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Computational physics : problem solving with Python

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Description

Creators/contributors, contents/summary.

• Introduction
• Computing Software Basics
• Errors and Uncertainties in Computations
• Monte Carlo: Randomness, Walks, and Decays
• Differentiation and Integration
• Matrix Computing
• Trial-and-Error Searching and Data Fitting
• Solving Differential Equations: Nonlinear Oscillations
• ODE Applications: Eigenvalues, Scattering, and Projectiles
• High-Performance Hardware and Parallel Computers
• Applied HPC: Optimization, Tuning, and GPU Programming
• Fourier Analysis: Signals and Filters
• Wavelet and Principal Components Analyses: Nonstationary Signals and Data Compression
• Nonlinear Population Dynamics
• Continuous Nonlinear Dynamics
• Fractals and Statistical Growth Models
• Thermodynamic Simulations and Feynman Path Integrals
• Molecular Dynamics Simulations
• PDE Reviewand Electrostatics via Finite Differences and Electrostatics via Finite Differences
• Heat Flow via Time Stepping
• Wave Equations I: Strings and Membranes
• Wave Equations II: QuantumPackets and Electromagnetic
• Electrostatics via Finite Elements
• Shocks Waves and Solitons
• Fluid Dynamics
• Integral Equations of Quantum Mechanics
• Appendix A Codes, Applets, and Animations

PHYS3820 Computational Physics

Phys3820 computational physics #.

Lecture notes for PHYS3820 Computational Physics at Valdosta State University . This course is designed using Computational Physics With Python by Eric Ayars (2013) and Computational Physics: Problem Solving with Computers by Landau, Paez, & Bordeianu (2007), where it will include summaries of the course material and code implementation/exercises.

Course Description: The course will serve as an introduction to scientific writing and computing, which includes basic computational skills (e.g., Python, GitHub, and LaTeX); Data fitting and interpolation; numerical integration and differentiation; and numerically solving ordinary differential equations (ODEs). To this end, students will complete 3 projects, where the results in each of the first two projects will be presented as a “paper” in the style of Physical Review Letters (2000 words). The topics of these projects are:

Crater counts on the Moon (data fitting), and

Projectile motion with atmospheric drag.

The final project will be assigned by the instructor at midterm on one of the following topics:

Ising Model

Pandemic SIR modeling

Quantum particle in a box

Logistic map

Damped driven oscillator

Brachistochrone

Chaotic scattering

will consist of a longer (3000 words) paper detailing the project, and a 15 minute oral (slide) presentation explaining the project to our peers.

Other Useful links #

Landau Computational Physics Course

Peter Young’s course at UCSC

Computational Physics by Richard Fitzpatrick at UT Austin

Computational Mechanics at UConn

Epidemic modeling from Simon Dobson at University of St. Andrews

Jupyter guide to linear algebra by Ben Vanderlei at the University of the Fraser Valley

Numerical methods for partial differential equations by by Bernard Knaepen & Yelyzaveta Velizhanina at Universite Libre de Bruxelles

Python for Dynamics and Evolution of Earth and Planets by Norwegian Research School

This work is licensed under a Creative Commons Attribution 4.0 International License .

Table of contents

Assignments, acknowledgements and support.

Computational Methods in Physics is an undergraduate class run in the Department of Physics at Arizona State University . The instructor is Oliver Beckstein .

The course provides an introduction to using the computer as a tool to solve problems in physics. Students will learn to analyze problems, select appropriate numerical algorithms, implement them using Python, a programming language widely used in scientific computing, and critically evaluate their numerical results. Problems will be drawn from diverse areas of physics.

For details about the class content, grading, and expectations please see the Syllabus (PDF) .

See the weekly schedule .

• Tue/Thu 1:30 pm – 2:45pm, PSH 355
• bring your laptop
• face covering are recommended (current university policies apply)

Resources for the interactive classes are provided in the GitHub repository Py4Phy/PHY432-resources .

For further details see the PHY432 Course Page .

See GitHub Classroom links in Canvas (ASU PHY432 Spring 2024) .

The two recommended books for the class are

• Computational Modeling and Visualization of Physical Systems with Python , Jay Wang (2016) Wiley-VCH. ISBN: 978-1-119-17918-4
• Computational Physics: Problem Solving with Python, 3rd Edition , Rubin H. Landau, Manuel J. Páez, Cristian C. Bordeianu. (2015) Wiley-VCH. ISBN: 978-3-527-41315-7

Additional books on online resources

• Effective Computation in Physics. Field Guide to Research with Python , Anthony Scopatz and Kathryn D. Huff. (2015) O’Reilly
• Software Carpentry (especially the lessons on the Unix Shell, Version Control with Git, and Programming with Python)

The class is supported by an Education Discount from the nice folks at GitHub Education and uses Classroom for GitHub .

PHYS 5041/6041: Computational Physics

Class information:.

