About the branch of mathematics other uses Calculus disambiguation pp move indef Merge from Infinitesimal calculus discuss Talk Calculus Merge with infinitesimal calculus date May 2011 CalculusCalculus Latin , wikt en calculus Latin calculus , a small stone used for counting is a branch of mathematics ... education . It has two major branches, differential calculus and integral calculus , which are related by the fundamental theorem of calculus . Calculus is the study of change, ref citation title Calculus ... in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis . Calculus has widespread applications in science ... alone is insufficient. Calculus has historically been called the calculus of infinitesimal s , or infinitesimal calculus . More generally, calculus plural calculi refers to any method or system of calculation ... calculi are propositional calculus , variational calculus , lambda calculus , pi calculus , and join calculus . History Attention leave dates as they are. We re not really that bothered, as the majority of Wikipedia dates state BC . Just think of it as Before Cronholm Main History of calculus Ancient File GodfreyKneller IsaacNewton 1689.jpg thumb 200px right Isaac Newton developed the use of calculus ... of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. Calculations of volumes and areas, one goal of integral calculus, can be found ... of integral calculus. ref Archimedes, Method , in The Works of Archimedes ISBN 978 0 521 66160 ... the volume of a sphere . ref cite book title Calculus Early Transcendentals edition 3 first1 Dennis ... many components of calculus such as the Taylor series , infinite series approximations, an integral .... Some consider the Yuktibh to be the first text on calculus. ref http www history.mcs.st andrews.ac.uk ... width 30em max width 30 cellspacing 5 style text align left The calculus was the first achievement ... more details
wiktionarypar calculusCalculus from Latin language Latin wikt en calculuscalculus Latin meaning pebble ... . Calculus may refer to In mathematics and computer science Calculus , also the calculus , short for differential calculus and integral calculus , which investigate motion and rates of change Logical calculus, a formal system that defines a language and rules to derive an expression from premises ... and integral calculus The calculus of sums and differences difference operator , also called the finite difference calculus, a discrete analogue of the calculus In symbolic logic the propositional calculus , specifies the rules of inference governing the logic of propositions the predicate calculus , specifies the rules of inference governing the logic of predicates a proof calculus , a framework for expressing systems of logical inference the sequent calculus , a proof calculus for first order logic Bondi k calculus Bondi k calculus , a method used in relativity theory Domain relational calculus , a calculus for the relational data model Epsilon calculus , a logical language which replaces quantifiers with the epsilon operator Functional calculus , a way to apply various types of functions to operators Join calculus , a theoretical model for distributed programming Lambda calculus ... Matrix calculus , a specialized notation for multivariable calculus over spaces of matrices Modal calculus , a common temporal logic used by formal verification methods such as model checking Non standard calculus , an approach to infinitesimal calculus using Robinson s infinitesimals Pi calculus ... Milner Refinement calculus , a way of refining models of programs into efficient programs Rho calculus , introduced as a general means to uniformly integrate rewriting and lambda calculus Schubert calculus , a branch of algebraic geometry Tuple calculus , a calculus for the relational data model, inspired the SQL language Umbral calculus , the combinatorics of certain operations on polynomials The calculus ... more details
The rho calculus is a formalism intended to combine the higher order facilities of lambda calculus with the pattern matching of term rewriting . External links http rho.loria.fr Site dedicated to research in the rho calculus formalmethods stub Category lambda calculus ... more details
Elementary calculus may refer to The elementary aspects of differential and integral calculus Elementary Calculus An Infinitesimal Approach , a book by Jerome Keisler. disambig ... more details
