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Terms like piecewise linear, piecewise smooth, piecewise continuous, and others are very common. The meaning of a function being piecewise P {\displaystyle P} , for a property P {\displaystyle P} is roughly that the domain of the function can be partitioned into pieces on which the property P {\displaystyle P} holds, but is used slightly ...
For functions in certain classes, the problem of determining: whether two functions are equal, known as the zero-equivalence problem (see Richardson's theorem); [4] the zeroes of a function; whether the indefinite integral of a function is also in the class. [5] Of course, some subclasses of these problems are decidable.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
A function property holds piecewise for a function, if the function can be piecewise-defined in a way that the property holds for every subdomain. Examples of functions with such piecewise properties are: Piecewise constant function, also known as a step function; Piecewise linear function; Piecewise continuous function
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Logarithms: the inverses of exponential functions; useful to solve equations involving exponentials. Natural logarithm; Common logarithm; Binary logarithm; Power functions: raise a variable number to a fixed power; also known as Allometric functions; note: if the power is a rational number it is not strictly a transcendental function. Periodic ...
The second problem also remains unsolved: no upper bound for the number of limit cycles is known for any n > 1, and this is what usually is meant by Hilbert's sixteenth problem in the field of dynamical systems. The Spanish Royal Society for Mathematics published an explanation of Hilbert's sixteenth problem. [2]
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