W5V5 Solving the 1D/2D Wave Equation with Python - Computers, Waves, Simulations: A Practical

Link to this course:
https://click.linksynergy.com/deeplink?id=Gw/ETjJoU9M&mid=40328&murl=https%3A%2F%2Fwww.coursera.org%2Flearn%2Fcomputers-waves-simulations
W5V5 Solving the 1D/2D Wave Equation with Python - Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python

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.

Excellent course for people wishing to learn about different numerical approaches for wave propagation. Python Notebooks really add to the learning experience.,Truly useful and challenging due to the mixture of concepts. Really made me integrate knowledge I had before about numerical methods and mathematics.
We start with the problem of function interpolation leading to the concept of Fourier series. We move to the discrete Fourier series and highlight their exact interpolation properties on regular spatial grids. We introduce the derivative of functions using discrete Fourier transforms and use it to solve the 1D and 2D acoustic wave equation. The necessity to simulate waves in limited areas leads us to the definition of Chebyshev polynomials and their uses as basis functions for function interpolation. We develop the concept of differentiation matrices and discuss a solution scheme for the elastic wave equation using Chebyshev polynomials.
W5V5 Solving the 1D/2D Wave Equation with Python - Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python
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