Merge from List of calculus topics date September 2011 The following outline is provided as an overview of and topical guide to calculusCalculus &ndash branch of mathematics focused on limit mathematics ... series . This subject constitutes a major part of modern mathematics education . Calculus is the study of change, ref citation title Calculus Concepts An Applied Approach to the Mathematics of Change ... to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis . Calculus ... for which Elementary algebra algebra alone is insufficient. Branches of calculus Differential calculus Integral calculus History of calculus main History of calculus General calculus concepts Derivative Differentiation rules Calculus with polynomials Fundamental theorem of calculus Differential calculus Integral calculus Law of continuity Limits of integration List of calculus topics List of important publications in mathematics Calculus Important publications in calculus Mathematics Multivariable calculus Non standard analysis Partial derivative Calculus scholars Gottfried Leibniz Isaac Newton Sir Isaac Newton Calculus lists main List of calculus topics Table of mathematical symbols See also Table of mathematical symbols References Reflist External links sisterlinks Calculus MathWorld urlname Calculus title Calculus PlanetMath urlname TopicsOnCalculus title Topics on Calculus id 7592 http djm.cc library Calculus Made Easy Thompson.pdf Calculus Made Easy 1914 by Silvanus P. Thompson Full text in PDF http www.calculus.org Calculus.org The Calculus page at University of California, Davis &ndash contains resources and links to other sites http www.math.temple.edu cow COW Calculus on the Web at Temple University contains resources ranging from pre calculus and associated algebra ... pre 9217 calculus.htm The Role of Calculus in College Mathematics from ERICDigests.org http ... more details
In mathematical logic , pattern calculus is a formalism that extends lambda calculus with abilities to match patterns against an arbitrary compound data structure path polymorphism and to include free variables in patterns pattern polymorphism . External links http www staff.it.uts.edu.au cbj patterns Pattern calculus research site formalmethods stub Category lambda calculus ... more details
The join calculus is a process calculus developed at INRIA . The join calculus was developed to provide a formal basis for the design of distributed programming languages, and therefore intentionally avoids communications constructs found in other process calculi, such as synchronous rendezvous rendezvous communications, which are difficult to implement in a distributed setting ref cite paper author Cedric Fournet, Georges Gonthier title The reflexive CHAM and the join calculus date 1995 url http citeseer.ist.psu.edu fournet95reflexive.html , pg. 1 ref . Despite this limitation, the join calculus is as expressive as the full Pi calculus math pi math calculus . Encodings of the math pi math calculus in the join calculus, and vice versa, have been demonstrated ref cite paper author Cedric Fournet, Georges Gonthier title The reflexive CHAM and the join calculus date 1995 url http citeseer.ist.psu.edu fournet95reflexive.html , pg. 2 ref . The join calculus is a member of the Pi calculus math pi math calculus family of process calculi, and can be considered, at its core, an asynchronous math pi math calculus with several strong restrictions ref cite paper author Cedric Fournet, Georges Gonthier title The reflexive CHAM and the join calculus date 1995 url http citeseer.ist.psu.edu fournet95reflexive.html ..., the join calculus offers at least one convenience over the math pi math calculus namely the use of multi .... Languages based on the join calculus The join calculus programming language is based on the join calculus process calculus. It is implemented as an interpreter written in OCaml , and supports statically ... detection ref cite paper author Cedric Fournet, Georges Gonthier title The Join Calculus A Language ... is a version of OCaml extended with join calculus primitives. Polyphonic C sharp Polyphonic C and its ... that uses Join calculus References references External links INRIA, http moscova.inria.fr join index.shtml Join Calculus homepage prog lang stub this is mostly related to parallel programming Category ... more details
Calculus on manifolds may refer to Calculus on Manifolds book Calculus on Manifolds book Calculus on differentiable manifold s See also Differential geometry mathdab Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
The calculus of structures is a proof calculus with deep inference for studying the structural proof theory of noncommutative logic . The calculus has since been applied to study linear logic , classical logic , modal logic , and process calculi , and many benefits are claimed to follow in these investigations from the way in which deep inference is made available in the calculus. References Alessio Guglielmi 2004 ., A System of Interaction and Structure . ACM Transactions on Computational Logic. Kai Br nnler 2004 . Deep Inference and Symmetry in Classical Proofs . Logos Verlag. External links http alessio.guglielmi.name res cos Calculus of structures homepage http www.informatik.uni leipzig.de ozan maude cos.html CoS in Maude page documenting implementations of logical system s in the calculus of structures, using the Maude system . Category Logical calculi logic stub ... more details
