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# Symbolic Math Toolbox

## Symbolic Computations in MATLAB

Symbolic Math Toolbox lets you perform symbolic computations from the MATLAB command line by defining symbolic math expressions and operating on them. Functions are called using the familiar MATLAB syntax and are available for integration, differentiation, simplification, equation solving, and other mathematical tasks.

Computing symbolic integrals in MATLAB using familiar MATLAB syntax.

### Integration, Differentiation, and Other Calculus

You can perform differentiation and definite and indefinite integration, calculate limits, compute series summation and product, generate the Taylor series, and compute Laplace, Fourier, and Z-transforms and their inverses. You can also perform vector calculus such as calculating the curl, divergence, gradient, Jacobian, Laplacian, and potential.

Computing analytical Jacobian in MATLAB.

### Formula Manipulation and Simplification

Symbolic Math Toolbox enables you to simplify long expressions into shorter forms, transform expressions to particular forms or rewrite them in specific terms, and replace parts of expressions with specified symbolic or numeric values.

### Equation Solving

You can analytically solve for well-posed systems of algebraic equations and ordinary differential equations to get exact answers that are free from numerical approximations.

Analytically solving systems of algebraic equations in MATLAB.

### Linear Algebra

You can perform matrix analysis on symbolic matrices such as computing norm, condition number, determinant, and characteristic polynomial. You can execute matrix operations and transformations with functions for computing the inverse and exponential, and for working with rows and columns of the matrix. You can also get symbolic expressions for the eigenvalues and eigenvectors and perform a symbolic singular value decomposition of a matrix.

### Mathematical Functions

Symbolic Math Toolbox includes the symbolic versions of many mathematical functions, such as logarithm, Dirac, gamma, Bessel, Airy, LambertW, hypergeom, and error functions.

### Executing MuPAD Statements

From MATLAB you can also execute statements written in the MuPAD language, which lets you fully access the functionality in the MuPAD engine.