• Instructor: Henry Schreiner @ CERN in Geneva, Switzerland via WebEx.
• M, W, F from 8:55 - 9:50 AM in Geo/Phys Room 300/Hauck. Remote attendance (by request) and recorded lectures will be available.
• Office hours: 10AM-11AM Monday and Friday via video chat (WebEx or Skype, TBD).
• Blackboard: meta_schreihf_2962 (Meta 18FS-Full) TOPICS IN PHYSICS (001)
• Lecture recordings: uc.box.com/v/PES0765
• Source files: github.com/henryiii/compclass .

Introduction:

This course is designed to introduce students to modern computational methods for physics data analysis and modeling. The course is intended for upper-level undergraduates and graduate students. The course was designed for physics students, but should also be appropriate for students in mathematics and other physical sciences. Some programming experience will be useful, but is not required. The course uses Python and looks at a variety of common problems and Scientific Python libraries. The aim of the course is to teach students how to solve problems and what to look for when searching for tools, rather than to teach all the details of specific tools. Common data manipulation and numerical analysis techniques will be investigated, with a strong focus on visualizing the results.

Prerequisites:

Some knowledge of multi-dimensional calculus, linear algebra, and ordinary differential equations.

Required textbook: Computational Physics: Problem Solving with Python , 3rd edition, by Landau, Páez, and Bordeianu (free Enlarged eTextbook Python Third Edition)

Recommended textbook: Python For Data Analysis , 2nd Edition, by Wes McKinney (Author of the Pandas library). This book covers modern Python syntax and the Numpy, Matplotlib, and Pandas libraries from a data scientist's perspective.

Expected outcome

Students should be able to solve a significant problem, use scientific Python tools, use the git version control system, and present their work.

Scientific computing in Python

The course will cover basics needed for modern scientific computing, including the shell, git, and Python. Students will learn to manipulate non-uniform data and visualize the results. Students will learn how to design a solution to a problem and present it to others. The course will also cover performance topics; students will learn to watch for slow code and optimize code performance.

Mathematical topics that will be covered

Uncertainty and error: A look at making a calculation based on physical measurements and interpreting the results.

Linear algebra: An introduction to vector and matrix manipulations and some assorted linear algebra topics.

Differentiation and Integration: Covering several integration and differentiation methods, Monte Carlo integration, as well as using packages.

Statistical distributions and fitting: Manually performing a linear regression, then using commonly used packages to perform the fitting. A look at correlation coefficients and visualization.

Differential equations.

Fourier analysis and filtering signals.

Machine Learning: A brief intro to Machine Learning, including a look at the toolkits for ML.

Term Project

Students will select and solve a specific problem and present the results.

• Weekly problem set: 45%
• Oral presentation: 20%
• Writeup: 20%
• JiTT Quizzes: 15%

Just in Time Teaching (JiTT) quizzes will be due at midnight before the class they cover. 25% of the grade for the JiTT quizzes will be based solely on on-time completion. These will test preparation (reading the material in the book or other recommended sources) before the class begins, and will help shape the lecture to provide the most relevant information.

Classroom Procedures/Policies

Technology use during/for class.

The class will be interactive; registered students have access to OSC computing resources. Students are expected to either use the computers in the classroom or their personal devices. Lectures are designed as notebook that students can follow along with during the class.

Attendance Policy

You are expected to attend each class if you can, and watch the recording if you are not available (with prior permission). All materials should be turned in promptly before the set deadlines - please contact me if you need an extension before a deadline is passed.

The University Rules, including the Student Code of Conduct, are applicable and should be followed in this class. Any violation will be dealt with on an individual basis according to the severity of the misconduct. For example, any material based heavily on outside sources should be attributed in a code comment or a similar manor.

Chapters in the required book are noted when applicable. This is a tentative schedule and subject to change.

Final writeup due during examinations week of 12-10.

I reserve the right to update this syllabus as class needs arise. Be assured that I will communicate to you any changes to our schedule, syllabus or policies quickly and efficiently through Blackboard.

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PHY432 — Computational Methods in Physics | Learning | Beckstein Lab

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PHY432 — Computational Methods in Physics

The course provides an introduction to using the computer as a tool to solve problems in physics. Students will learn to analyze problems, select appropriate numerical algorithms, implement them using Python , a programming language widely used in scientific computing, and critically evaluate their numerical results. Problems will be drawn from diverse areas of physics.

This class starts in Spring 2022 as PHY 432 . (The class was running as PHY 494 from Spring 2016 to Spring 2021.)

For a brief overview, see this page and the Syllabus .

The topics of the class include applications in electrostatics and heat transfer as well as applications such as writing a molecular dynamics code to simulate liquid argon or simulating the lenses in an transmission electron microscope.

Students worked on Final Projects in 2019 as diverse as path integral Monte Carlo, simulations of celestial bodies such as Jupiter’s Trojan asteroids or the solar system, electrons in J J Thompson’s classical experiment, molecular dynamics of organic molecules or rock salt crystals, or the collective behavior of self driving cars. The Final Projects in 2016 included navigation in the solar system, real time digital soundeffect processing, and agent-based modeling such as generating a winning strategy for Black Jack.