Notability date October 2008 Maplets for Calculus are a collection of Java applet s written in the computer algebra system CAS Maple software Maple , which teach calculus. They were written by Philip Yasskin at Texas A&M University and Douglas Meade at the University of South Carolina. In March 2008, Maplets for Calculus received the 2008 ICTCM Award for Excellence and Innovation in Using Technology to Enhance the Teaching and Learning of Mathematics at the 20th ICTCM International Conference on Technology in Collegiate Mathematics . ref http archives.math.utk.edu ICTCM v20.html Proceedings of ICTCM 20 ref External links http m4c.math.tamu.edu Maplets for Calculus website http arxiv.org PS cache arxiv pdf 1008 1008.0011v1.pdf Parallel and distributed Gr obner bases computation in JAS References reflist DEFAULTSORT Maplets For Calculus Category Educational math software Category Calculus math stub software stub ... more details
Unreferenced date November 2009 Italictitle Taxobox name Caseolus calculus status VU status system IUCN2.3 regnum Animal ia phylum Mollusca classis Gastropoda unranked superfamilia clade Heterobranchia br clade Euthyneura br clade Panpulmonata br clade Eupulmonata br clade Stylommatophora br informal group Sigmurethra superfamilia Helicoidea familia Hygromiidae genus Caseolus species C. calculus binomial Caseolus calculus binomial authority Caseolus calculus Common name Madeiran land snail is a species of small air breathing land snail s, Terrestrial animal terrestrial pulmonate gastropod mollusks in the family Hygromiidae , the hairy snails and their allies. Distribution and conservation status This species lives in Europe . It is mentioned in annexes II and IV of Habitats Directive . References reflist External links Caseolus calculus at http www.iucnredlist.org apps redlist details 3990 0 IUCN Red List Category Caseolus Hygromiidae stub sr Caseolus calculus ... more details
In computer science , Api calculus was introduced in 2002 as an extension of pi calculus to address some of the limitations of pi calculus for modeling intelligent agents ref http www.cs.siu.edu rahimi rahimi ch7.pdf Rahimi 2002 Shahram Rahimi, Maria Cobb, Dia Ali, Fred Petry, A Modeling Tool for Intelligent Agent Based Systems Api Calculus, Soft Computing Agents A New Perspective for Dynamic Systems, the International Series Frontiers in Artificial Intelligence and Application by IOS Press, pp. 165 186, 2002. ref . More specifically, it addresses knowledge representation , organizational grouping and migration of agents among groups. Moreover, it has the potential for modeling the security aspects of Agent based model agent based systems . Api calculus introduces three new concepts over ordinary pi calculus and its extensions, the higher order and polyadic pi calculi. To represent knowledge inherent in an autonomous agent, the concept of a knowledge unit is introduced. A knowledge unit is an intelligence entity that can perform inference. Agents have the capability to add drop facts i.e. Predicate logic predicate s or Propositional calculus propositions to from a knowledge unit and also modify its structure by adding new rules or eliminating existing ones. Each mobile agent is capable of carrying one or more knowledge units and sending and receiving them to from other agents. However, the concept of knowledge unit only provides an abstraction level with no resources for intelligence modeling. Moreover, api calculus introduces milieu , a new level of abstraction that is in between single mobile agents and the system as a whole. And lastly, Api calculus introduces the notion of term . A term consists of a name, a rule fact used to create or modify knowledge units , or a function, where a name can be a channel or a variable.In the standard pi calculus, names are the only terms. References references DEFAULTSORT Api Calculus Category Process calculi comp sci stub ... more details
