Equation solving, formula simplification, calculus,
linear algebra, statistics, number theory, and more

MuPAD^{®} provides extensive capabilities for a wide variety
of mathematical tasks, including differentiation, integration, simplification,
transforms, linear algebra operations, equation solving, and discrete
mathematics. The emphasis is on performing computations analytically
and returning general results with a complete case analysis. Many
functions can relax this requirement and return results valid in the
majority of cases. In addition, MuPAD provides functions that
use numerical methods where analytical methods cannot achieve required
results. Thus, you can use numeric methods to solve algebraic and
differential equations, compute integrals, perform linear algebra
operations, compute Fast Fourier Transforms, and more.

Frequently Used Topics

- Equation Solving

Solve algebraic and differential equations analytically or numerically

- Formula Manipulation and Simplification

Simplify or modify expressions, substitute parts of expressions, evaluate expressions or subexpressions

- Calculus

Differentiation, integration, series operations, limits, and transforms

- Linear Algebra

Matrix analysis, linear equations, eigenvalues, singular values, matrix exponential, factorization

- Polynomial Algebra

Polynomials, their properties, and operations on them, orthogonal polynomials, Groebner bases

- Mathematical Constants and Functions

Mathematical constants, complex numbers, logarithms, exponential, trigonometric, hyperbolic, and special functions

- Numbers and Precision

Variable-precision arithmetic, elementary number-theoretic operations

- Statistics

Algorithms and tools for organizing, analyzing, and modeling statistical data

- Discrete Mathematics

Elementary number-theoretic operations, linear optimizations, graph theory, and more

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