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Advanced Calculus

Advanced Calculus Pdf/ePub eBook Author: ,
Editor: World Scientific Publishing Company
ISBN: 9814583952
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Advanced Calculus by , 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 Made Easy

Calculus Made Easy Pdf/ePub eBook Author: Silvanus Phillips Thompson
Editor: Read Books Ltd
ISBN: 1446547728
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Calculus Made Easy by Silvanus Phillips Thompson Summary

This antiquarian volume contains a concise exposition of elementary calculus, being a very simple introduction to differential and integral calculus. In writing this text the author has aimed to furnish in the most practical and understandable manner, the fundamentals of calculus, specially designed for those with an interest in the topic but with limited previous knowledge and an understandable reticence about beginning their calculus adventure. Written in clear, simple language and full of useful information and clear explanations, this text is ideal for the student and anyone with a desire to advance their mathematical knowledge. The chapters of this volume include: 'To Deliver You From the Preliminary Terrors', 'On Different Degrees of Smallness', 'On Relative Growings', 'Simplest Cases', 'What to do with Constants', 'Successive Differentiation', 'When Time Varies', 'Introducing a Useful Dodge', 'Geometrical Meaning of Differentiation', et cetera. We are republishing this vintage work now complete with a specially commissioned new biography of the author.

Differential and Integral Calculus

Differential and Integral Calculus Pdf/ePub eBook Author: Richard Courant
Editor: John Wiley & Sons
ISBN: 1118031490
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Differential and Integral Calculus by Richard Courant Summary

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.

Fundamentals of Calculus

Fundamentals of Calculus Pdf/ePub eBook Author: Carla C. Morris,Robert M. Stark
Editor: John Wiley & Sons
ISBN: 1119015316
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Fundamentals of Calculus by Carla C. Morris,Robert M. Stark Summary

Features the techniques, methods, and applications of calculus using real-world examples from business and economics as well as the life and social sciences An introduction to differential and integral calculus, Fundamentals of Calculus presents key topics suited for a variety of readers in fields ranging from entrepreneurship and economics to environmental and social sciences. Practical examples from a variety of subject areas are featured throughout each chapter and step-by-step explanations for the solutions are presented. Specific techniques are also applied to highlight important information in each section, including symbols interspersed throughout to further reader comprehension. In addition, the book illustrates the elements of finite calculus with the varied formulas for power, quotient, and product rules that correlate markedly with traditional calculus. Featuring calculus as the “mathematics of change,” each chapter concludes with a historical notes section. Fundamentals of Calculus chapter coverage includes: Linear Equations and Functions The Derivative Using the Derivative Exponents and Logarithms Differentiation Techniques Integral Calculus Integrations Techniques Functions of Several Variables Series and Summations Applications to Probability Supplemented with online instructional support materials, Fundamentals of Calculus is an ideal textbook for undergraduate students majoring in business, economics, biology, chemistry, and environmental science.

Calculus With Applications

Calculus With Applications Pdf/ePub eBook Author: Peter D. Lax,Maria Shea Terrell
Editor: Springer Science & Business Media
ISBN: 1461479460
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Calculus With Applications by Peter D. Lax,Maria Shea Terrell Summary

Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory.

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.

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.

CALCULUS

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.

A Textbook of B.Sc. Mathematics (Differential Calculus) (For 1st Year, 1st Semester of Telangana Universities)

A Textbook of B.Sc. Mathematics (Differential Calculus) (For 1st Year, 1st Semester of Telangana Universities) Pdf/ePub eBook Author: Rao, Venkateswara V., Murthy, Krishna N., Sarma B.V.S.S., Sastry Anjaneya S. & Ranganatham S.
Editor: S. Chand Publishing
ISBN: 9352830385
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A Textbook of B.Sc. Mathematics (Differential Calculus) (For 1st Year, 1st Semester of Telangana Universities) by Rao, Venkateswara V., Murthy, Krishna N., Sarma B.V.S.S., Sastry Anjaneya S. & Ranganatham S. Summary

A Textbook of B.Sc. Mathematics

TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY AND THEIR APPLICATIONS

TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY AND THEIR APPLICATIONS Pdf/ePub eBook Author: Quddus Khan
Editor: Misha Books
ISBN: 9389055326
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TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY AND THEIR APPLICATIONS by Quddus Khan Summary

