About the branch of mathematics other uses Calculus disambiguation pp move indef CalculusCalculus Latin , wikt en calculus Latin calculus , a small stone used for counting is a branch of mathematics focused ... 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 Concepts An Applied ... is the study of operations and their application to solving equations. A course in calculus is a gateway ... called mathematical analysis . Calculus has widespread applications in science , economics , and engineering .... Historically, calculus was called the calculus of infinitesimal s , or infinitesimal calculus . More generally, calculus plural calculi refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well known calculi are propositional calculus , variational calculus , lambda calculus , pi calculus , and join calculus . History Attention ... 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 in his Newton s laws of motion ... calculus, but does not seem to have developed these ideas in a rigorous or systematic way. Calculations of volumes and areas, one goal of integral calculus, can be found in the Egyptian mathematics ... calculus. ref Archimedes, Method , in The Works of Archimedes ISBN 978 0 521 66160 7 ref The method ... of a sphere . ref cite book title Calculus Early Transcendentals edition 3 first1 Dennis G. last1 Zill ... introduced were disreputable at first. The formal study of calculus combined Cavalieri s infinitesimals with the calculus of finite differences developed in Europe at around the same time. The combination ... Gregory , the latter two proving the Fundamental theorem of calculus second fundamental theorem of calculus around 1675. The product rule and chain rule , the notion of higher derivative s, Taylor ... 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
wiktionarypar calculusCalculus Latin for pebble , pl. calculi in its most general sense is any method or system of calculation . 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 ... differential 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 Functional calculus , a way to apply various types of functions to operators Join calculus , a theoretical model for distributed programming Lambda calculus , a formulation of the theory of reflexive functions that has deep connections to computational theory 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 , a formulation of the theory of concurrent, communicating processes that was invented by Robin 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 Tuple calculus , a calculus for the relational data model, inspired the SQL language Umbral calculus , the combinatorics of certain operations on polynomials The calculus of variations , a field ... more details
Geometric calculus may refer to Calculus on a geometric algebra , developed by David Hestenes and others. A non Newtonian calculus based on the geometric average, developed by Grossman and Katz. mathdab ... 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
see also List of calculus topics Calculus is a central branch of mathematics , developed from algebra ... of Limit mathematics limits . Therefore calculus depends not only on algebraic and geometric ... onwards. Those concepts are now formulated as mathematical analysis but much of calculus was developed ... scaffolding. In more technical language, the key concepts are Derivative Differential calculus ... s graph. Integral Integral calculus &ndash studies the accumulation of quantities, such as areas ... to each other, as shown by the fundamental theorem of calculus . This theorem is central both ... equation s. The following outline is provided as an overview of and topical guide to calculus Essence of calculusCalculus main 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 Limits of integration List of calculus topics List of important publications in mathematics Calculus Important publications in calculus Mathematics Multivariable calculus Nonstandard 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 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 http integrals.wolfram.com ... The Role of Calculus in College Mathematics from ERICDigests.org http ocw.mit.edu OcwWeb Mathematics ... 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
Descartes Descartes . It consisted of differential calculus and integral calculus , respectively ... from his fluxional calculus, preferring to talk of velocities as in For by the ultimate ... , and his notation for them is the current symbolism in calculus, though Newton s occasionally appears in physics and other fields. In early calculus the use of infinitesimal quantities ... and integral calculus were made firm. In Cauchy s writing, we find a versatile spectrum ... to base calculus on limits instead of infinitesimal quantities. This approach formalized by Weierstrass came to be known as the standard calculus . Informally, the name infinitesimal calculus became ... 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 of infinitesimal calculus Differential calculus Differential and Integral calculus integral calculus together, the original infinitesimal calculus , due to Newton and Leibniz. Standard calculus based on the approach of Weierstrass Non standard calculus based on Robinson s approach to infinitesimals Bibliography Baron, Margaret E. The origins of the infinitesimal calculus. Dover Publications, Inc., New York, 1987. Baron, Margaret E. The origins of the infinitesimal calculus. Pergamon Press, Oxford Edinburgh ... Calculus Category History of mathematics Category History of calculus ca C lcul infinitesimal da Infinitesimalregning ... la Calculus infinitesimalis sk Diferenci lny a integr lny po et sl Infinitezimalni ra un ... 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
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
Unreferenced date November 2009 Italictitle Taxobox name Caseolus calculus status VU status system IUCN2.3 regnum Animal ia phylum Mollusca classis Gastropoda unranked familia 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
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
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
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 obsolescent, see though 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 ... be used to calculate the Exponential function exponential of T efficiently. The polynomial calculus ... calculus the ideal defined above is now trivial. Thus one is interested in functional calculi ... 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
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
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 to define ... 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 theorems ... calculus are used to study many objects of interest in the physical world. In particular, class ... of vector calculus including gradient , divergence , and Curl mathematics curl . Multivariable calculus ... of the degrees of freedom are often used to model these systems, and multivariable calculus provides tools for characterizing the system dynamics . Multivariable calculus is used in many fields of natural ... using a different kind of mathematics, such as stochastic calculus . See also List of multivariable calculus topics Multivariate statistics External links http academicearth.org courses multivariable calculus UC Berkeley Video Course Multivariable Calculus 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 A Very Quick Review , Prof Blair Perot, University of Massachusetts Amherst Category Multivariable calculus eo ... 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
