Symbolic Maths in MATLAB

Symbolic Mathematics

Symbolic mathematics performs calculations using exact mathematical expressions and variables rather than only numerical approximations.

Symbolic Variable

A symbolic variable represents an unknown mathematical quantity without assigning it a numerical value. Example: syms x creates x as a symbolic variable.

syms Command

The syms command creates symbolic variables that can be used in symbolic expressions, equations, derivatives, integrals, and other exact calculations. Example: syms x y

Symbolic Expression

A symbolic expression is a mathematical expression containing symbolic variables that MATLAB can manipulate algebraically. Example: x^2 + 3*x + 2.

Symbolic Equation

A symbolic equation represents an equality between symbolic expressions and is created using ==. Example: x^2 == 4.

solve Function

The solve function finds exact or symbolic solutions to symbolic equations. Example: solve(x^2 == 4, x) returns the solutions for x.

subs Function

The subs function substitutes specified values or expressions for symbolic variables. Example: subs(x^2 + 1, x, 3) substitutes 3 for x.

Symbolic Assumption

A symbolic assumption restricts the possible values or properties of a symbolic variable, such as requiring it to be real, positive, or an integer.

assume Function

The assume function assigns a mathematical assumption to an existing symbolic variable. Example: assume(x > 0) restricts x to positive values.

Symbolic Function

A symbolic function represents a mathematical function symbolically and can depend on one or more symbolic variables. Example: syms f(x) defines f as a symbolic function of x.

diff Function

The diff function symbolically differentiates an expression or symbolic function. Example: diff(x^3, x) returns 3*x^2.

Symbolic Derivative

A symbolic derivative is an exact derivative obtained algebraically from a symbolic expression rather than estimated from sampled numerical data.

int Function

The int function performs symbolic integration. Example: int(x^2, x) returns x^3/3.

Symbolic Integral

A symbolic integral is an exact antiderivative or definite integral calculated from a symbolic mathematical expression.

taylor Function

The taylor function generates a Taylor-series approximation of a symbolic expression about a specified expansion point.

Taylor-Series Approximation

A Taylor-series approximation represents a function near an expansion point using a polynomial constructed from the function's derivatives.

Symbolic Differential Equation

A symbolic differential equation contains an unknown symbolic function and one or more of its derivatives.

dsolve Function

The dsolve function symbolically solves ordinary differential equations and can incorporate specified initial or boundary conditions.

Symbolic Unit

A symbolic unit represents a physical measurement unit that MATLAB can attach to symbolic quantities for unit-aware calculations.

units Function

The units function provides symbolic physical units for constructing quantities and performing unit-aware symbolic calculations.

unitConvert Function

The unitConvert function converts symbolic quantities from one compatible physical unit to another.