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95 relations: Applied mathematics, Asymptote, Baker–Campbell–Hausdorff formula, Banach algebra, Binomial theorem, C99, Carlitz exponential, Cauchy product, Chain rule, Characterization (mathematics), Characterizations of the exponential function, Chemistry, Complex logarithm, Complex number, Complex plane, Compound interest, Computer algebra system, Continued fraction, Derivative, Differential equation, Double exponential function, E (mathematical constant), Economics, Eli Maor, Engineering, Entire function, Euler's continued fraction formula, Euler's formula, Exponential decay, Exponential field, Exponential growth, Exponential map (Lie theory), Exponentiation, Exsecant, Fixed point (mathematics), Functional (mathematics), Generalized continued fraction, Graph of a function, Half-exponential function, Hewlett-Packard, Holomorphic function, HP-41C, Hyperbolic function, Interest, Inverse function, Jacob Bernoulli, Johann Bernoulli, Lacunary value, Leonhard Euler, Lie algebra, ..., Lie group, Limit of a function, Line (geometry), Linear function, List of exponential topics, List of integrals of exponential functions, Logarithmic spiral, Malthusian catastrophe, Mathematical and theoretical biology, Mathematical object, Mathematics, Matrix (mathematics), Matrix exponential, Mittag-Leffler function, Multiplicative calculus, Multivalued function, Natural logarithm, Origin (mathematics), P-adic exponential function, Padé approximant, Padé table, Paul Halmos, Physics, Picard theorem, Picard–Lindelöf theorem, Polynomial, Power series, Proportionality (mathematics), Pure mathematics, Radioactive decay, Radius of convergence, Ratio test, Real number, Round-off error, Series (mathematics), Slope, Tangent, Taylor series, Tetration, Transcendental function, Trigonometric functions, Unrestricted algorithm, Versine, Walter Rudin, William Kahan. Expand index (45 more) »
Applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry.
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Asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.
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Baker–Campbell–Hausdorff formula
In mathematics, the Baker–Campbell–Hausdorff formula is the solution to the equation for possibly noncommutative and in the Lie algebra of a Lie group.
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Banach algebra
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, i.e. a normed space and complete in the metric induced by the norm.
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Binomial theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
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C99
C99 (previously known as C9X) is an informal name for ISO/IEC 9899:1999, a past version of the C programming language standard.
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Carlitz exponential
In mathematics, the Carlitz exponential is a characteristic p analogue to the usual exponential function studied in real and complex analysis.
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Cauchy product
In mathematics, more specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series.
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Chain rule
In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.
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Characterization (mathematics)
In mathematics, the statement that "Property P characterizes object X" means that not only does X have property P, but that X is the only thing that has property P. In other words, P is a defining property of X. It is also common to find statements such as "Property Q characterises Y up to isomorphism".
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Characterizations of the exponential function
In mathematics, the exponential function can be characterized in many ways.
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Chemistry
Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.
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Complex logarithm
In complex analysis, a complex logarithm of the non-zero complex number, denoted by, is defined to be any complex number for which.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
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Compound interest
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
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Computer algebra system
A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.
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Continued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Double exponential function
A double exponential function is a constant raised to the power of an exponential function.
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E (mathematical constant)
The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.
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Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
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Eli Maor
Eli Maor, an Israel-born historian of mathematics, is the author of several books about the history of mathematics.
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Engineering
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
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Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic at all finite points over the whole complex plane.
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Euler's continued fraction formula
In the analytic theory of continued fractions, Euler's continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction.
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Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
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Exponential decay
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
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Exponential field
In mathematics, an exponential field is a field that has an extra operation on its elements which extends the usual idea of exponentiation.
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Exponential growth
Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.
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Exponential map (Lie theory)
In the theory of Lie groups, the exponential map is a map from the Lie algebra \mathfrak g of a Lie group G to the group, which allows one to recapture the local group structure from the Lie algebra.
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Exponentiation
Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.
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Exsecant
The exsecant (exsec, exs) and excosecant (excosec, excsc, exc) are trigonometric functions defined in terms of the secant and cosecant functions.
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Fixed point (mathematics)
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.
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Functional (mathematics)
In mathematics, the term functional (as a noun) has at least two meanings.
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Generalized continued fraction
In complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary real or complex values.
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Graph of a function
In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.
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Half-exponential function
In mathematics, a half-exponential function is a function ƒ that, if composed with itself, results in an exponential function: Another definition is that ƒ is half-exponential if it is non-decreasing and ƒ−1(xC) ≤ o(log x).
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Hewlett-Packard
The Hewlett-Packard Company (commonly referred to as HP) or shortened to Hewlett-Packard was an American multinational information technology company headquartered in Palo Alto, California.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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HP-41C
The HP-41C series are programmable, expandable, continuous memory handheld RPN calculators made by Hewlett-Packard from 1979 to 1990.
