Symbolic Math Toolbox

Symbolic Math Toolbox is a MATLAB toolbox for deriving, analyzing, and exploring symbolic math equations for use in engineering and scientific workflows. It provides functions in areas such as calculus, linear algebra, algebraic and differential equations, transforms, and equation simplification. You can then export results to MATLAB functions, Simulink function blocks, or Simscape components.

You can analytically perform differentiation, integration, simplification, transforms, and equation solving, using either analytical methods or variable-precision arithmetic, with results displayed in mathematical notation. You can also compute Jacobians and gradients for linearization, solve parametric matrix systems for exact eigenvalues, and perform dimensional analysis with unit conversions.

Yes, the toolbox lets you solve linear and nonlinear algebraic and differential equations analytically, as well as perform equation simplification and substitution.

Yes, you can solve and decompose symbolic matrix systems to obtain exact eigenvalues and reusable parametric results. This lets you analyze how parameters affect system behavior before substituting numerical values.

Symbolic Math Toolbox supports Laplace, Fourier, Z-, and Hilbert transforms and their inverses. These let you obtain exact transfer-function and frequency-domain representations from first-principles models, so you can analyze and explore stability, phase, and system behavior before committing to numerical simulation.

Yes, you can compute exact gradients and Jacobians of symbolic models to linearize nonlinear dynamics around operating points. This lets you derive and verify linearized system representations and analyze sensitivity to parameter changes using exact derivatives rather than numerical approximations.

You can share your work with other MATLAB users as live scripts or convert them to HTML, Word, LaTeX, or PDF documents.

Yes, you can generate MATLAB functions, Simulink function blocks, custom equation-based Simscape components, and C or Fortran code directly from symbolic expressions. This lets you take first-principles derivations — such as transfer functions, equations of motion, or control laws — and deploy them directly into engineering simulation and production workflows.

Yes, the toolbox provides built-in functions to plot symbolic expressions and functions using extended MATLAB graphics capabilities and visualize the behavior of symbolic expressions using animations.

Variable-precision arithmetic in Symbolic Math Toolbox lets you to explicitly set the number of significant digits in your computations. You can increase precision to avoid hidden round-off errors in ill-conditioned or large-scale engineering problems, or reduce precision to speed up calculations when full accuracy isn’t needed.

Yes, you can perform dimensional analysis, verify dimensional compatibility and consistency of units in symbolic calculations, create custom unit systems, and convert between existing unit systems.