Mathematics Calculator

The Mathematics Calculator provides a unified computational core for symbolically manipulating and numerically evaluating mathematical expressions. It accepts an input expression and optional variable values or function definitions, enabling both exact symbolic results and decimal approximations. It is intended for students, researchers, and engineers who need quick verification, algebraic derivation, or model exploration without installing software.

Conceptually, the tool parses the input into a structured representation, applies algebraic rules to simplify or transform the expression, and, when requested, computes derivatives, integrals, limits, or series. For numeric evaluation, it substitutes given values and returns results with a user-controlled precision. Matrix operations such as determinants, inverses, and eigenvalues are handled on multi-dimensional data.

Unique value lies in combining symbolic and numeric capabilities within a compact, web-accessible core. It supports user-defined functions, parameterized expressions, and basic systems of equations, enabling rapid prototyping of mathematical models and identities. Output formats adapt to mode, offering exact forms for symbolic work and fixed-decimal results for numeric tasks, with matrices presented as nested arrays.

Common use cases include verifying identities, solving homework problems, computing derivatives for optimization, evaluating definite integrals, and exploring parameter effects in models. The tool emphasizes correctness, precision control, and straightforward interpretation of results, making it suitable for classroom demonstrations, research prototyping, and quick checks during development.