More footnotes date May 2010 The Calculus Ratiocinator is a theoretical universal logical calculation ... contrasting points of view on what Leibniz meant by calculus ratiocinator . The first is associated ... The received point of view in analytic philosophy and formal logic , is that the calculus ratiocinator ... point of view understands that the calculus ratiocinator is a formal inference engine what ... Peirce C.S. Peirce s writings on logic in the 1880s. Frege intended his concept script to be a calculus ratiocinator as well as a lingua characteristica . That part of formal logic relevant to the calculus comes under the heading of proof theory . From this perspective the calculus ratiocinator is only ... a logical calculus . The synthetic view A contrasting point of view stems from Herbert Spencer ... the calculus ratiocinator as referring to a calculating machine . The cybernetician Norbert Wiener considered Leibniz s calculus ratiocinator a forerunner to the modern day digital computer cquote ... idea of a computing machine is nothing but a mechanization of Leibniz s calculus ratiocinator . Wiener ... machines in the Metal. ... just as the calculus of arithmetic lends itself to a mechanization ... of the present day, so the calculus ratiocinator of Leibniz contains the germs of the machina ratiocinatrix ... calculations which was also called a Stepped Reckoner . As a computing machine, the ideal calculus ratiocinator would perform Leibniz s integral and differential calculus. In this way the meaning ... the calculus ratiocinator as an algorithm which, when applied to the symbols of any formula of the characteristica ... Hartley Rogers, Jr. 1963 p. 934 . A classic discussion of the calculus ratiocinator is Couturat 1901 chpts. 3,4 , who maintained that the characteristica universalis and thus the calculus ... , calculus ratiocinator , and encyclopedia form three pillars of Leibniz s project. Notes references .... 161 166. External links http www.ontology.co two views language.htm Language as Calculus versus ... more details
Merge to Calculus discuss Talk Calculus Merge with infinitesimal calculus date May 2011 multiple image footer Gottfried Wilhelm Leibniz left and Isaac Newton right , developers of infinitesimal calculus ... IsaacNewton 1689.jpg alt2 Isaac Newton width2 184 Infinitesimal calculus is the part of mathematics ... math tfrac 1 infty math in area calculations, preparing the ground for integral calculus ref Scott, J.F. ... . Infinitesimal calculus consists of differential calculus and integral calculus , respectively ... from his fluxional calculus, preferring to talk of velocities as in For by the ultimate velocity ... , and his notation for them is the current symbolism in calculus. Further development In early calculus the use of infinitesimal quantities was unrigorous and was fiercely criticized by a number ... of differential and integral calculus were made firm. Cauchy developed a versatile spectrum of foundational ... infinitesimals. Following the work of Weierstrass, it eventually became common to base calculus ... as the standard calculus. Informally, the expression infinitesimal calculus became commonly used ... After many years of the infinitesimal approach to calculus having fallen into disuse other than as an introductory ... in a manner that allows a Leibniz like development of the usual rules of calculus. Varieties multiple image footer Differential calculus left and Integral calculus right . width1 200 image1 ... width2 150 Differential and integral calculus Main Differential calculus Integral calculus The original infinitesimal calculus , attributed to Newton and Leibniz. Differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change while integral calculus ... Limit at infinity graph.png thumb left 200px Limit of the function at infinity. Standard calculus Main Calculus It is based on the approach that took Weierstrass, replacing infinitesimals by Limit of a function ..., but use the ordinary real number real number system . In this treatment, calculus is a collection ... more details
Attributional calculus is a logic and representation system defined by Ryszard S. Michalski. It combines elements of predicate logic , propositional calculus , and multi valued logic . Attributional calculus provides a formal language for natural induction , an inductive learning process whose results are in forms natural to people. References Michalski, R.S., ATTRIBUTIONAL CALCULUS A Logic and Representation Language for Natural Induction, Reports of the Machine Learning and Inference Laboratory, MLI 04 2, George Mason University, Fairfax, VA, April, 2004. Compu AI stub Category Artificial intelligence Category Systems of formal logic ... more details
Relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus , that are part of the relational model for databases and provide a declarative way to specify database queries. This in contrast to the relational algebra which is also part of the relational model but provides a more procedural way for specifying queries. The relational algebra might suggest these steps to retrieve the phone numbers and names of book stores that supply Some Sample Book Join book stores and titles over the BookstoreID. Restrict the result of that join to tuples for the book Some Sample Book . Project the result of that restriction over StoreName and StorePhone. The relational calculus would formulate a descriptive, declarative way Get StoreName and StorePhone for supplies such that there exists a title BK with the same BookstoreID value and with a BookTitle value of Some Sample Book . The relational algebra and the relational calculus are essentially logical equivalence logically equivalent for any algebraic expression, there is an equivalent expression in the calculus, and vice versa. This result is known as Codd s theorem . References cite book first Christopher J. last Date authorlink Christopher J. Date year 2004 title An Introduction to Database Systems edition 8th publisher Addison Wesley isbn 0 321 19784 4 databases DEFAULTSORT Relational Calculus Category Logical calculi Category Relational model database stub de Kalk l Datenbank es C lculo relacional ja ru zh ... more details
Unreferenced date June 2007 The term ethical calculus , when used generally, refers to any method of determining a course of action in a circumstance that is not explicitly evaluated in one s ethical code . A formal philosophy of ethical calculus is a recent development in the study of ethics , combining elements of natural selection , self organizing systems , emergence , and algorithm theory. Ethical calculus is based on the premise that moral and ethical codes are emergent algorithm s, epiphenomena of large groups of sentient beings, and that a given moral code or ethical code behaves in organic ways, seeking to prolong itself. According to ethical calculus, the most ethical course of action in a situation is an absolute, but rather than being based on a static ethical code, the ethical code itself is a function of circumstances. The ideal Ethic is the course of action taken in a given situation by an omnipotent, omniscient being. The optimal ethic is the best possible course of action taken by an individual with the given limitations. The standard of judgment is the continuation of situations in which ethics are relevant. While ethical calculus is, in some ways, similar to moral relativism , the former finds its grounds in the circumstance while the latter depends on social and cultural context for moral judgment. Ethical calculus would most accurately be regarded as a form of dynamic moral absolutism . See also felicific calculus science of morality ethics moral absolutism morality Category Ethics ... more details
calculus cTopic Multivariable calculus Multivariable calculus also known as multivariate calculus is the extension of calculus in one Variable mathematics variable to calculus in more than one variable ... expressions of the derivative. In vector calculus , the del operator math nabla math is used ... such as surfaces and curves . Fundamental theorem of calculus in multiple dimensions In single variable calculus, the fundamental theorem of calculus establishes a link between the derivative and the integral. The link between the derivative and the integral in multivariable calculus is embodied by the famous integral theorems of vector calculus Gradient theorem Stokes theorem Divergence theorem Green s theorem In a more advanced study of multivariable calculus, it is seen that these four ... calculus are used to study many objects of interest in the physical world. In particular ... of vector calculus including gradient , divergence , and Curl mathematics curl . Multivariable calculus can be applied to analyze determinism deterministic systems that have multiple degrees ... calculus provides tools for characterizing the system dynamics . Multivariable calculus is used in many ... be studied using a different kind of mathematics, such as stochastic calculus . Quantitative analysts in finance also often use multivariate calculus to predict future trends in the stock market. See also List of multivariable calculus topics Multivariate statistics External links http www.youtube.com ... lectures on Multivariable Calculus, Fall 2009, Professor Edward Frenkel http www.youtube.com user MIT g c 4C4C8A7D06566F38 MIT video lectures on Multivariable Calculus, Fall 2007 http www.math.gatech.edu cain notes calculus.html Multivariable Calculus A free online textbook by George Cain and James Herod http math.etsu.edu Multicalc Multivariable Calculus Online A free online textbook by Jeff Knisley http www.ecs.umass.edu mie faculty perot mie440 Multivariable 20Calculus.pdf Multivariable Calculus ... more details