This book is intended to serve as a Textbook for Undergraduate and Post - graduate students of Mathematics. It will be useful to the researchers working in the field of Differential geometry and its applications to general theory of relativity and other applied areas. It will also be helpful in preparing for the competitive examinations like IAS, IES, NET, PCS, and UP Higher Education exams. The text starts with a chapter on Preliminaries discussing basic concepts and results which would be taken for general later in the subsequent chapters of this book. This is followed by the Study of the Tensors Algebra and its operations and types, Christoffel's symbols and its properties, the concept of covariant differentiation and its properties, Riemann's symbols and its properties, and application of tensor in different areas in part – I and the study of the Theory of Curves in Space, Concepts of a Surface and Fundamental forms, Envelopes and Developables, Curvature of Surface and Lines of Curvature, Fundamental Equations of Surface Theory, Theory of Geodesics, Differentiable Manifolds and Riemannian Manifold and Application of Differential Geometry in Part –II. KEY FEATURES: Provides basic Concepts in an easy to understand style; Presentation of the subject in a natural way; Includes a large number of solved examples and illuminating illustrations; Exercise questions at the end of the topic and at the end of each chapter; Proof of the theorems are given in an easy to understand style; Neat and clean figures are given at appropriate places; Notes and remarks are given at appropriate places.

Calculus Know-It-ALL

Calculus Know-It-ALL Pdf/ePub eBook Author: Stan Gibilisco
Editor: McGraw Hill Professional
ISBN: 0071549323
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Calculus Know-It-ALL by Stan Gibilisco Summary

Master calculus from the comfort of home! Want to "know it ALL" when it comes to calculus? This book gives you the expert, one-on-one instruction you need, whether you're new to calculus or you're looking to ramp up your skills. Providing easy-to-understand concepts and thoroughly explained exercises, math whiz Stan Gibilisco serves as your own private tutor--without the expense! His clear, friendly guidance helps you tackle the concepts and problems that confuse you the most and work through them at your own pace. Train your brain with ease! Calculus Know-It-ALL features: Checkpoints to help you track your knowledge and skill level Problem/solution pairs and chapter-ending quizzes to reinforce learning Fully explained answers to all practice exercises A multiple-choice exam to prepare you for standardized tests "Extra Credit" and "Challenge" problems to stretch your mind Stan's expert guidance gives you the know-how to: Understand mappings, relations, and functions Calculate limits and determine continuity Differentiate and integrate functions Analyze graphs using first and second derivatives Define and evaluate inverse functions Use specialized integration techniques Determine arc lengths, surface areas, and solid volumes Work with multivariable functions Take college entrance examinations with confidence And much more!

A Course in Calculus and Real Analysis

A Course in Calculus and Real Analysis Pdf/ePub eBook Author: Sudhir R. Ghorpade,Balmohan V. Limaye
Editor: Springer Science & Business Media
ISBN: 0387364250
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A Course in Calculus and Real Analysis by Sudhir R. Ghorpade,Balmohan V. Limaye Summary

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.

Best Practices for Flipping the College Classroom

Best Practices for Flipping the College Classroom Pdf/ePub eBook Author: Julee B. Waldrop,Melody A. Bowdon
Editor: Routledge
ISBN: 1317693787
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Best Practices for Flipping the College Classroom by Julee B. Waldrop,Melody A. Bowdon Summary

Best Practices for Flipping the College Classroom provides a comprehensive overview and systematic assessment of the flipped classroom methodology in higher education. The book: Reviews various pedagogical theories that inform flipped classroom practice and provides a brief history from its inception in K–12 to its implementation in higher education. Offers well-developed and instructive case studies chronicling the implementation of flipped strategies across a broad spectrum of academic disciplines, physical environments, and student populations. Provides insights and suggestions to instructors in higher education for the implementation of flipped strategies in their own courses by offering reflections on learning outcomes and student success in flipped classrooms compared with those employing more traditional models and by describing relevant technologies. Discusses observations and analyses of student perceptions of flipping the classroom as well as student practices and behaviors particular to flipped classroom models. Illuminates several research models and approaches for use and modification by teacher-scholars interested in building on this research on their own campuses. The evidence presented on the flipped classroom methodology by its supporters and detractors at all levels has thus far been almost entirely anecdotal or otherwise unreliable. Best Practices for Flipping the College Classroom is the first book to provide faculty members nuanced qualitative and quantitative evidence that both supports and challenges the value of flipping the college classroom.

The Hitchhiker's Guide to Calculus

The Hitchhiker's Guide to Calculus Pdf/ePub eBook Author: Michael Spivak
Editor: American Mathematical Soc.
ISBN: 1470449625
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The Hitchhiker's Guide to Calculus by Michael Spivak Summary

The Hitchhiker's Guide to Calculus begins with a rapid view of lines and slope. Spivak then takes up non-linear functions and trigonometric functions. He places the magnifying glass on curves in the next chapter and effortlessly leads the reader to the idea of derivative. In the next chapter he tackles speed and velocity, followed by the derivative of sine. Maxima and minima are next. Rolle's theorem and the MVT form the core of Chapter 11, "Watching Experts at Play." The Hitchhiker's Guide to Calculus closes with a chapter on the integral, the fundamental theorem, and applications of the integral.

