Function of several real variablesMathematical function with multiple real-number argumentsIn mathematics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The "input" variables take real values, while the "output", also called the "value of the function", may be real or complex.
Even and odd functionsIn mathematics, an even function is a real function such that f(−x)=f(x){\displaystyle f(-x)=f(x)} for every x{\displaystyle x} in its domain. Similarly, an odd function is a function such that f(−x)=−f(x){\displaystyle f(-x)=-f(x)} for every x{\displaystyle x} in its domain.
Volume elementIn mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates.
Multivariable calculusCalculus of functions of several variables Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to functions of several variables: the differentiation and integration of functions involving multiple variables (multivariate), rather than just one. Multivariable calculus may be thought of as an elementary part of calculus on Euclidean space.Fubini's theoremFubini's theorem gives the conditions under which a double integral can be computed as an iterated integral, i.e. by integrating in one variable at a time. Intuitively, just as the volume of a loaf of bread is the same whether one sums over standard slices or over long thin slices, the value of a double integral does not depend on the order of integration when the hypotheses of the theorem are satisfied.
IntegralOperation in calculusA definite integral of a function can be represented as the signed area of the region bounded by its graph and the horizontal axis; in the above graph as an example, the integral of f(x){\displaystyle f(x)} between a{\displaystyle a} and b{\displaystyle b} is the yellow (−) area subtracted from the blue (+) area
VolumeVolume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length and height (cubed) is interrelated with volume.
AreaArea is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat.
SphereA sphere (from Ancient Greek (sphaîra)'ball') is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the center of the sphere, and the distance r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental surface in many fields of mathematics.
Cartesian coordinate systemIn geometry, a Cartesian coordinate system (UK: , US: ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicularoriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system. The point where the axes meet is called the origin and has (0, 0) as coordinates. The axes directions represent an orthogonal basis.
MathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.
Number lineA number line is a graphical representation of a straight line that serves as spatial representation of numbers, usually graduated like a ruler with a particular origin point representing the number zero and evenly spaced marks in either direction representing integers, imagined to extend infinitely.
Partition of a setIn mathematics, a partition of a set is a grouping of its elements into non-emptysubsets, in such a way that every element is included in exactly one subset. Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a setoid, typically in type theory and proof theory.*As an Amazon Associate I earn from qualifying purchases.