 # 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)
• 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:

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

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