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Hyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
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Interest
Interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (i.e., the amount borrowed), at a particular rate.
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Jacob Bernoulli
Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.
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Johann Bernoulli
Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.
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Lacunary value
In complex analysis, a subfield of mathematics, a lacunary value or gap of a complex-valued function defined on a subset of the complex plane is a complex number which is not in the image of the function.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Lie algebra
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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Limit of a function
Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.
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Line (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
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Linear function
In mathematics, the term linear function refers to two distinct but related notions.
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List of exponential topics
This is a list of exponential topics, by Wikipedia page.
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List of integrals of exponential functions
The following is a list of integrals of exponential functions.
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Logarithmic spiral
A logarithmic spiral, equiangular spiral or growth spiral is a self-similar spiral curve which often appears in nature.
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Malthusian catastrophe
A Malthusian catastrophe (also known as Malthusian check or Malthusian spectre) is a prediction of a forced return to subsistence-level conditions once population growth has outpaced agricultural production - that there will be too many people and not enough food.
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Mathematical and theoretical biology
Mathematical and theoretical biology is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories.
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Mathematical object
A mathematical object is an abstract object arising in mathematics.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
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Mittag-Leffler function
In mathematics, the Mittag-Leffler function Eα,β is a special function, a complex function which depends on two complex parameters α and β.
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Multiplicative calculus
In mathematics, a multiplicative calculus is a system with two multiplicative operators, called a "multiplicative derivative" and a "multiplicative integral", which are inversely related in a manner analogous to the inverse relationship between the derivative and integral in the classical calculus of Newton and Leibniz.
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Multivalued function
In mathematics, a multivalued function from a domain to a codomain is a heterogeneous relation.
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Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
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Origin (mathematics)
In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space.
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P-adic exponential function
In mathematics, particularly ''p''-adic analysis, the p-adic exponential function is a p-adic analogue of the usual exponential function on the complex numbers.
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Padé approximant
In mathematics a Padé approximant is the 'best' approximation of a function by a rational function of given order – under this technique, the approximant's power series agrees with the power series of the function it is approximating.
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Padé table
In complex analysis, a Padé table is an array, possibly of infinite extent, of the rational Padé approximants to a given complex formal power series.
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Paul Halmos
Paul Richard Halmos (Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-Jewish-born American mathematician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces).
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Picard theorem
In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function.
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Picard–Lindelöf theorem
In mathematics, in the study of differential equations, the Picard–Lindelöf theorem, Picard's existence theorem or Cauchy–Lipschitz theorem is an important theorem on existence and uniqueness of solutions to first-order equations with given initial conditions.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Power series
In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.
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Proportionality (mathematics)
In mathematics, two variables are proportional if there is always a constant ratio between them.
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Pure mathematics
Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.
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Radioactive decay
Radioactive decay (also known as nuclear decay or radioactivity) is the process by which an unstable atomic nucleus loses energy (in terms of mass in its rest frame) by emitting radiation, such as an alpha particle, beta particle with neutrino or only a neutrino in the case of electron capture, gamma ray, or electron in the case of internal conversion.
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Radius of convergence
In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges.
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Ratio test
In mathematics, the ratio test is a test (or "criterion") for the convergence of a series where each term is a real or complex number and is nonzero when is large.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Round-off error
A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.
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Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
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Slope
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
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Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Tetration
In mathematics, tetration (or hyper-4) is the next hyperoperation after exponentiation, and is defined as iterated exponentiation.
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Transcendental function
A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.
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Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
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Unrestricted algorithm
An unrestricted algorithm is an algorithm for the computation of a mathematical function that puts no restrictions on the range of the argument or on the precision that may be demanded in the result.
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Versine
The versine or versed sine is a trigonometric function already appearing in some of the earliest trigonometric tables.
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Walter Rudin
Walter Rudin (May 2, 1921 – May 20, 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison.
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William Kahan
William "Velvel" Morton Kahan (born June 5, 1933) is a Canadian mathematician and computer scientist who received the Turing Award in 1989 for "his fundamental contributions to numerical analysis", was named an ACM Fellow in 1994, and inducted into the National Academy of Engineering in 2005.
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Redirects here:
Base e anti-logarithm, Base e antilogarithm, Cb^x, Complex exponential function, E to the x, E**x, E^X-1, E^x, E^x-1, Exp (programming), Exp(x), Exp(x)-1, Exp-1, Exp1m, Exp1m(x), Expm1, Expm1(x), Exponent of e, Exponential Function, Exponential equation, Exponential equations, Exponential minus 1, Exponential minus 1 function, Exponentials, Natural exponent, Natural exponential, Natural exponential function, Natural exponential minus 1, Real exponential function, ⅇ.
References
[1] https://en.wikipedia.org/wiki/Exponential_function
