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Advanced Calculus

Advanced Calculus Pdf/ePub eBook Author: Lynn Harold Loomis,Shlomo Sternberg
Editor: World Scientific Publishing Company
ISBN: 9814583952
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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Summary

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 Pdf/ePub eBook Author: Morris Kline
Editor: Courier Corporation
ISBN: 0486134768
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Calculus by Morris Kline Summary

Application-oriented introduction relates the subject as closely as possible to science with explorations of the derivative; differentiation and integration of the powers of x; theorems on differentiation, antidifferentiation; the chain rule; trigonometric functions; more. Examples. 1967 edition.

A Tour of the Calculus

A Tour of the Calculus Pdf/ePub eBook Author: David Berlinski
Editor: Vintage
ISBN: 030778973X
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A Tour of the Calculus by David Berlinski Summary

Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review


Calculus Pdf/ePub eBook Author: Ron Larson,Bruce H. Edwards
Editor: Nelson Education
ISBN: 1337275344
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Calculus by Ron Larson,Bruce H. Edwards Summary

With a long history of innovation in the calculus market, the Larson CALCULUS program has been widely praised by a generation of students and professors for solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title in the series is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. For use in or out of the classroom, the companion website offers free access to multiple tools and resources to supplement students’ learning. Stepped-out solution videos with instruction are available at for selected exercises throughout the text. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Fractional Calculus for Hydrology, Soil Science and Geomechanics

Fractional Calculus for Hydrology, Soil Science and Geomechanics Pdf/ePub eBook Author: Ninghu Su
Editor: CRC Press
ISBN: 1351032402
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Fractional Calculus for Hydrology, Soil Science and Geomechanics by Ninghu Su Summary

This book is an unique integrated treatise, on the concepts of fractional calculus as models with applications in hydrology, soil science and geomechanics. The models are primarily fractional partial differential equations (fPDEs), and in limited cases, fractional differential equations (fDEs). It develops and applies relevant fPDEs and fDEs mainly to water flow and solute transport in porous media and overland, and in some cases, to concurrent flow and energy transfer. It is an integrated resource with theory and applications for those interested in hydrology, hydraulics and fluid mechanics. The self-contained book summaries the fundamentals for porous media and essential mathematics with extensive references supporting the development of the model and applications.


Calculus Pdf/ePub eBook Author: James Stewart
Editor: Nelson Education
ISBN: 1285740629
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Calculus by James Stewart Summary

James Stewart’s CALCULUS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart’s trademark style, while instructors have turned to his approach time and time again. In the Eighth Edition of CALCULUS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart’s texts best-sellers continue to provide a strong foundation for the Eighth Edition. From the most unprepared student to the most mathematically gifted, Stewart’s writing and presentation serve to enhance understanding and build confidence. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

The History of the Calculus and Its Conceptual Development

The History of the Calculus and Its Conceptual Development Pdf/ePub eBook Author: Carl B. Boyer
Editor: Courier Corporation
ISBN: 0486175383
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The History of the Calculus and Its Conceptual Development by Carl B. Boyer Summary

Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz.

Calculus For Dummies

Calculus For Dummies Pdf/ePub eBook Author: Mark Ryan
Editor: John Wiley & Sons
ISBN: 1119297435
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Calculus For Dummies by Mark Ryan Summary

Calculus For Dummies, 2nd Edition (9781119293491) was previously published as Calculus For Dummies, 2nd Edition (9781118791295). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be. Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is—simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win. Includes foundations in algebra, trigonometry, and pre-calculus concepts Explores sequences, series, and graphing common functions Instructs you how to approximate area with integration Features things to remember, things to forget, and things you can't get away with Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.


CALCULUS Pdf/ePub eBook Author: Dinesh Khattar,Kavita Gupta
Editor: PHI Learning Pvt. Ltd.
ISBN: 8120353609
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CALCULUS by Dinesh Khattar,Kavita Gupta Summary

Written from examination point of view, this textbook provides the basic concepts of calculus to the undergraduate students of all disciplines (Honours courses) other than Mathematics (Hons.) of all Central Universities of India following Choice Based Credit System (CBCS) including University of Delhi. The text follows a student-centric approach which communicates the practical aspects of Mathematics in such a way that it drives out the common fear of learning any mathematical subject. The concepts are properly supported by illustrations followed by several varied types of examples to provide students an integrated view of theory and applications. There are about four hundred examples in this book and the concepts are explained geometrically through numerous figures. A large number of self-practice problems with hints and answers have been added in each chapter to enable students to learn. Most of the questions conform to the examination-style universities of Indian. SALIENT FEATURES • Gives step by step procedure of solving worked problems for better understanding • Includes Chapter Objectives at the beginning of each chapter. • Familiarizes students with the basic techniques of calculus used in analysing the behaviour of a function.

Non-Newtonian Calculus

Non-Newtonian Calculus Pdf/ePub eBook Author: Michael Grossman,Robert Katz
Editor: Non-Newtonian Calculus
ISBN: 9780912938011
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Non-Newtonian Calculus by Michael Grossman,Robert Katz Summary

The non-Newtonian calculi provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They appear to have considerable potential for use as alternatives to the classical calculus of Newton and Leibniz. It may well be that these calculi can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.

