Numerical Methods: Practical Intro with Python
Master numerical methods for solving partial differential equations using Python in this comprehensive course.
Master numerical methods for solving partial differential equations using Python in this comprehensive course.
Dive into the world of numerical methods for solving partial differential equations with this comprehensive course. Using Python and Jupyter notebooks, you'll learn to implement various techniques including finite-difference, pseudospectral, and linear/spectral finite-element methods. The course focuses on practical applications, particularly in solving the 1D and 2D scalar wave equations. You'll gain hands-on experience in developing computational algorithms, visualizing results, and understanding the fundamental mathematical principles behind these methods. The course covers essential topics such as Taylor series, Fourier series, function interpolation, and numerical integration, while also introducing concepts in wave physics, discretization, and parallel programming.
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What you'll learn
Understand and implement the finite-difference method for solving partial differential equations
Master the pseudospectral method and its application to wave equations
Learn the principles and implementation of the linear finite-element method
Develop skills in spectral element methods for improved accuracy
Gain practical experience in Python programming for numerical simulations
Understand the mathematical foundations of numerical methods, including Taylor series and Fourier analysis
Skills you'll gain
This course includes:
5 Hours PreRecorded video
9 quizzes
Access on Mobile, Tablet, Desktop
FullTime access
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There are 9 modules in this course
This course provides a comprehensive introduction to numerical methods for solving partial differential equations, with a focus on practical implementation using Python. It covers a range of techniques including finite-difference, pseudospectral, and finite-element methods, applied primarily to the acoustic and elastic wave equations. The course is structured to build understanding progressively, starting with basic concepts of discretization and wave physics, then moving through various numerical methods. Each topic is accompanied by Python implementations in Jupyter notebooks, allowing students to see the direct connection between mathematical theory and computational practice. The course also covers important practical aspects such as stability analysis, boundary conditions, and strategies for ensuring solution accuracy.
Week 01 - Discrete World, Wave Physics, Computers
Module 1 · 2 Hours to complete
Week 02 The Finite-Difference Method - Taylor Operators
Module 2 · 4 Hours to complete
Week 03 The Finite-Difference Method - 1D Wave Equation - von Neumann Analysis
Module 3 · 2 Hours to complete
Week 04 The Finite-Difference Method in 2D - Numerical Anisotropy, Heterogeneous Media
Module 4 · 7 Hours to complete
Week 06 The Linear Finite-Element Method - Static Elasticity
Module 6 · 2 Hours to complete
Week 07 The Linear Finite-Element Method - Dynamic Elasticity
Module 7 · 2 Hours to complete
Week 08 The Spectral-Element Method - Lagrange Interpolation, Numerical Integration
Module 8 · 3 Hours to complete
Week 09 The Spectral Element Method - 1D Elastic Wave Equation, Convergence Test
Module 9 · 3 Hours to complete
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Instructor
Professor of Seismology and Expert in Wave Propagation at LMU Munich
Heiner Igel is a distinguished geophysicist who studied geophysics in Karlsruhe and Edinburgh. He earned his doctoral degree in 1993 from the Institut de Physique du Globe in Paris, where he developed parallel forward and inverse modeling tools for wave propagation problems. Following this, he worked at the Institute of Theoretical Geophysics in Cambridge, UK, focusing on wave simulation techniques for both regional and global seismic wave propagation. In 1999, he became a Professor of Seismology at Ludwig-Maximilians-University Munich. His current research interests include full-waveform inversion, high-performance computing, and rotational ground motions. Igel is also a member of the German National Academy of Sciences.
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