# Documentation

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# Mathematics

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.

• 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