Symbolic Math Toolbox User’s Guide R2025a

For MATLAB users who need exact answers rather than floating-point approximations, the Symbolic Math Toolbox User’s Guide is the official reference for symbolic math workflows in R2025a. Written by The MathWorks, Inc., it documents how the toolbox represents mathematical objects, manipulates expressions, and connects symbolic results to numerical computation, visualization, and generated code.

What the Guide Covers 💻

The guide moves from foundational concepts to applied technical work. Early chapters show how to create symbolic numbers, variables, expressions, functions, and matrices, then explain how assumptions affect symbolic results. Later sections address algebraic equations, systems of equations, differential equations, differential algebraic equations, transforms, linear algebra, and plotting.

• Creating and using symbolic scalars, vectors, matrices, matrix variables, and matrix functions
• Choosing between syms and sym and controlling output formats
• Working with variable-precision arithmetic and units of measurement
• Solving algebraic, differential, and partial differential equations
• Applying Fourier, Laplace, and Z-transforms
• Performing calculus operations such as differentiation, integration, simplification, and substitution
• Exploring linear algebra topics including singular value decomposition, Jordan canonical form, and eigenvalues
• Generating C or Fortran code from symbolic expressions

From Symbolic Variables to Full Workflows ⚙️

The guide is structured around practical workflows rather than isolated function calls. It explains how symbolic objects behave, how to set and clear assumptions, and how precision choices influence results. Examples throughout the documentation connect symbolic techniques to engineering and scientific problems, including mechanics, circuits, control, heat transfer, and financial modeling.

Solving Equations and Modeling Systems 🧠

Equation solving receives substantial attention. The guide covers algebraic equations, systems of linear and nonlinear equations, parametric solutions, ordinary differential equations, partial differential equations, and differential algebraic equations. It also shows how to select numeric or symbolic solvers and how to use transforms to solve differential equations and difference equations.

Calculus, Linear Algebra, and Visualization 📐

For readers working in calculus and linear algebra, the documentation details differentiation, integration, simplification, expansion, factoring, partial fraction decomposition, and substitution. Matrix-focused chapters cover symbolic matrix computation, linear algebraic operations, singular value decomposition, Jordan canonical form, eigenvalues, and matrix rotations. Plotting sections demonstrate how to visualize symbolic expressions and analytical results.

Built for MATLAB Users

This user’s guide is intended for engineers, scientists, researchers, educators, and students who already work with MATLAB and want to add symbolic computation to their workflow. It is also useful for technical professionals who need to verify numerical results, derive equations, or generate code from symbolic expressions. The material assumes familiarity with MATLAB syntax and mathematical concepts, making it most appropriate for intermediate and advanced users.

Why This R2025a Release Matters

Release R2025a is the version documented in this guide. The revision history shows a long lineage dating back to the first printing in 1993, with online-only revisions tracking each MATLAB release. For anyone maintaining models, teaching symbolic methods, or documenting technical work, this edition provides the release-specific reference that matches R2025a behavior and syntax.

Add It to Your Technical Library

Keep this guide nearby when symbolic results need to be exact, reproducible, and ready for the next step in a MATLAB project. It is a focused reference for turning symbolic math from a specialized tool into a reliable part of everyday technical computing.