How to read mathematics reading mathematics is not the same as reading a novel. Finally they show how the calculus of finite differences can be derived in an analogous manner. 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. Ecs 20 chapter 4, logic using propositional calculus 0. The ideas are presented in a way to give only the essence of the ideas, techniques, and proofs. From there, i will prove q analogs of the binomial theorem and taylors theorem.
The first two thirds of volume 1 deals with the calculus of functions of one variable, including infinite series and an introduction to differential equations. 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. The first q analogue of the wellknown bernstein polynomials was introduced by lupas in the year 1987. It defines qcalculus and hcalculus, where h ostensibly stands for plancks constant while q stands for quantum. As you read mathematics, you must work alongside the text itself.
But it is easiest to start with finding the area under the curve of a function like this. Therefore expressions that differ only in the names of bound variables are identified. Integration can be used to find areas, volumes, central points and many useful things. 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. Discrete individually separate and distinct as opposed to continuous and capable of infinitesimal change. Here we present necessary definitions and facts from the q calculus. Our aim is to present new proofs of some results from q calculus. A blog by oliver knill on matters mathematics related to quantum calculus, or discrete geometry including graph theory or algebraic combinatorics. The last third of volume 1 introduces linear algebra with applications to geometry and analysis. 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. Discrete mathematics introduction to propositional logic. Mar 28, 2014 get full course delivered at your home. Integration is a way of adding slices to find the whole. A background of the usage of the q calculus in the context of geometric funciton.
The first qanalogue of the wellknown bernstein polynomials was introduced by lupas in the year 1987. Quantum calculus, sometimes called calculus without limits, is equivalent to traditional infinitesimal calculus without the notion of limits. Pdf in this article, we let pcq denote the class of q convex functions. Anthony ciavarella july 1, 2016 abstract in this talk, i will present a q analog of the classical derivative from calculus. The two parameters are related by the formula where is the reduced planck constant. The notes were written by sigurd angenent, starting from an extensive collection of notes and problems compiled by joel robbin.
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. We propose qversions of some basic concepts of continuous variational calculus such as. Pdf in this article, we let pcq denote the class of qconvex functions. Pdf introduction to lambda calculus semantic scholar. In the first part, we discuss the concepts of q kderivative and q kintegral, and establish their basic properties.
These apparently disconnected themes, formalized in integral calculus and di erential calculus, respectively, come together in. We follow the terminology and notations used in the books 8, 9, 11. This notes contains the following subcategories calculus, introduction to number theory and vector calculus. Thomas calculus th edition pdf is a perfect textbook to familiarize yourself with basic and intermediate college calculus lessons and training.
This monograph is an introduction to combining approximation theory and qcalculus with applications, by using well known operators. This can be further developed and completed by the reader. Sengupta 1162011 introduction there are two fundamental notions that led to the development of calculus historically. 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. If time permits, i will show some applications of the q. If time permits, i will show some applications of the q calculus in number theory and physics. In this chapter, we will develop the concept of a limit by example. 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. Integral calculus joins integrates the small pieces together to find how much there is. Here is a nice diversion for anyone who knows what is the derivative of a simple function. We will use limits to analyze asymptotic behaviors of functions and their graphs.
Introduction of qcalculus request pdf researchgate. Mooculus massive open online calculus calculus this document was typeset on april 10, 2014. First it gives a very clear and rather complete introduction to qanalogues of elementary calculus, which the authors call quantumcalculus. This monograph is an introduction to combining approximation theory and q calculus with applications, by using well known operators. 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. 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. Properties of limits will be established along the way. A new notation and a new method for qhypergeometric series. Quantum calculus trends in abstract and applied analysis. This leads us into the exciting world of quantum calculus, also known as qcalculus. This category contains pages that are part of the calculus book. Applications of qcalculus in operator theory ali aral.
The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q calculus before delving into more advanced material. Partitions, generalized vandermonde determinants and representation theory. 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. Introduction to logic using propositional calculus and proof 1. If you have ever taking a course in college level calculus, you will find this book very useful to. Calculusintroduction wikibooks, open books for an open world. The eulerlagrange equation and its appli cations to the isoperimetric. Math 221 1st semester calculus lecture notes version 2.
This is the mathematics all of us need in order to function in the real world. Easily find the introduction to thermodynamics with calculus equation that youre looking for. Calculusintroduction wikibooks, open books for an open. Request pdf introduction of qcalculus in the field of approximation theory, the applications of qcalculus are new area in last 25 years. A background of the usage of the qcalculus in the context of geometric funciton. As applications, we study initial and boundary value problems of impulsive q kdifference equations and inclusions equipped with different kinds of boundary conditions. You can view a list of all subpages under the book main page not including the book main page itself, regardless of. Here are my online notes for my calculus i course that i teach here at lamar university. In the field of approximation theory, the applications of q calculus are new area in last 25 years.
The lessons in this course are organized as follows. This notes contain real numbers, functions, derivatives, integration theory and sequences. The scope is broader than is usual in an introduction, embracing not only the differential. Limits will be formally defined near the end of the chapter.
In what follows, q is a real number satisfying 0 q q natural number is defined by. The conventional approach to calculus is founded on limits. 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. This is a history of qcalculus with a new notation and a new method for qhypergeometric series. In 1997 phillips considered another qanalogue of the classical bernstein polynomials. Given the series 42, 43, 3, 18, 34, the differential of this series would be 1, 40, 15, 16. The slos identify the knowledge and skills you should have. Introduction in this chapter we introduce limits and derivatives. In the field of approximation theory, the applications of qcalculus are new area in last 25 years.
Jul 17, 2017 today we introduce propositional logic. In precise terms, we study quantum calculus on finite intervals. Differential calculus cuts something into small pieces to find how it changes. Introduction to thermodynamics with calculus equations. These results occur in many applications as physics, quantum theory, number theory, statistical. It defines q calculus and h calculus, where h ostensibly stands for plancks constant while q stands for quantum. If time permits, i will show some applications of the qcalculus in number theory and physics. From there, i will prove qanalogs of the binomial theorem and taylors theorem.
This leads us into the exciting world of quantum calculus, also known as q calculus. The second theme is an application to number theory. In 1997 phillips considered another q analogue of the classical bernstein polynomials. Michael spivak brandeis university calculus on manifolds a modern approach to classical theorems. Lecture notes in calculus pdf 206p this is useful notes for calculus. We talk about what statements are and how we can determine truth values. Quantum derivatives and integrals play a leading role in the understanding of com. If a page of the book isnt showing here, please add text bookcat to the end of the page concerned. This chapter will jump directly into the two problems that the subject was invented to solve. If you dont know the difference between 15,000 and 150,000, you probably shouldnt try to buy a new car. Anthony ciavarella july 1, 2016 abstract in this talk, i will present a qanalog of the classical derivative from calculus. In this section we mention some basic definitions of qcalculus, which would be used throughout the book. Applications of qcalculus in operator theory springerlink.
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