A First Course In Calculus

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 741 pages
File Size : 47,5 Mb
Release : 2012-09-17
Category : Mathematics
ISBN : 9781441985323

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A First Course in Calculus by Serge Lang Pdf

This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.

Author : Serge Lang
Publisher : Unknown
Page : 0 pages
File Size : 53,7 Mb
Release : 1964
Category : Calculus
ISBN : LCCN:cvx00871171

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A First Course in Calculus by Serge Lang Pdf

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461300779

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Short Calculus by Serge Lang Pdf

From the reviews "This is a reprint of the original edition of Lang’s ‘A First Course in Calculus’, which was first published in 1964....The treatment is ‘as rigorous as any mathematician would wish it’....[The exercises] are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging....There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." --Mathematical Gazette

Author : Mark Kot
Publisher : American Mathematical Society
Page : 298 pages
File Size : 42,9 Mb
Release : 2014-10-06
Category : Mathematics
ISBN : 9781470414955

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A First Course in the Calculus of Variations by Mark Kot Pdf

This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.

Author : Daniel J. Velleman
Publisher : Courier Dover Publications
Page : 737 pages
File Size : 41,8 Mb
Release : 2017-01-18
Category : Mathematics
ISBN : 9780486809366

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Calculus: A Rigorous First Course by Daniel J. Velleman Pdf

Designed for undergraduate mathematics majors, this rigorous and rewarding treatment covers the usual topics of first-year calculus: limits, derivatives, integrals, and infinite series. Author Daniel J. Velleman focuses on calculus as a tool for problem solving rather than the subject's theoretical foundations. Stressing a fundamental understanding of the concepts of calculus instead of memorized procedures, this volume teaches problem solving by reasoning, not just calculation. The goal of the text is an understanding of calculus that is deep enough to allow the student to not only find answers to problems, but also achieve certainty of the answers' correctness. No background in calculus is necessary. Prerequisites include proficiency in basic algebra and trigonometry, and a concise review of both areas provides sufficient background. Extensive problem material appears throughout the text and includes selected answers. Complete solutions are available to instructors.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 624 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210689

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Calculus of Several Variables by Serge Lang Pdf

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

Author : Zbigniew H. Nitecki
Publisher : American Mathematical Society
Page : 491 pages
File Size : 44,5 Mb
Release : 2022-01-11
Category : Mathematics
ISBN : 9781470466756

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Calculus Deconstructed by Zbigniew H. Nitecki Pdf

Calculus Deconstructed is a thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof. This book is appropriate for a beginning Honors Calculus course assuming high school calculus or a "bridge course" using basic analysis to motivate and illustrate mathematical rigor. It can serve as a combination textbook and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive historical notes explore the arguments of the originators of the subject. No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof (reductio ad absurdum, induction, contrapositives, etc.) are introduced by example along the way. Between the text and exercises, proofs are available for all the basic results of calculus for functions of one real variable.

Author : Thomas M. K. Davison,James Stewart,Bryan Ferroni
Publisher : McGraw-Hill Ryerson
Page : 128 pages
File Size : 49,8 Mb
Release : 2002
Category : Calculus
ISBN : 0070922055

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Solutions Manual for Calculus, a First Course by Thomas M. K. Davison,James Stewart,Bryan Ferroni Pdf

Author : Louis-Pierre Arguin
Publisher : American Mathematical Society
Page : 270 pages
File Size : 52,7 Mb
Release : 2021-11-22
Category : Mathematics
ISBN : 9781470464882

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A First Course in Stochastic Calculus by Louis-Pierre Arguin Pdf

A First Course in Stochastic Calculus is a complete guide for advanced undergraduate students to take the next step in exploring probability theory and for master's students in mathematical finance who would like to build an intuitive and theoretical understanding of stochastic processes. This book is also an essential tool for finance professionals who wish to sharpen their knowledge and intuition about stochastic calculus. Louis-Pierre Arguin offers an exceptionally clear introduction to Brownian motion and to random processes governed by the principles of stochastic calculus. The beauty and power of the subject are made accessible to readers with a basic knowledge of probability, linear algebra, and multivariable calculus. This is achieved by emphasizing numerical experiments using elementary Python coding to build intuition and adhering to a rigorous geometric point of view on the space of random variables. This unique approach is used to elucidate the properties of Gaussian processes, martingales, and diffusions. One of the book's highlights is a detailed and self-contained account of stochastic calculus applications to option pricing in finance. Louis-Pierre Arguin's masterly introduction to stochastic calculus seduces the reader with its quietly conversational style; even rigorous proofs seem natural and easy. Full of insights and intuition, reinforced with many examples, numerical projects, and exercises, this book by a prize-winning mathematician and great teacher fully lives up to the author's reputation. I give it my strongest possible recommendation. —Jim Gatheral, Baruch College I happen to be of a different persuasion, about how stochastic processes should be taught to undergraduate and MA students. But I have long been thinking to go against my own grain at some point and try to teach the subject at this level—together with its applications to finance—in one semester. Louis-Pierre Arguin's excellent and artfully designed text will give me the ideal vehicle to do so. —Ioannis Karatzas, Columbia University, New York

Author : George Pedrick
Publisher : Springer Science & Business Media
Page : 293 pages
File Size : 51,8 Mb
Release : 2012-09-10
Category : Mathematics
ISBN : 9781441985545

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A First Course in Analysis by George Pedrick Pdf

This text on advanced calculus discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The reader will find the focus of attention shifted from the learning and applying of computational techniques to careful reasoning from hypothesis to conclusion. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation.

Author : John B. Conway
Publisher : Cambridge University Press
Page : 357 pages
File Size : 51,6 Mb
Release : 2018
Category : Mathematics
ISBN : 9781107173149

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A First Course in Analysis by John B. Conway Pdf

This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.

Author : M.H. Protter,C.B. Jr. Morrey
Publisher : Springer Science & Business Media
Page : 520 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461599906

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A First Course in Real Analysis by M.H. Protter,C.B. Jr. Morrey Pdf

The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.

Author : Dan Saracino
Publisher : Waveland Press
Page : 320 pages
File Size : 40,7 Mb
Release : 2008-09-02
Category : Mathematics
ISBN : 9781478610137

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Abstract Algebra by Dan Saracino Pdf

The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.

Author : Sunanda Roy
Publisher : Cambridge Scholars Publishing
Page : 364 pages
File Size : 42,7 Mb
Release : 2020-03-17
Category : Business & Economics
ISBN : 9781527548534

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A First Course in Mathematical Economics by Sunanda Roy Pdf

The book studies a set of mathematical tools and techniques most necessary for undergraduate economics majors as they transition from largely non-technical first-year principles courses into calculus-based upper-level courses in economics. The book’s presentation style places more emphasis on the intuition underlying the mathematical concepts and results discussed and less on proofs and technical details. Its discussion topics have been chosen in terms of their immediate usefulness for beginners, while examples and applications are drawn from material that is familiar from introductory economics courses.

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 43,6 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.