Calculus Deconstructed
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Calculus Deconstructed
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Author : Zbigniew H. Nitecki
language : en
Publisher: MAA
Release Date : 2009-05-21
Calculus Deconstructed written by Zbigniew H. Nitecki and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-21 with Mathematics categories.
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 basica 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.
From Calculus To Analysis
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Author : Rinaldo B. Schinazi
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-25
From Calculus To Analysis written by Rinaldo B. Schinazi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-25 with Mathematics categories.
This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. From Calculus to Analysis prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.
Introduction To Calculus And Analysis Ii 1
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Author : Richard Courant
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-12-14
Introduction To Calculus And Analysis Ii 1 written by Richard Courant and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-14 with Mathematics categories.
From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991
A Course In Multivariable Calculus And Analysis
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Author : Sudhir R. Ghorpade
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-20
A Course In Multivariable Calculus And Analysis written by Sudhir R. Ghorpade and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-20 with Mathematics categories.
This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple integrals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Moreover, the emphasis is on a geometric approach to such basic notions as local extremum and saddle point. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike. There is also an informative section of "Notes and Comments’’ indicating some novel features of the treatment of topics in that chapter as well as references to relevant literature. The only prerequisite for this text is a course in one-variable calculus.
Elementary Analysis
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Author : Kenneth A. Ross
language : en
Publisher: CUP Archive
Release Date : 2014-01-15
Elementary Analysis written by Kenneth A. Ross and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with Mathematics categories.
Calculus And Analysis
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Author : Horst R. Beyer
language : en
Publisher: John Wiley & Sons
Release Date : 2010-04-26
Calculus And Analysis written by Horst R. Beyer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-26 with Mathematics categories.
A NEW APPROACH TO CALCULUS THAT BETTER ENABLES STUDENTS TO PROGRESS TO MORE ADVANCED COURSES AND APPLICATIONS Calculus and Analysis: A Combined Approach bridges the gap between mathematical thinking skills and advanced calculus topics by providing an introduction to the key theory for understanding and working with applications in engineering and the sciences. Through a modern approach that utilizes fully calculated problems, the book addresses the importance of calculus and analysis in the applied sciences, with a focus on differential equations. Differing from the common classical approach to the topic, this book presents a modern perspective on calculus that follows motivations from Otto Toeplitz's famous genetic model. The result is an introduction that leads to great simplifications and provides a focused treatment commonly found in the applied sciences, particularly differential equations. The author begins with a short introduction to elementary mathematical logic. Next, the book explores the concept of sets and maps, providing readers with a strong foundation for understanding and solving modern mathematical problems. Ensuring a complete presentation, topics are uniformly presented in chapters that consist of three parts: Introductory Motivations presents historical mathematical problems or problems arising from applications that led to the development of mathematical solutions Theory provides rigorous development of the essential parts of the machinery of analysis; proofs are intentionally detailed, but simplified as much as possible to aid reader comprehension Examples and Problems promotes problem-solving skills through application-based exercises that emphasize theoretical mechanics, general relativity, and quantum mechanics Calculus and Analysis: A Combined Approach is an excellent book for courses on calculus and mathematical analysis at the upper-undergraduate and graduate levels. It is also a valuable resource for engineers, physicists, mathematicians, and anyone working in the applied sciences who would like to master their understanding of basic tools in modern calculus and analysis.
Advanced Calculus Revised Edition
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Author : Lynn Harold Loomis
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-26
Advanced Calculus Revised Edition written by Lynn Harold Loomis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-26 with Mathematics categories.
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.
Calculus And Analysis In Euclidean Space
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Author : Jerry Shurman
language : en
Publisher: Springer
Release Date : 2016-11-26
Calculus And Analysis In Euclidean Space written by Jerry Shurman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-26 with Mathematics categories.
The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skills of geometric intuition (the visual cortex being quickly instinctive) algebraic manipulation (symbol-patterns being precise and robust) incisive use of natural language (slogans that encapsulate central ideas enabling a large-scale grasp of the subject). Thinking in these ways renders mathematics coherent, inevitable, and fluid. The prerequisite is single-variable calculus, including familiarity with the foundational theorems and some experience with proofs.
Calculus In 3d
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Author : Zbigniew Nitecki
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-16
Calculus In 3d written by Zbigniew Nitecki and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-16 with Mathematics categories.
Calculus in 3D is an accessible, well-written textbook for an honors course in multivariable calculus for mathematically strong first- or second-year university students. The treatment given here carefully balances theoretical rigor, the development of student facility in the procedures and algorithms, and inculcating intuition into underlying geometric principles. The focus throughout is on two or three dimensions. All of the standard multivariable material is thoroughly covered, including vector calculus treated through both vector fields and differential forms. There are rich collections of problems ranging from the routine through the theoretical to deep, challenging problems suitable for in-depth projects. Linear algebra is developed as needed. Unusual features include a rigorous formulation of cross products and determinants as oriented area, an in-depth treatment of conics harking back to the classical Greek ideas, and a more extensive than usual exploration and use of parametrized curves and surfaces. Zbigniew Nitecki is Professor of Mathematics at Tufts University and a leading authority on smooth dynamical systems. He is the author of Differentiable Dynamics, MIT Press; Differential Equations, A First Course (with M. Guterman), Saunders; Differential Equations with Linear Algebra (with M. Guterman), Saunders; and Calculus Deconstructed, AMS.
Elements Of Real Analysis
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Author : Charles Denlinger
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2011
Elements Of Real Analysis written by Charles Denlinger and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
A student-friendly guide to learning all the important ideas of elementary real analysis, this resource is based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors.