn a lot even though I am an undergrad. ( FTD from Colorado School of Mines)

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