Mathematical, Computational, & Engineering Physics

Usage Requirements: Internet Connection

Wolfram Alpha is an online calculator that is capable of easily converting between units, numerical calculations using fundamental constants, and doing calculations that are more advanced than other online calculators, such as solving systems of equations, matrix manipulation, and solving differential equations.

Contributor: Ricky Dube, Indiana University - Bloomington

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Ansys is a company which provides analytical tools for modeling physical phenomena in mechanical systems. They provide products for analyzing fulid mechanics (Ansys Fluent), 3D design (Ansys Discover), structural mechanics (Ansys Mechanical), thermal load in electronics (Ansys Icepak), electromagnetic fields (Ansys HFSS), optics (Ansys Zemax OpticStudio), and more. There are also simulation options to assist in product design.

Contributor: Amelia Binau on behalf of Brenna McConnell, Indiana University - Bloomington

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Language Requirement(s): Variable (software only) - C, Fortran, Python, and more. Usage Requirements: Internet connection for general catalog, relevant compiler for software.

It's in the name! NIST Digital Library of Mathematical Functions is a simple, yet well-updated, website from the American National Institute of Standards and Technology (NIST) features a catalog of mathematical functions, many of which are heavily relevant to physics. An online companion NIST Handbook of Mathematical Functions. It also contains a helpful guide to available mathematical software for different applications, many of which are open-source and require languages such as C, Fortran, or Python.

Contributor: Amelia Binau, Indiana University - Bloomington

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Usage Requirements: Requires C++ and Linux (Native) or WSL for Windows/MacOS. Relies heavily on MPI for parallel processing. Scales from multi-core laptops to massive supercomputers. Processes case directories containing custom syntax plaintext dictionaries (e.g., controlDict). Works offline.

A premier, industry-standard, open-source toolbox for Computational Fluid Dynamics (CFD). Users configure mesh, physics, and boundary conditions via structured text files to simulate complex fluid flows, heat transfer, and chemical reactions, flattening the financial barrier for researchers conduction advanced fluid analysis.

Contributor: Neil Ghugare, University of Florida, The Ohio State University

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Language Requirement(s): MATLAB. Usage Requirements: MATLAB environment.

Chebfun is a MATLAB package created in 2002 that allows the user to work with and visualize a plethora of advanced mathematical functions. It serves as the primary tool for examples in the textbook Approximation Theory and Approximation Practice, of which example codes and the first 6 chapters are available online. Work with linear and nonlinear ODEs, integration methods, Chebyshev expansions, complex analysis, Fourier analysis, PDEs, multivariate approximation methods, and more. Chebfun is well-documented, featuring a guide which includes its extensions Diskfun and Spherefun. Must be awfully fun!

Contributor: Amelia Binau, Indiana University - Bloomington

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Language Requirement(s): Python. Usage Requirements: Python-compatible IDE.

Need more precision in your calculations than base Python offers? mpmath allows the user to carry out calculations, whether real or complex, to an arbitrary decimal precision and also includes a robust library of special functions. With co-implementation of gmpy2, users may arithmetically manipulate data at precisions over 100 decimal points. This package is integrated into popular packages/systems such as Sage and SymPy.

Contributor: Amelia Binau, Indiana University - Bloomington

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Language Requirement(s): Variable. Usage Requirements: Familiarity with Kaggle (tutorials available).

Need data for ML analysis of fluid dynamics? BLASTNet is a project designed to compile open-source datasets on hydrodynamic systems for training machine learning algorithms. BLASTNet's website contains tutorials for accessing data through Kaggle (where most of its content is stored) and training ML's. Study homogeneous isotropic turbulence, shocks, channeled flow, jet fuel flows, and even propagation of wildfires. Added plus, most datasets are well-introduced with a summary of theoretical background in BLASTNet's catalog.

Contributor: Amelia Binau, Indiana University - Bloomington

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