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 pt C lculo biliar bovino zh ... more details
Quantum calculus 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 ... of classical calculus. Integration q integral A function F x is a q antiderivative of f ... for some positive integer math n math in the classical calculus is math nx n 1 math . The corresponding expressions in q calculus and h calculus are math D q x n frac q n 1 q 1 x n 1 n q x n 1 math with the q .... The expression math n q x n 1 math is then the q 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 analog of math x n math is instead the falling ... notions of Taylor expansion , et cetera, and even arrive at q calculus analogues for all of the usual ... is the appropriate analogue for the cosine . History The h calculus is just the calculus of finite ... of fields, among them combinatorics and fluid mechanics . The q calculus, while dating in a sense ... also Noncommutative geometry Quantum differential calculus Time scale calculus q analog References ... , Pokman Cheung , Quantum calculus , Universitext, Springer Verlag, 2002. ISBN 0 387 95341 8 Category Mathematical analysis Category Differential calculus math stub pl Analiza kwantowa ... 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 ... links http www.ontology.co two views language.htm Language as Calculus versus Language as Universal ... more details
The fluent calculus is a formalism for expressing dynamical domains in first order logic . It is a variant of the situation calculus the main difference is that situations are considered representations of states. A binary function symbol math circ math is used to concatenate the terms that represent facts that hold in a situation. For example, that the box is on the table in the situation math s math is represented by the formula math exists t . s on box,table circ t math . The frame problem is solved by asserting that the situation after the execution of an action is identical to the one before but for the conditions changed by the action. For example, the action of moving the box from the table to the floor is formalized as math State Do move box,table,floor , s circ on box,table State s circ on box,floor math This formula states that the state after the move is added the term math on box,floor math and removed the term math on box,table math . Axioms specifying that math circ math is commutative and non idempotent are necessary for such axioms to work. See also Frame problem Situation calculus Event calculus References M. Thielscher 1998 . http www.ep.liu.se ej etai 1998 006 Introduction to the fluent calculus . Electronic Transactions on Artificial Intelligence , 2 3 4 179 192. M. Thielscher 2005 . Reasoning Robots The Art and Science of Programming Robotic Agents. Volume 33 of Applied Logic Series. Springer, Dordrecht. logic stub Category Logical calculi ... more details
In mathematics, a multiplicative calculus is a system with two multiplicative operators, appropriately ... and integral in the Calculus classical calculus of Newton and Leibniz. The multiplicative calculi provide alternatives to the classical calculus, which has an additive derivative and an additive integral. For example, infinitely many Non Newtonian calculus non Newtonian calculi are multiplicative calculi, including the geometric calculus and the bigeometric calculus discussed below. ref name nnc Michael Grossman and Robert Katz. http books.google.com books?q 22Non Newtonian Calculus 22&btnG Search Books&as brr 0 Non Newtonian Calculus , ISBN 0912938013, 1972. ref Multiplicative derivatives Geometric calculus The classical derivative is math f x lim h to 0 f x h f x over h math The geometric ... Multiplicative calculus and its applications , Journal of Mathematical Analysis and Applications ... . In the geometric calculus, the exponential functions are the functions having a constant derivative ... in the classical calculus, the well known geometric average is the natural average in the geometric calculus. ref name nnc Bigeometric calculus A similar definition to the geometric derivative is the bigeometric ... used in economics . In the bigeometric calculus, the power functions are the functions having a constant ... calculus in dimensional spaces , Chaos, Solitons, & Fractals Volume 12, Issue 13, October ... Basic definitions . Discrete calculus Just as differential equations have a discrete analog in difference ... details product integral In 1887, Vito Volterra proposed a multiplicative calculus starting with a multiplicative .... ref Volterra s calculus was later reformulated with a multiplicative derivative as a starting point ... a number of publications on what they called non Newtonian calculus . The geometric calculus ref ... And Integral Calculus E2 80 8E 22&lr &start 10&as brr 3 The First Nonlinear System of Differential And Integral Calculus , ISBN 0977117006, 1979. ref and the bigeometric calculus ref name bc Michael ... 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 See also The Third Manifesto Tutorial D D data language specification D4 programming language an implementation of D Aldat Relational Algebra 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
Duration calculus DC is an interval logic for real time computing real time systems . It was originally developed by Zhou Chaochen with the help of Anders P. Ravn and C. A. R. Hoare on the European ESPRIT Basic Research Action BRA ProCoS project on Provably Correct Systems . ref Zhou Chaochen , C. A. R. Hoare and Anders P. Ravn , A Calculus of Durations, Information Processing Letters , 40 5 269 276, December 1991. ref ref Zhou Chaochen and Michael R. Hansen , Duration Calculus A Formal Approach to Real Time Systems . Springer Science Business Media Springer Verlag , Monographs in Theoretical Computer Science, An EATCS Series, 2003. ISBN 3 540 40823 1. ref DC is mainly useful at the requirements level of the software development process for real time systems. Some tools are available e.g., DCVALID, ref http www.tcs.tifr.res.in pandya dcvalid.html DCVALID A tool for model checking Duration Calculus formulae , TIFR , India. ref IDLVALID, ref http www.tcs.tifr.res.in pandya idlvalid.html IDLVALID Model checking dense time Duration Calculus formulae , TIFR, India. ref etc. . Subsets of Duration Calculus have been studied e.g., using discrete time rather than continuous time . DC is especially espoused by UNU IIST in Macau and the Tata Institute of Fundamental Research in Mumbai , which are major centres of excellence for the approach. See also Interval Temporal Logic ITL Temporal logic Temporal Logic of Actions TLA Modal logic References reflist External links http www.iist.unu.edu dc Duration Calculus Virtual Library entry formalmethods stub Category 1991 introductions Category Formal specification languages Category Temporal logic ... more details
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