Kirb y k irb 1 has developed a calculus to manipulat e handle decom positions of 4m anifolds w hich can be used to prove that tw o such m anifolds are isom orphic. Pdf in this article, we let pcq denote the class of q convex functions. In the field of approximation theory, the applications of qcalculus are new area in last 25 years. The lesson focus at the beginning of each lesson identifies one or more specific learning outcomes slos that are addressed in the lesson. First it gives a very clear and rather complete introduction to qanalogues of elementary calculus, which the authors call quantumcalculus.
Ecs 20 chapter 4, logic using propositional calculus 0. Integration is a way of adding slices to find the whole. In the field of approximation theory, the applications of q calculus are new area in last 25 years. Anthony ciavarella july 1, 2016 abstract in this talk, i will present a qanalog of the classical derivative from calculus. It is a wellknown experience that the only truly enjoyable and profitable way of studying mathematics is the method of filling in the details by ones own efforts. This leads us into the exciting world of quantum calculus, also known as q calculus. The conventional approach to calculus is founded on limits. This is a history of qcalculus with a new notation and a new method for qhypergeometric series. If you have ever taking a course in college level calculus, you will find this book very useful to.
Pdf introduction to lambda calculus semantic scholar. The first q analogue of the wellknown bernstein polynomials was introduced by lupas in the year 1987. If a page of the book isnt showing here, please add text bookcat to the end of the page concerned. If you dont know the difference between 15,000 and 150,000, you probably shouldnt try to buy a new car. In 1997 phillips considered another q analogue of the classical bernstein polynomials. Easily find the introduction to thermodynamics with calculus equation that youre looking for. This notes contain real numbers, functions, derivatives, integration theory and sequences. Request pdf introduction of qcalculus in the field of approximation theory, the applications of qcalculus are new area in last 25 years. Introduction of qcalculus request pdf researchgate.
Anthony ciavarella july 1, 2016 abstract in this talk, i will present a q analog of the classical derivative from calculus. Logic is the study of the principles of reasoning, especially of the structure of propositions as distinguished from their content and of method and validity in deductive reasoning. Introduction in this chapter we introduce limits and derivatives. It defines q calculus and h calculus, where h ostensibly stands for plancks constant while q stands for quantum. Calculusintroduction wikibooks, open books for an open. Partitions, generalized vandermonde determinants and representation theory. Arithmetic college calculus abstract mathematics in elementary school you largely learn arithmetic and the basic notions of shape. Introduction to logic using propositional calculus and proof 1. In 1997 phillips considered another qanalogue of the classical bernstein polynomials.
It defines qcalculus and hcalculus, where h ostensibly stands for plancks constant while q stands for quantum. Integration can be used to find areas, volumes, central points and many useful things. Lets assume that the captain turns off the engine at the point p,q on the curve y x 2, and then try to determine what values p and q must have so that the resulting tangent line to the curve will go through the point 3,5. This category contains pages that are part of the calculus book. The last third of volume 1 introduces linear algebra with applications to geometry and analysis. You can view a list of all subpages under the book main page not including the book main page itself, regardless of whether theyre categorized, here. In precise terms, we study quantum calculus on finite intervals. Michael spivak brandeis university calculus on manifolds a modern approach to classical theorems. These apparently disconnected themes, formalized in integral calculus and di erential calculus, respectively, come together in. Mooculus massive open online calculus calculus this document was typeset on april 10, 2014. Calculus, originally called infinitesimal calculus or the calculus of infinitesimals, is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The scope is broader than is usual in an introduction, embracing not only the differential. This notes contains the following subcategories calculus, introduction to number theory and vector calculus.
This monograph is an introduction to combining approximation theory and q calculus with applications, by using well known operators. This chapter will jump directly into the two problems that the subject was invented to solve. A new notation and a new method for qhypergeometric series. This leads us into the exciting world of quantum calculus, also known as qcalculus. Quantum calculus trends in abstract and applied analysis. Jul 17, 2017 today we introduce propositional logic. These results occur in many applications as physics, quantum theory, number theory, statistical. If time permits, i will show some applications of the q. A background of the usage of the qcalculus in the context of geometric funciton. This can be further developed and completed by the reader. Here we present necessary definitions and facts from the q calculus. Pdf in this article, we let pcq denote the class of qconvex functions. Sengupta 1162011 introduction there are two fundamental notions that led to the development of calculus historically.
