Calculus A Rigorous First Course

Author: Daniel J. Velleman
Publisher: Courier Dover Publications
ISBN: 9780486809366
Size: 12.15 MB
Format: PDF, ePub, Mobi
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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.

A First Course In Calculus

Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 9781441985323
Size: 15.72 MB
Format: PDF, ePub, Docs
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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.

Short Calculus

Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 9781461300779
Size: 13.11 MB
Format: PDF, Kindle
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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

A First Course In Real Analysis

Author: Murray H. Protter
Publisher: Springer Science & Business Media
ISBN: 9781441987440
Size: 11.62 MB
Format: PDF, Kindle
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Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.

A First Course In Mathematical Analysis

Author: David Alexander Brannan
Publisher: Cambridge University Press
ISBN: 9781139458955
Size: 15.10 MB
Format: PDF, ePub, Docs
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Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject.

The Calculus Primer

Author: William L. Schaaf
Publisher: Courier Corporation
ISBN: 9780486485799
Size: 14.17 MB
Format: PDF, ePub
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This comprehensive but concise introductory workbook is less rigorous than most calculus texts. Its informal and accessible treatment explains functions, derivatives, differentiation of algebraic functions and transcendental functions, partial differentiation, indeterminate forms, general and special methods of integration, the definite integral, partial integration, and other fundamentals. 1963 edition.

Calculus Deconstructed

Author: Zbigniew H. Nitecki
Publisher: MAA
ISBN: 0883857561
Size: 15.47 MB
Format: PDF, ePub, Docs
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A thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous experience of calculus techniques. This book can be used as a textbook for an undergraduate course on calculus or as a reference for self-study.