Time and requirements

All times and dates to be confirmed.

• Spring 2022: listed as PHY 432
• TTh 1:30pm — 2:45pm
• PHY 252 is a pre- or co-requisite.
• Programming experience as taught in PHY 202 (online) or equivalent required.

If possible, bring your own laptop (Linux, MacOS, Windows).

Course Description

The course provides a practical introduction to using the computer as a tool to solve problems in physics. Students will learn how to work in a scientific computing environment, to analyze a physical problem, select appropriate numerical algorithms to solve the problem, and to implement them. The course will introduce the students to computer graphics and object oriented design. Students will work in teams, critically evaluate their approaches and results, and present them in a professional manner to their peers. The instructor will introduce problems and guide students to their solution.

This is a three-credit hour course. It will be taught in a computer laboratory/studio setting. The emphasis is on practical work , with the instructor initially introducing the problem, and the students then pursuing pre-structured programming exercises and projects. Assessment will primarily focus on projects, including group projects, in which students solve a problem as a small team and present their work as a short report or as a presentation.

In order to facilitate the interactive setting, the capacity will be capped at 24 students. The class is designed to work equally well for remote and in-person students.

PHY 252 is a co-requisite.

Basic programming experience in Python is required; the Online class PHY 202 (by the same instructor) is recommended and can be taken in the preceding Spring, Summer, or Fall semester.

Learning outcomes

Students will learn to program computers in order to solve physical problems. In particular, they will be able to write object oriented code in the open source Python programming language, which is widely used in science and engineering and in some of the biggest tech companies such as Google.

Students will also learn how to solve problems in teams and to communicate their work clearly and effectively.

By the completion of the course, students should be able to quickly apply their knowledge to problems they encounter in other courses and experimental and theoretical research projects.

List of topics

• Working in a scientific computing environment: basic Linux and command line.
• Version control with git
• Programming in Python (including object oriented programming and use of the numpy library).
• Plotting and visualization with matplotlib .
• Numerics fundamentals: numbers, errors
• Differentiation and Integration
• Ordinary differential equations ( ODE ), integration of equations of motion
• Linear algebra (vectors, matrices, eigenvalue problems, SVD )
• Root finding and optimization
• Partial differential equations ( PDE ) e.g. Poisson’s equation, diffusion equation, wave equation
• Monte Carlo methods (importance sampling, Ising model)

For mode details see the course modules overview .

Books and Resources

Recommended text books.

• Computational Modeling and Visualization of Physical Systems with Python , Jay Wang (2016) Wiley- VCH . ISBN : 978-1-119-17918-4
• Computational Physics: Problem Solving with Python, 3rd Edition , Rubin H. Landau, Manuel J. Páez, Cristian C. Bordeianu. (2015) Wiley- VCH . ISBN : 978-3-527-41315-7

Additional books and online resources

• Effective Computation in Physics. Field Guide to Research with Python , Anthony Scopatz and Kathryn D. Huff. (2015) O’Reilly
• A Survey of Computational Physics , Rubin Landau, Manuel J. Páez, and Cristian C. Bordeianu. (2011) Princeton University Press. Free online ComPADRE edition and PDF
• Software Carpentry (especially the lessons on the Unix Shell , Version Control with Git , and Programming with Python )

Course website

• Course page py4phy.github.io/PHY432
• PHY432 GitHub site

For a number of lessons in Spring 2020, videos were created, which you can look at to get a feel for the class.

Discuss: “PHY432 — Computational Methods in Physics”

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• Phone: +1 480 727 9765

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Computational Physics: Problem Solving with Python 4th Edition

Purchase options and add-ons.

• An exceptionally broad range of topics, from simple matrix manipulations to intricate computations in nonlinear dynamics
• A whole suite of supplementary material: Python programs, Jupyter notebooks and videos

Computational Physics is ideal for students in physics, engineering, materials science, and any subjects drawing on applied physics.

• ISBN-10 3527414258
• ISBN-13 978-3527414253
• Edition 4th
• Publisher Wiley-VCH
• Publication date March 25, 2024
• Language English
• Dimensions 6.69 x 1.2 x 9.61 inches
• Print length 592 pages
• See all details

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Cristian C. Bordeianu, PhD, taught Physics and Computer Science at the Military College “Stefan cel Mare,” Campulung Moldovenesc, Romania.

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• Publisher ‏ : ‎ Wiley-VCH; 4th edition (March 25, 2024)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 592 pages
• ISBN-10 ‏ : ‎ 3527414258
• ISBN-13 ‏ : ‎ 978-3527414253
• Item Weight ‏ : ‎ 2.44 pounds
• Dimensions ‏ : ‎ 6.69 x 1.2 x 9.61 inches
• #64 in Fractal Mathematics
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