Symbolic Math Toolbox provides an easy, intuitive, and complete environment to interactively learn and apply algebra, calculus, and ordinary differential equations.

You can perform common analytical computations such as differentiation and integration to get closed-form results, simplifying and manipulating expressions for greater insight, solving algebraic and ordinary differential equations. You can visualize analytical solutions in 2D and 3D with plotting functions for curves, surfaces, contours, and meshes. You can document and share your calculations in an intuitive mathematical typeset.

In addition to providing exact rational math, Symbolic Math Toolbox provides variable precision, allowing algorithms to run in a higher or lower precision than MATLAB's built-in double. This enables you to get high precision results when numerical accuracy is critical, such as this 32-digit answer.

Symbolic Math Toolbox also includes units for working with dimensioned physical quantities. You can convert between units, create your own custom units, and check the correctness and consistency of equations with units.

Symbolic Math Toolbox can be used in a variety of disciplines in engineering and science for mathematical modeling. For example, in optimization problems, you can get results quicker and avoid errors associated with numerical approximations by symbolically calculating exact gradients and Hessians and supplying them to the optimization solvers. This 100-variable optimization problem runs almost 100 times faster when the analytical derivatives are supplied.

You can integrate symbolic results with broader MATLAB and Simulink applications by converting symbolic expressions into numeric MATLAB functions, Simulink, and Simscape blocks.

For more information, return to the Symbolic Math Toolbox page or choose a link below.