Unreferenced date December 2009 Policy Debate In policy debate , impact calculus is a type of argumentation which seeks to compare the impacts presented by both teams. Basic impact calculus There are three basic types of impact calculus that compare the impacts of the plan to the impacts of a disadvantage Probability one impact is more likely e.g. Economic collapse is more probable than an outbreak of grey goo , therefore the risk of economic collapse outweighs the risk of a grey goo disaster. Timeframe one impact will happen faster e.g. An asteroid impact will cause extinction before Global warming will, therefore an asteroid impact outweighs Global Warming. Magnitude one impact is bigger e.g. Nuclear war kills more people than car accidents. Other types of impact calculus Some other more sophisticated arguments are also considered impact calculus Impact inclusivity one impact is inclusive of the other e.g. Global war is inclusive of a Taiwan war, therefore global war outweighs Taiwan war. X creates Y one impact causes the other impact to happen e.g. War causes genocide, therefore war outweighs genocide Internal link shortcircuiting one impact prevents a positive impact from happening e.g. Nuclear war halts space colonization, therefore nuclear war outweighs space colonization Reversibility e.g. Civil liberties lost in the name of security during a time of crisis can be restored later, but deaths caused by a lack of security are irreversible. Framework arguments can also be considered impact calculus. Arguments as to why the judge policy debate judge should adopt a utilitarianism ... perspective may change the way they compare impacts. Impact calculus and new arguments Basic impact calculus arguments may be made at any time and are generally not considered new arguments, even ... forms of impact calculus should generally be brought up earlier in the debate and evidenced if possible. DEFAULTSORT Impact Calculus Category Policy debate ... more details
In mathematics , a functional calculus is a theory allowing one to apply mathematical function s to mathematical operator s. It is now a branch more accurately, several related areas of the field of functional analysis , connected with spectral theory . Historically, the term was also used synonymously with calculus of variations this usage is obsolete, but see functional derivative . Sometimes it is used in relation to types of functional equation , or in logic for systems of predicate calculus . If f is a function, say a numerical function of a real number , and M is an operator, there is no particular reason why the expression f M should make sense. If it does, then we are no longer using f on its original function domain . In the tradition of operational calculus , algebraic expressions in operators are handled irrespective of their meaning. This passes nearly unnoticed if we talk about squaring a matrix , though, which is the case of f x x sup 2 sup and M an n × n matrix mathematics matrix . The idea of a functional calculus is to create a principled approach to this kind of overloading of the notation. The most immediate case is to apply polynomial function s to a square matrix , extending what has just been discussed. In the finite dimensional case, the polynomial functional calculus yields quite a bit of information about the operator. For example, consider the family of polynomials which annihilates an operator T . This family is an ideal ring theory ideal in the ring ... calculus is not as informative in the infinite dimensional case. Consider the unilateral shift with the polynomials calculus the ideal defined above is now trivial. Thus one is interested in functional ... be. For technical accounts see holomorphic functional calculus continuous functional calculus Borel functional calculus . References Springer id F f042030 title Functional calculus DEFAULTSORT Functional Calculus Category Functional calculus de Funktionalkalk l nl Functionele calculus ... more details
Geometric calculus extends the geometric algebra to include differentiation and integration including differential geometry and differential forms. ref David Hestenes , Garrett Sobczyk Clifford Algebra to Geometric Calculus, a Unified Language for mathematics and Physics Dordrecht Boston G.Reidel Publ.Co., 1984, ISBN 90 277 2561 6 ref File Geometric Calculus Family Tree.png right 300px thumb Figure 1 from 32 A diagram of the history of Geometric Calculus Given a geometric algebra, the vector derivative is defined as the operator math 1 . Essentially, the vector derivative is defined so that the GA version of Green s theorem is true, math oint A dA nabla f oint dA dx f math and then one can write math nabla f nabla cdot f nabla wedge f math as a geometric product, effectively generalizing Stokes theorem including the differential forms version of it . In math 1D math when A is a curve with endpoints math a math and math b math , then math oint A dA nabla f oint dA dx f math reduces to math int a b dx nabla f int a b dx cdot nabla f int a b df f b f a math or the fundamental theorem of integral calculus. Also developed are the concept of vector manifold and geometric integration theory which generalizes Cartan s differential forms . References reflist differential geometry stub Category Calculus ... more details