Multiple Integrals in the Calculus of Variations

Multiple Integrals in the Calculus of Variations Pdf/ePub eBook Author: Charles Bradfield Morrey Jr.
Editor: Springer Science & Business Media
ISBN: 354069952X
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Multiple Integrals in the Calculus of Variations by Charles Bradfield Morrey Jr. Summary

From the reviews: "...the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. ...The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book." M. R. Hestenes in Journal of Optimization Theory and Applications "The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems." L. Schmetterer in Monatshefte für Mathematik "The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book." M. Coroi-Nedeleu in Revue Roumaine de Mathématiques Pures et Appliquées

Advanced Calculus

Advanced Calculus Pdf/ePub eBook Author: James J. Callahan
Editor: Springer Science & Business Media
ISBN: 9781441973320
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Advanced Calculus by James J. Callahan Summary

With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.

Functional Fractional Calculus for System Identification and Controls

Functional Fractional Calculus for System Identification and Controls Pdf/ePub eBook Author: Shantanu Das
Editor: Springer Science & Business Media
ISBN: 3540727035
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Functional Fractional Calculus for System Identification and Controls by Shantanu Das Summary

In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.

A First Course in the Calculus of Variations

A First Course in the Calculus of Variations Pdf/ePub eBook Author: Mark Kot
Editor: American Mathematical Society
ISBN: 1470414953
FileSize: 1970kb
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A First Course in the Calculus of Variations by Mark Kot Summary

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.

Calculus of Variations

Calculus of Variations Pdf/ePub eBook Author: I. M. Gelfand,S. V. Fomin
Editor: Courier Corporation
ISBN: 0486135012
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Calculus of Variations by I. M. Gelfand,S. V. Fomin Summary

Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.

Advances in Fractional Calculus

Advances in Fractional Calculus Pdf/ePub eBook Author: J. Sabatier,O. P. Agrawal,J. A. Tenreiro Machado
Editor: Springer Science & Business Media
ISBN: 1402060424
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Advances in Fractional Calculus by J. Sabatier,O. P. Agrawal,J. A. Tenreiro Machado Summary

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Introduction to Integral Calculus

Introduction to Integral Calculus Pdf/ePub eBook Author: Ulrich L. Rohde,G. C. Jain,Ajay K. Poddar,A. K. Ghosh
Editor: John Wiley & Sons
ISBN: 1118130332
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Introduction to Integral Calculus by Ulrich L. Rohde,G. C. Jain,Ajay K. Poddar,A. K. Ghosh Summary

An accessible introduction to the fundamentals of calculusneeded to solve current problems in engineering and the physicalsciences I ntegration is an important function of calculus, andIntroduction to Integral Calculus combines fundamental conceptswith scientific problems to develop intuition and skills forsolving mathematical problems related to engineering and thephysical sciences. The authors provide a solid introduction tointegral calculus and feature applications of integration,solutions of differential equations, and evaluation methods. Withlogical organization coupled with clear, simple explanations, theauthors reinforce new concepts to progressively build skills andknowledge, and numerous real-world examples as well as intriguingapplications help readers to better understand the connectionsbetween the theory of calculus and practical problem solving. The first six chapters address the prerequisites needed tounderstand the principles of integral calculus and explore suchtopics as anti-derivatives, methods of converting integrals intostandard form, and the concept of area. Next, the authors reviewnumerous methods and applications of integral calculus,including: Mastering and applying the first and second fundamental theoremsof calculus to compute definite integrals Defining the natural logarithmic function using calculus Evaluating definite integrals Calculating plane areas bounded by curves Applying basic concepts of differential equations to solveordinary differential equations With this book as their guide, readers quickly learn to solve abroad range of current problems throughout the physical sciencesand engineering that can only be solved with calculus. Examplesthroughout provide practical guidance, and practice problems andexercises allow for further development and fine-tuning of variouscalculus skills. Introduction to Integral Calculus is an excellentbook for upper-undergraduate calculus courses and is also an idealreference for students and professionals who would like to gain afurther understanding of the use of calculus to solve problems in asimplified manner.

The Calculus

The Calculus Pdf/ePub eBook Author: Otto Toeplitz
Editor: University of Chicago Press
ISBN: 9780226806693
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The Calculus by Otto Toeplitz Summary

When first published posthumously in 1963, this bookpresented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique approach, Toeplitz summarized and elucidated the major mathematical advances that contributed to modern calculus. Reissued for the first time since 1981 and updated with a new foreword, this classic text in the field of mathematics is experiencing a resurgence of interest among students and educators of calculus today.

Malliavin Calculus for Lévy Processes with Applications to Finance

Malliavin Calculus for Lévy Processes with Applications to Finance Pdf/ePub eBook Author: Giulia Di Nunno,Bernt Øksendal,Frank Proske
Editor: Springer Science & Business Media
ISBN: 9783540785729
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Malliavin Calculus for Lévy Processes with Applications to Finance by Giulia Di Nunno,Bernt Øksendal,Frank Proske Summary

This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.