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

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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....

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

筛选依据：

创建者 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.

创建者 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.

创建者 M V 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.

创建者 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!

创建者 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 !

创建者 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.

创建者 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 !!

创建者 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.

创建者 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.

创建者 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.

创建者 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!

创建者 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!

创建者 Eigil L

•Dec 21, 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.

创建者 jorge g

•Aug 2, 2020

This is a very useful course that helps to wrap up the knowledge acquired in advanced lectures during the master's program. Professor Igel is a good lecturer who knows how to transmit his knowledge.

创建者 Bin C

•Aug 23, 2020

Very good Course to get an Overview over Numerical Methods with a lot of examples and additional content! I highly recommend this course as a teaching assistant in fields of numerical methods!

创建者 Alejandro V

•Aug 20, 2020

¡Fantástico curso introductorio! Muy bien explicado por parte del profesor, muy buenas libretas de Python y, no menos importante, despierta las ganas de aprender más.

Muy recomendado

创建者 Rakesh m

•Jul 12, 2020

This is an excellent course as I have found. The instructor has taught us many important concepts including the detailed codes. I would love to join further courses from Prof. Igel.

创建者 Yerson L

•Aug 11, 2020

An excellent course highly recommended, but be careful, its level is quite advanced, it requires knowledge of python, partial differential equations and advanced numerical methods

创建者 Miguel A M

•Jul 11, 2021

Great course, I hope there will be a followup covering all the parts Prof. Igel mentioned in the final lecture. Amazing balance theory/practice and fantastic Jupyter Notebooks

创建者 Junyi L

•Mar 29, 2020

I really learned a lot of basic ideas and mathematical knowledge of numerical methods, and realized corresponding algorithms to solve research problems through python.

创建者 gkkclouds

•Jun 18, 2019

This course teaches me systematically the all kinds of methods to solve the wave-equation of the derivative form. And I want to know the all answers of the tests.

创建者 Alan D

•Jul 17, 2020

Excellent course for people wishing to learn about different numerical approaches for wave propagation. Python Notebooks really add to the learning experience.

创建者 葉政凱

•Dec 21, 2019

This course is a great introduction to numerical methods.

I hope that Dr. Igel will provide more courses on writing effective code for numerical methods.

创建者 J Z

•Sep 30, 2020

Truly useful and challenging due to the mixture of concepts. Really made me integrate knowledge I had before about numerical methods and mathematics.