MATLAB for Physics

As one of the most popular software environments for scientific computing and data visualization, MATLAB from MathWorks is a natural choice for applications in experimental and computational physics. As a high-level programming language, it is user-friendly even for absolute beginners in programming. The need for MATLAB in experimental data analysis is mostly in the representation of data, error analysis, and graphical interpretation of the results. On the other hand, the possibility for symbolic math notation and a vast number of prebuilt packages for optimized computations make MATLAB an appropriate choice for modeling physical systems and simulating their behavior.

Since there are many research branches of modern physics that cannot be imagined without the accompanying simulations and numerical methods, many undergraduate and graduate schools include courses in MATLAB for physics. The following list of topics is a good sample for curriculum of such a course, covering both the computational physics knowledge and MATLAB programming skills:

• Numerical algebra: solutions of linear and nonlinear equations
  • Numerical derivation and integration
  • Newton’s method
• Random processes
  • Generation of pseudo-random numbers
  • Random walk
  • Diffusion-limited aggregation
• Interpolation and extrapolation
• Zero finding
• Finite difference approximation
• Ordinary differential equations (ODE) and systems of ODEs
• Numerical methods for solving ordinary differential equations (ODE)
  • Linear multistep methods
  • Euler method and backward Euler method
  • Taylor methods
  • Runge-Kutta methods (implicit and explicit)
  • Adams-Moulton methods
  • Adams-Bashforth methods
• Partial differential equations
• General linear models
• Model fitting
• Three body problem (in general case, n-body problem)
• Fourier analysis (Continuous and Discrete Fourier Transform, Fast Fourier Transform, Spectral Analysis)
• Eigenvalues and singular values
• MATLAB programming
  • Basics: variables, indexing, values, assignment statement, floating-point arithmetic
  • Vector and matrix notation
  • Workspace
  • Scripts and functions
  • Control flow (break, continue, return, if/else, for, parfor, switch-case, etc.)
  • Figures, 2D and 3D plotting (plot, surf, mesh grid, scatter plot)
  • Creating GUI
  • Code vectorization
  • Profiling and debugging the code
• Quantitative data analysis
• Data visualization

Since our tutors are proficient either in general or specifically computational/numerical physics or computer science with applications in physics, most likely you will find a professional to assist you. Let us mention some specific problems our experts have helped students so far: random walk simulations (with fixed and random path lengths), harmonic motion of a pendulum, Lorenz model, numerical analysis of vertical motion with resistance, Laplace’s equation for a finite-sized capacitor, Schrodinger equation in one dimension...

Due to the rise in popularity of the field, many educational materials and practical solutions can be found on the Internet. Some of the good places to start would be the following:

• Series of video tutorials, shared by University of Manchester: https://www.youtube.com/watch?v=MPndYWOs43Y&list=PLAOZch2HHHpWyLHySb80Qvf0thrVs5FSY
• Beginner introduction to all details of MATLAB interface and most frequent functions for application in physics, used at theS. Particle Accelerator School: http://uspas.fnal.gov/materials/14UNM/Matlab_1.pdf
• A short introduction to data analysis with MATLAB with examples in experimental physics lab, used at George Mason University: http://physics.gmu.edu/~rubinp/courses/407/Matlab2.pdf
• Another guide for beginners, with colorful examples, from University of Osnabrück, Germany: http://www.home.uni-osnabrueck.de/phertel/pdf/ml.pdf
• MATLAB: An Introduction with Applications, Amos Gilat, 3rd Ed., John Wiley & Sons https://majackmer85.files.wordpress.com/2014/11/tercera-edtion-matlab.pdf
• A presentation on using MATLAB for solving ordinary differential equations, Washington University St. Louis https://sites.physics.wustl.edu/gradcomputer/wiki/images/6/67/Ogliore_Lecture_1.pdf

For going into more details and hands-on experience, try the following:

• A free textbook by Clive Moler and The MathWorks, Numerical computing with MATLAB: https://www.mathworks.com/moler/index_ncm.html
  accompanied by toolbox containing examples in MATLAB code:
  https://www.mathworks.com/matlabcentral/fileexchange/37976-numerical-computing-with-matlab
• Not-so-brief tutorial for MATLAB for physics from Brigham Young University: https://www.physics.byu.edu/courses/computational/phys330/matlab.pdf
• Textbook Physical Modeling in MATLAB (http://greenteapress.com/wp/physical-modeling-in-matlab/) and a GitHub repository with coding examples, both by Professor Allen Downey: https://github.com/AllenDowney/PhysicalModelingInMATLAB
• Solution book for Computational Physics by Giordano and Nakanishi (https://www.amazon.com/Computational-Physics-2nd-Nicholas-Giordano/dp/0131469908) in MATLAB: https://www.physics.purdue.edu/~hisao/book/www/Computational%20Physics%20using%20MATLAB.pdf
• A free online book on Computational Physics using MATLAB, by Professor Kevin Berwick: https://www.pdfdrive.net/computational-physics-using-matlab-department-of-physics-d10041116.html
• MATLAB’s courseware for teaching (and learning) physics with MATLAB: https://www.mathworks.com/academia/courseware/teaching-physics-with-matlab.html
• Scientific journal covering the recent findings (not exclusively in MATLAB): https://www.journals.elsevier.com/journal-of-computational-physics

To fulfill our tutoring mission of online education, our college homework help and online tutoring centers are standing by 24/7, ready to assist college students who need homework help with all aspects of MATLAB for physics. Our physics tutors can help with all your projects, large or small, and we challenge you to find better online MATLAB for physics tutoring anywhere.