I need Matlab for theoretical physics course/research projects. I am uncertain about which products/toolboxes to get.

I have opted for Differential Equations Toolbox, Math Symbolic Toolbox, Optimization and Global Optimization toolbox. Other than these I have no idea what I need and what I don't. Can anyone from theoretical background help me pick the products.

Answer 1

[Stephen23]

This is what my AI tool recommended for you:

• MATLAB (base) – superb built-in linear algebra, FFTs, ODE/BVP solvers (ode45/ode15s/bvp4c), sparse matrices.
• Symbolic Math Toolbox – algebra/calculus, simplification, exact solutions, LaTeX export.

Very likely useful (add if they match your work):

• Optimization Toolbox – local/convex optimization, least squares, constrained problems.
• Global Optimization Toolbox – nonconvex/rough landscapes (GA, particles, pattern search).
• Partial Differential Equation (PDE) Toolbox – FEM for elliptic/parabolic/hyperbolic PDEs on 2D/3D geometries.
• Parallel Computing Toolbox – speed up Monte Carlo / parameter sweeps (multicore, clusters, GPU arrays).
• Statistics and Machine Learning Toolbox – uncertainty quantification, regression, distributions, Monte Carlo design.

Nice to have, situational:

• Curve Fitting Toolbox – quick model fitting & confidence intervals.
• Control System Toolbox – if you do dynamical-systems/control theory (LTI models, state-space, frequency domain).
• Signal Processing Toolbox – advanced spectral/time-frequency work beyond base FFTs.
• Image Processing / Computer Vision – if your research involves data from images/fields.

Notes that usually surprise people

• You don’t need a “Differential Equations Toolbox.” MATLAB already includes a very capable ODE/DDE/BVP suite in base MATLAB. Many physics problems (classical mechanics, mean-field models, simple field equations after discretization) can be done with what you already get.
• PDE Toolbox is worth it only if you want a turnkey FEM stack (meshing, boundary conditions, eigenmodes, post-processing) on nontrivial geometries. If you plan to roll your own finite differences/spectral methods, base MATLAB is enough.
• Global Optimization is optional—get it if your cost surface is nonconvex (fitting multi-well potentials, phase-field models with many local minima, etc.).
• Parallel Computing quickly pays off for parameter scans, Monte Carlo, inverse problems, or large PDE meshes. It also unlocks GPU arrays (handy for big linear algebra and FFTs).
• Many universities have a Campus-Wide License that already includes most/all toolboxes—check first; you might not need to pick and choose.

Examples

• Analytical + small-scale numerics (most theory courses):MATLAB + Symbolic (add Optimization if you do variational problems/fitting).
• Nonlinear fits & inverse problems:MATLAB + Optimization (+ Global Optimization) + Statistics.
• PDEs on real geometries / eigenmodes / FEM:MATLAB + PDE Toolbox (+ Parallel Computing).
• Heavy Monte Carlo / parameter sweeps / big matrices:MATLAB + Parallel Computing (+ Statistics).
• Time-frequency or signals in physics experiments:MATLAB + Signal Processing (+ Wavelet if your analysis uses it).

Quick sanity checklist

• Working mostly with closed-form algebra/calculus or perturbation theory? → Symbolic is key.
• Doing variational principles / constrained minimization? → Optimization (and maybe Global).
• Solving PDEs on disks, cavities, beams, meshes without writing your own FEM? → PDE Toolbox.
• Running long sweeps / Monte Carlo? → Parallel Computing (+ Statistics).
• Mostly ODEs/BVPs on simple domains? → Base MATLAB already has you covered.

[Ansh]

That's very helpful, thank you.

[Walter Roberson]

In my experience, the Global Optimization toolbox tends to get used a fair bit.

When I am spinning up an installation that does not have particular needs, I install MATLAB, Optimization Toolbox, Global Optimization Toolbox, and Symbolic Toolbox, as those toolboxes contain tools that I use frequently.

[Torsten]

A physics student without Simulink ? Unthinkable ... Ok, theoretical physics - I don't know if it's useful here.

[John D'Errico]

I wondered if MATLAB central should have a page where such questions can be asked and answered atomatically. And it does have that, already. Here is the response from the AI Chat Playground. (Not as extensive a response as @Stephen23 was given though.)

For your theoretical physics course and research projects using MATLAB, consider the following toolboxes that are particularly useful:

1. Symbolic Math Toolbox: This toolbox allows you to perform symbolic computations, which is essential for theoretical physics. You can manipulate mathematical expressions symbolically, solve equations, and perform calculus operations.

syms x

f = sin(x)^2 + cos(x)^2;

simplify(f) % This will return 1

1. MATLAB's Optimization Toolbox: Useful for solving optimization problems that often arise in physics research.

f = @(x) (x(1)-1)^

+ (x(2)-2)^2; % Objective function

x0 = [0,0]; % Initial guess

options = optimoptions('fminunc','Display','iter');

[x,fval] = fminunc(f,x0,options);

1. Deep Learning Toolbox: If your research involves machine learning, this toolbox supports physics-informed machine learning (PIML) and physics-informed neural networks (PINNs), which can be beneficial for modeling physical systems.

% Example of defining a simple neural network

layers = [

featureInput(1)

fullyConnectedLayer(10)

reluLayer

fullyConnectedLayer(1)

regressionLayer];

1. Partial Differential Equation Toolbox: This toolbox is essential for solving PDEs, which are common in theoretical physics.

model = creatpde();

geometryFromEdges(model,@LShape);

applyBoundaryCondition(model,'dirichlet','Edge',1,'u',0);

generateMesh(model);

results = solvepde(mo);

1. Statistics and Machine Learning Toolbox: Useful for data analysis and statistical modeling, which can be important in experimental physics.matlab data = randn(100,1); % Example data pd = fitdist(data,'Normal'); % Fit a normal distribution ```

These toolboxes will provide a robust foundation for your theoretical physics work in MATLAB.

Answer 2

[Sam Chak]

Hi @Ansh

If you need to analyze theoretical and experimental data with uncertainties in measurements and to model complex physical systems, then consider obtaining the following toolboxes as well:

Curve Fitting Toolbox

Deep Learning Toolbox

Statistics and Machine Learning Toolbox

[Ansh]

Thank you so much.