Differential And Integral Calculus Theory And Cases
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Differential and Integral Calculus Theory and Cases by Carlos Polanco Pdf
Differential and Integral Calculus - Theory and Cases is a complete textbook designed to cover basic calculus at introductory college and undergraduate levels. Chapters provide information about calculus fundamentals and concepts including real numbers, series, functions, limits, continuity, differentiation, antidifferentiation (integration) and sequences. Readers will find a concise and clear study of calculus topics, giving them a solid foundation of mathematical analysis using calculus. The knowledge and concepts presented in this book will equip students with the knowledge to immediately practice the learned calculus theory in practical situations encountered at advanced levels. Key Features: - Complete coverage of basic calculus, including differentiation and integration - Easy to read presentation suitable for students - Information about functions and maps - Case studies and exercises for practical learning, with solutions - Case studies and exercises for practical learning, with solutions - References for further reading
Exterior Calculus: Theory and Cases by Carlos Polanco Pdf
Exterior calculus is a branch of mathematics which involves differential geometry. In Exterior calculus the concept of differentiations is generalized to antisymmetric exterior derivatives and the notions of ordinary integration to differentiable manifolds of arbitrary dimensions. It therefore generalizes the fundamental theorem of calculus to Stokes' theorem. This textbook covers the fundamental requirements of exterior calculus in curricula for college students in mathematics and engineering programs. Chapters start from Heaviside-Gibbs algebra, and progress to different concepts in Grassman algebra. The final section of the book covers applications of exterior calculus with solutions. Readers will find a concise and clear study of vector calculus and differential geometry, along with several examples and exercises. The solutions to the exercises are also included at the end of the book. This is an ideal book for students with a basic background in mathematics who wish to learn about exterior calculus as part of their college curriculum and equip themselves with the knowledge to apply relevant theoretical concepts in practical situations.
Differential and Integral Calculus, Volume 1 by Richard Courant Pdf
The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of "function" and "limit", and offers detailed explanations that illustrate the "why" as well as the "how". Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems.
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.
Excerpt from Advanced Calculus: A Text Upon Select Parts of Differential Calculus, Differential Equations, Integral Calculus, Theory of Functions It is probable that almost every teacher of advanced calculus feels the need of a text suited to present conditions and adaptable to his use. To write such a book is extremely difficult, for the attainments of students who enter a second course in calculus are different, their needs are not uniform, and the viewpoint of their teachers is no less varied. Yet in view of the cost of time and money involved in producing an Advanced Calculus, in proportion to the small number of students who will use it, it seems that few teachers can afford the luxury of having their own text; and that it consequently devolves upon an author to take as nu selfish and unprejudiced a View of the subject as possible, and, so far as in him lies, to produce a book which shall have the maximum flexibility and adaptability. It was the recognition of this duty that has kept the present work in a perpetual state of growth and modification during five or six years of composition: Every attempt has been made to write in such a manner that the individual teacher may feel the minimum embarrassment in picking and choosing What seems to him best to meet the needs of any particular class. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Excerpt from Advanced Calculus: A d104 Upon Select Parts of Differential Calculus, Differential Equations, Integral Calculus, Theory of Functions, With Numerous Exercises It is probable that almost every teacher of advanced calculus feels the need of a text suited to present conditions and adaptable to his use. To write such a book is extremely difficult, for the attainments of students who enter a second course in calculus are different, their needs are not uniform, and the viewpoint of their teachers is no less varied. Yet in view of the cost of time and money involved in producing an Advanced Calculus, in proportion to the small number of students who will use it, it seems that few teachers can afford the luxury of having their own text; and that it consequently devolves upon an author to take as un selfish and unprejudiced a view of the subject as possible, and, so far as In him lies, to produce a book which shall have the maximum flexibility and adaptability. It was the recognition of this duty that has kept the present work in a perpetual state of growth and modification during five or six years of composition. Every attempt has been made to write in such a manner that the individual teacher may feel the minimum embarrassment in picking and choosing what seems to him best to meet the needs of any particular class. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Differential and Integral Calculus (Classic Reprint) by Clyde E. Love Pdf