Calculus medicine Calculus bovis ref Ingredients, AN KUNG NIU HUANG WAN Bezoar Chest Functioning Pills , Peking Tung Jen Tang, Peking, China. 1980. ref , niu huang or ox bezoar s are dried gallstone s of cattle used in Chinese herbology , where they are claimed to remove toxins from the body. In Asian countries calculus bovis are harvested when cattle Bos taurus domesticus Gmelin are slaughtered. Their gall bladder s are taken out, the bile is filtered, and the stones are cleaned and dried. In western countries they are usually discarded. Calculus bovis have a color varying from golden yellow to brownish yellow. The shape of a stone is variable and depends on how it was formed, becoming spherical, oval, triangular, tubular or irregular. Since natural calculus bovis are scarce they can be very expensive. There are artificial calculus bovis used as substitutes. These are manufactured from cholic acid derived from bovine bile ref http www.nzp.co.nz products.php?cid 1&pid 1 ref , but it is said that the effect may not be the same. References reflist Category Traditional Chinese medicine Category Article Feedback 5 pt C lculo biliar bovino zh ... more details
Quantum calculus , sometimes called calculus without limits , is equivalent to traditional infinitesimal calculus without the notion of Limit of a function limits . It defines q calculus and h calculus . h ostensibly stands for Planck s constant while q stands for quantum. The two parameters are related by the formula math q e i h e 2 pi i hbar , math where math scriptstyle hbar frac h 2 pi , math is the reduced Planck constant . Differentiation In the q calculus and h calculus, differential of a function differentials of functions are defined as math d q f x f qx f x , math and math d h f x f x h f x , math respectively. Derivative s of functions are then defined as fractions by the q derivative math D q f x frac d q f x d q x frac f qx f x q 1 x math and by math D h f x frac d h f x d h x frac f x h f x h math In the Limit of a function limit , as h goes to 0, or equivalently as q goes to 1, these expressions take on the form of the derivative of classical calculus. Integration q integral A function F x is a q antiderivative of f x if D sub q sub F x f x . The q antiderivative or q ... calculus is math nx n 1 math . The corresponding expressions in q calculus and h calculus are math ... calculus analogue of the simple power rule for positive integral powers. In this sense, the function math x n math is still nice in the q calculus, but rather ugly in the h calculus the h calculus ... cetera, and even arrive at q calculus analogues for all of the usual functions one would want to have ... . History The h calculus is just the calculus of finite differences , which had been studied ... mechanics . The q calculus, while dating in a sense back to Leonhard Euler and Carl Gustav Jacobi ... calculus Time scale calculus q analog References reflist this section is for references ... reading should go into further reading Victor Kac , Pokman Cheung , Quantum calculus , Universitext ... calculus mathanalysis stub pl Analiza kwantowa ... more details
Stochastic calculus is a branch of mathematics that operates on stochastic process es. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly. The best known stochastic process to which stochastic calculus is applied is the Wiener process named in honor of Norbert Wiener , which is used for modeling Brownian motion as described by Louis Bachelier in 1900 and by Albert Einstein in 1905 and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The main flavours of stochastic calculus are the It calculus and its variational relative the Malliavin calculus . For technical reasons the It integral is the most useful for general classes of processes but the related Stratonovich integral is frequently useful in problem formulation particularly in engineering disciplines. The Stratonovich integral can readily be expressed in terms of the It integral. The main benefit of the Stratonovich integral is that it obeys the usual chain rule and does therefore not require ... when developing stochastic calculus on manifolds other than R sup n sup . The dominated ... results without re expressing the integrals in It form. It integral main It calculus The It integral is central to the study of stochastic calculus. The integral math int H ,dX math is defined ... integral. Applications A very important application of stochastic calculus is in quantitative ... date August 2011 References Fima C Klebaner, 2012, Introduction to Stochastic Calculus with Application ... http arxiv.org PS cache arxiv pdf 0712 0712.3908v2.pdf Preprint Category Stochastic calculus Category Mathematical finance Category Integral calculus ar de Stochastische ... more details
Encyclopedia
top