Limits will be formally defined near the end of the chapter. Applications of qcalculus in operator theory springerlink. From there, i will prove qanalogs of the binomial theorem and taylors theorem. We will use limits to analyze asymptotic behaviors of functions and their graphs. Here are my online notes for my calculus i course that i teach here at lamar university. The second theme is an application to number theory. We follow the terminology and notations used in the books 8, 9, 11.
Discrete individually separate and distinct as opposed to continuous and capable of infinitesimal change. Integral calculus joins integrates the small pieces together to find how much there is. Our aim is to present new proofs of some results from q calculus. Here is a nice diversion for anyone who knows what is the derivative of a simple function. Mar 28, 2014 get full course delivered at your home. We propose qversions of some basic concepts of continuous variational calculus such as. The simplest introduction to differential calculus involves an explicit series of numbers. The ideas are presented in a way to give only the essence of the ideas, techniques, and proofs. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn calculus i or needing a refresher in some of the early topics in calculus.
A background of the usage of the q calculus in the context of geometric funciton. The constant h 4 is the best possible integral inequalities of the form have an interest in itself, and also have important applications in the theory of ordinary differential equations and boundary value problems see 1, 2, 4. Applications of qcalculus in operator theory ali aral. Calculus, originally called infinitesimal calculus or the calculus of infinitesimals, is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations it has two major branches, differential calculus and integral calculus. Math 221 1st semester calculus lecture notes version 2. Quantum calculus, sometimes called calculus without limits, is equivalent to traditional infinitesimal calculus without the notion of limits. You will see what the questions are, and you will see an important part of the answer. Introduction to thermodynamics with calculus equations. The first qanalogue of the wellknown bernstein polynomials was introduced by lupas in the year 1987. The lessons in this course are organized as follows. Given the series 42, 43, 3, 18, 34, the differential of this series would be 1, 40, 15, 16. Differential calculus cuts something into small pieces to find how it changes. A blog by oliver knill on matters mathematics related to quantum calculus, or discrete geometry including graph theory or algebraic combinatorics. The two parameters are related by the formula where is the reduced planck constant.
As you read mathematics, you must work alongside the text itself. In this chapter, we will develop the concept of a limit by example. You can view a list of all subpages under the book main page not including the book main page itself, regardless of. Discrete mathematics introduction to propositional logic. Quantum derivatives and integrals play a leading role in the understanding of com. In what follows, q is a real number satisfying 0 q q natural number is defined by. Quantum calculus is the modern name for the investigation of calculus without limits. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of qcalculus before delving into more advanced material. Lecture notes in calculus pdf 206p this is useful notes for calculus. Therefore expressions that differ only in the names of bound variables are identified. From there, i will prove q analogs of the binomial theorem and taylors theorem.
The modern theory of differential and integral calculus began in the xviith century with the works of newton and leibniz. We talk about what statements are and how we can determine truth values. The slos identify the knowledge and skills you should have. As applications, we study initial and boundary value problems of impulsive q kdifference equations and inclusions equipped with different kinds of boundary conditions. The eulerlagrange equation and its appli cations to the isoperimetric. Lets assume that the captain turns off the engine at the point p, q on the curve y x 2, and then try to determine what values p and q must have so that the resulting tangent line to the curve will go through the point 3,5. Finally they show how the calculus of finite differences can be derived in an analogous manner. How to read mathematics reading mathematics is not the same as reading a novel. This monograph is an introduction to combining approximation theory and qcalculus with applications, by using well known operators.
In the first part, we discuss the concepts of q kderivative and q kintegral, and establish their basic properties. Calculusintroduction wikibooks, open books for an open world. If time permits, i will show some applications of the qcalculus in number theory and physics. If time permits, i will show some applications of the q calculus in number theory and physics. Thomson pdf at calculus made easy being a very simplest introduction to those beautiful methods of recknoning which are generally called by the terrifying names of the differntial calculus and the integral calculus. In the years thereafter, numerous generalizations, extensions and variations of the opial inequality have appeared see 12, 14. This is the mathematics all of us need in order to function in the real world.
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