Mathematics for Degree Students (For B.Sc. First Year)

Mathematics for Degree Students (For B.Sc. First Year) Pdf/ePub eBook Author: Mittal P.K.
Editor: S. Chand Publishing
ISBN: 8121932408
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Mathematics for Degree Students (For B.Sc. First Year) by Mittal P.K. Summary

Algebra >Functions And Relations >Congruence Of Integers >Some Special Types Of Matrices >Elementary Operations And Inverse Of A Matrix >Linear Dependance Of Vectors >Rank Of A Matrix >Linear Equations >Characteristic Roots Of Vectors >Theory Of Equations

Practice Makes Perfect Calculus

Practice Makes Perfect Calculus Pdf/ePub eBook Author: Dr. William Clark,Sandra McCune
Editor: McGraw Hill Professional
ISBN: 0071638164
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Practice Makes Perfect Calculus by Dr. William Clark,Sandra McCune Summary

For students who need to polish their calculus skills for class or for a critical exam, this no-nonsense practical guide provides concise summaries, clear model examples, and plenty of practice, practice, practice. About the Book With more than 1,000,000 copies sold, Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Calculus, students will enjoy the same clear, concise approach and extensive exercises to key fields they've come to expect from the series--but now within mathematics. Practice Makes Perfect: Calculus is not focused on any particular test or exam, but complementary to most calculus curricula. Because of this approach, the book can be used by struggling students needing extra help, readers who need to firm up skills for an exam, or those who are returning to the subject years after they first studied it. Its all-encompassing approach will appeal to both U.S. and international students. Features More than 500 exercises and answers covering all aspects of calculus. Successful series: "Practice Makes Perfect" has sales of 1,000,000 copies in the language category--now applied to mathematics. Large trim allows clear presentation of worked problems, exercises, and explained answers.

CALCULUS OF VARIATIONS WITH APPLICATIONS

CALCULUS OF VARIATIONS WITH APPLICATIONS Pdf/ePub eBook Author: A. S. GUPTA
Editor: PHI Learning Pvt. Ltd.
ISBN: 8120311205
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CALCULUS OF VARIATIONS WITH APPLICATIONS by A. S. GUPTA Summary

Calculus of variations is one of the most important mathematical tools of great scientific significance used by scientistis and engineers. Unfortunately, a few books that are available are written at a level which is not easily comprehensible for postgraduate students.This book, written by a highly respected academic, presents the materials in a lucid manner so as to be within the easy grasp of the students with some background in calculus, differential equations and functional analysis. The aim is to give a thorough and systematic analysis of various aspects of calculus of variations.

Methods of Mathematics Applied to Calculus, Probability, and Statistics

Methods of Mathematics Applied to Calculus, Probability, and Statistics Pdf/ePub eBook Author: Richard W. Hamming
Editor: Courier Corporation
ISBN: 0486138879
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Methods of Mathematics Applied to Calculus, Probability, and Statistics by Richard W. Hamming Summary

This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.

DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS

DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS Pdf/ePub eBook Author: ZAFAR AHSAN
Editor: PHI Learning Pvt. Ltd.
ISBN: 8120352696
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DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS by ZAFAR AHSAN Summary

Primarily intended for the undergraduate students of mathematics, physics and engineering, this text gives in-depth coverage of differential equations and the methods for solving them. The book begins with the definitions, the physical and geometric origins of differential equations, and the methods for solving the first order differential equations. Then it goes on to give the applications of these equations to such areas as biology, medical sciences, electrical engineering and economics. The text also discusses, systematically and logically, higher order differential equations and their applications to telecommunications, civil engineering, cardiology and detection of diabetes, as also the methods of solving simultaneous differential equations and their applications. Besides, the book provides a detailed discussion on Laplace transforms and their applications, partial differential equations and their applications to vibration of stretched string, heat flow, transmission lines, etc., and calculus of variations and its applications. The book, which is a happy fusion of theory and application, would also be useful to postgraduate students.NEW TO THIS EDITION • New sections on: (a) Equations reducible to linear partial differential equations (b) General method for solving the second order non-linear partial differential equations (Monge’s Method) (c) Lagrange’s equations of motion • Number of solved examples in Chapters 5, 7, 8, 9 and 10.

Engineering Mathematics Volume III (Linear Algebra and Vector Calculus) (For 1st Year, 2nd Semester of JNTU, Kakinada)

Engineering Mathematics Volume III (Linear Algebra and Vector Calculus) (For 1st Year, 2nd Semester of JNTU, Kakinada) Pdf/ePub eBook Author: Iyenger T.K.V./ Gandhi, Krishna B./ Ranganatham S. & Prasad M.V.S.S.N.
Editor: S. Chand Publishing
ISBN: 9352832434
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Engineering Mathematics Volume III (Linear Algebra and Vector Calculus) (For 1st Year, 2nd Semester of JNTU, Kakinada) by Iyenger T.K.V./ Gandhi, Krishna B./ Ranganatham S. & Prasad M.V.S.S.N. Summary

Engineering Mathematics