Excerpt from Differential and Integral Calculus In the treatment of each topic, the text is intended to contain a precise statement of the fundamental principle involved, and to insure the student's clear understanding of this principle, Without distracting his attention by the discussion of a multitude of details. The accompanying exercises are intended to present the problem in hand in a great variety of forms and guises, and to train the stu dent in adapting the general methods of the text to fit these various forms. The constant aim is to prevent the work from degenerating into mere mechanical routine, as it so often tends to do. Wherever possible, except in the purely formal parts of the course, the summarizing of the theory into rules or formulas which can be applied blindly has been avoided. For instance, in the chapter on geo metric applications of the definite integral, stress is laid on the fact that the basic formulas are those of elemen tary geometry, and special formulas involving a coordinate system are omitted. Where the passage from theory to practice would be too difficult for the average student, worked examples are inserted. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Integral Calculus for Beginners by Alfred Lodge Pdf
This is a companion volume to Professor Lodge's Differential Calculus for Beginners. In that volume the student was prepared to practice retracing his steps, and thus, without the use of the integral notation, to perform the operation of integration or anti-differentiation in simple cases. Hence the author is in a position to commence this volume by exhibiting an integral as the limit of a sum; and that no time is wasted in getting to business is evidenced by the fact that the centre of gravity of a parabolic area is worked out at p. 9. The standard methods of integration are clearly explained and illustrated in the first five chapters. The most novel feature of the book is perhaps the seventh chapter dealing with approximate methods of integration. Here, after the well-known rules of Simpson and Weddle, approximate formulae, recently devised by Mr. R. W. K. Edwards and Professor Lodge himself, are given, for dealing with the case in which the curvilinear boundary of a required area cuts the axis at right angles; a case for which, as is well known, rules of the Simpson type are not well fitted. Interesting approximate formulae for the elliptic integrals are also given. A chapter on Moments of Inertia is very welcome, and the book concludes with a chapter on the Gamma functions and with chapters on the differential equations, other than partial, of most frequent occurrence. The suggestion may be submitted for consideration in a future edition that, while doubtless the theory of Amster's planimeter is too difficult for a first book on the Integral Calculus, yet some of the earlier instruments described in Professor Henrici's British Association report (1894) perform the process of summing up ydx in an obvious manner; and the Integraphs of Professors Boys and Abdank Abakanowicz are also exceedingly interesting concrete embodiments of Integration, viewed as the converse of differentiation. Professor Lodge's book is likely to maintain the position which his book on the Differential Calculus has won. -The Mathematical Gazette.
Advanced Calculus: A Text Upon Select Parts of Differential Calculus, Differential Equations, Integral Calculus, Theory of Functions; Wit by Edwin Bidwell Wilson Pdf
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Elements of the Differential, and Integral Calculus (Revised by William Anthony Granville Pdf
Excerpt from Elements of the Differential, and Integral Calculus (Revised: Edition) That teachers and students of the Calculus have shown such a generous appreciation of Granville's "Elements of the Differential and Integral Calculus" has been very gratifying to the author. In the last few years considerable progress has been made in the teaching of the elements of the Calculus, and in this revised edition of Granville's "Calculus" the latest and best methods are exhibited, - methods that have stood the test of actual classroom work. Those features of the first edition which contributed so much to its usefulness and popularity have been retained. The introductory matter has been cut down somewhat in order to get down to the real business of the Calculus sooner. As this is designed essentially for a drill book, the pedagogic principle that each result should be made intuitionally as well as analytically evident to the student has been kept constantly in mind. The object is not to teach the student to rely on his intuition, but, in some cases, to use this faculty in advance of analytical investigation. Graphical illustration has been drawn on very liberally. This Calculus is based on the method of limits and is divided into two main parts, - Differential Calculus and Integral Calculus. As special features, attention may be called to the effort to make perfectly clear the nature and extent of each new theorem, the large number of carefully graded exercises, and the summarizing into working rules of the methods of solving problems. In the Integral Calculus the notion of integration over a plane area has been much enlarged upon, and integration as the limit of a summation is constantly emphasized. The existence of the limit e has been assumed and its approximate value calculated from its graph. A large number of new examples have been added, both with and without answers. At the end of almost every chapter will be found a collection of miscellaneous examples. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Differential and Integral Calculus for Beginners by Edwin Edser Pdf
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