A First Course in Calculus

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Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1441985328

Category: Mathematics

Page: 731

View: 8795

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.

A Course in Multivariable Calculus and Analysis

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Author: Sudhir R. Ghorpade,Balmohan V. Limaye

Publisher: Springer Science & Business Media

ISBN: 1441916210

Category: Mathematics

Page: 475

View: 8326

This self-contained textbook gives a thorough exposition of multivariable calculus. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. 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. 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.

Calculus of Several Variables

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Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461210682

Category: Mathematics

Page: 619

View: 8218

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

Calculus II

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Author: Jerrold Marsden,A. Weinstein

Publisher: Springer Science & Business Media

ISBN: 9780387909752

Category: Mathematics

Page: 345

View: 5317

The second of a three-volume work, this is the result of the authors'experience teaching calculus at Berkeley. The book covers techniques and applications of integration, infinite series, and differential equations, the whole time motivating the study of calculus using its applications. The authors include numerous solved problems, as well as extensive exercises at the end of each section. In addition, a separate student guide has been prepared.

Advanced Calculus

A Geometric View

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Author: James J. Callahan

Publisher: Springer Science & Business Media

ISBN: 9781441973320

Category: Mathematics

Page: 526

View: 7146

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.

Multivariable Calculus with Applications

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Author: Peter D. Lax,Maria Shea Terrell

Publisher: Springer

ISBN: 3319740733

Category: Mathematics

Page: 483

View: 468

This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics.

Calculus With Applications

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Author: Peter D. Lax,Maria Shea Terrell

Publisher: Springer Science & Business Media

ISBN: 1461479460

Category: Mathematics

Page: 503

View: 2798

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.

Elementary Analysis

The Theory of Calculus

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Author: Kenneth A. Ross

Publisher: Springer Science & Business Media

ISBN: 1461462711

Category: Mathematics

Page: 412

View: 1781

For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging. The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

Inside Calculus

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Author: George R. Exner

Publisher: Springer Science & Business Media

ISBN: 038722646X

Category: Mathematics

Page: 212

View: 5015

The approach here relies on two beliefs. The first is that almost nobody fully understands calculus the first time around. The second is that graphing calculators can be used to simplify the theory of limits for students. This book presents the theoretical pieces of introductory calculus, using appropriate technology, in a style suitable to accompany almost any first calculus text. It offers a large range of increasingly sophisticated examples and problems to build an understanding of the notion of limit and other theoretical concepts. Aimed at students who will study fields in which the understanding of calculus as a tool is not sufficient, the text uses the "spiral approach" of teaching, returning again and again to difficult topics, anticipating such returns across the calculus courses in preparation for the first analysis course. Suitable as the "content" text for a transition to upper level mathematics course.

Second Year Calculus

From Celestial Mechanics to Special Relativity

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Author: David M. Bressoud

Publisher: Springer Science & Business Media

ISBN: 1461209595

Category: Mathematics

Page: 404

View: 1080

Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.

Aspects of Calculus

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Author: Gabriel Klambauer

Publisher: Springer Science & Business Media

ISBN: 1461395615

Category: Mathematics

Page: 516

View: 7714

This book is intended for students familiar with a beginner's version of differential and integral calculus stressing only manipulation offormulas and who are now looking for a closer study of basic concepts combined with a more creative use of information. The work is primarily aimed at students in mathematics, engineering, and science who find themselves in transition from elementary calculus to rigorous courses in analysis. In addition, this book may also be of interest to those preparing to teach a course in calculus. Instead of exposing the reader to an excess of premature abstractions that so easily can degenerate into pedantry, I felt it more useful to stress instruc tive and stimulating examples. The book contains numerous worked out examples and many of the exercises are provided with helpful hints or a solution in outline. For further exercises the interested reader may want to consult a problem book by the author entitled Problems and Propositions in Analysis (New York: Marcel Dekker, 1979). For the history of calculus I recommend the book by C. B. Boyer, The Concepts of the Calculus (New York: Dover, 1949).

Introduction to Calculus and Classical Analysis

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Author: Omar Hijab

Publisher: Springer

ISBN: 3319284002

Category: Mathematics

Page: 427

View: 3667

This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This third edition includes corrections as well as some additional material. Some features of the text include: The text is completely self-contained and starts with the real number axioms; The integral is defined as the area under the graph, while the area is defined for every subset of the plane; There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; and There are 385 problems with all the solutions at the back of the text.

Short Calculus

The Original Edition of “A First Course in Calculus”

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Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461300770

Category: Mathematics

Page: 260

View: 1640

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

Calculus: A Historical Approach

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Author: W.M. Priestley

Publisher: Springer Science & Business Media

ISBN: 1468493493

Category: Mathematics

Page: 441

View: 337

This book is for students being introduced to calculus, and it covers the usual topics, but its spirit is different from wh at might be expected. Though the approach is basically historical in nature, emphasis is put upon ideas and their place-not upon events and their dates. Its purpose is to have students to learn calculus first, and to learn incidentally something about the nature of mathematics. Somewhat to the surprise of its author, the book soon became animated by a spirit of opposition to the darkness that separates the sciences from the humanities. To fight the speil of that darkness anything at hand is used, even a few low tricks or bad jokes that seemed to offer a slight promise of success. To lighten the darkness, to illuminate some of the common ground shared by the two cultures, is a goal that justifies almost any means. It is possible that this approach may make calculus more fun as weil. Whereas the close ties of mathematics to the sciences are weil known, the ties binding mathematics to the humanities are rarely noticed. The result is a distorted view of mathematics, placing it outside the mainstream of liberal arts studies. This book tries to suggest gently, from time to time, where a kinship between mathematics and the humanities may be found.

A Course in Calculus and Real Analysis

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Author: Sudhir R. Ghorpade,Balmohan V. Limaye

Publisher: Springer Science & Business Media

ISBN: 0387305300

Category: Mathematics

Page: 432

View: 6537

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.

Intermediate Calculus

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Author: Murray H. Protter,Charles B. Jr. Morrey

Publisher: Springer Science & Business Media

ISBN: 1461210860

Category: Mathematics

Page: 655

View: 9087

Calculus: A Liberal Art

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Author: W.M. Priestley

Publisher: Springer Science & Business Media

ISBN: 1461216583

Category: Mathematics

Page: 404

View: 843

Presenting mathematics as forming a natural bridge between the humanities and the sciences, this book makes calculus accessible to those in the liberal arts. Much of the necessary geometry and algebra are exposed through historical development, and a section on the development of calculus offers insights into the place of mathematics in the history of thought.

Mathematics and Its History

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Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 144196052X

Category: Mathematics

Page: 662

View: 5999

From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Calculus with Vectors

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Author: Jay Treiman

Publisher: Springer

ISBN: 3319094386

Category: Mathematics

Page: 399

View: 3453

Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additionally, the material presented is intentionally non-specific to any software or hardware platform in order to accommodate the wide variety and rapid evolution of tools used. Technology is referenced in the text and is required for a good number of problems.

Calculus Two

Linear and Nonlinear Functions

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Author: Francis J. Flanigan,Jerry L. Kazdan

Publisher: Springer Science & Business Media

ISBN: 9780387973883

Category: Mathematics

Page: 622

View: 1888

Calculus and linear algebra are two dominant themes in contemporary mathematics and its applications. The aim of this book is to introduce linear algebra in an intuitive geometric setting as the study of linear maps and to use these simpler linear functions to study more complicated nonlinear functions. In this way, many of the ideas, techniques, and formulas in the calculus of several variables are clarified and understood in a more conceptual way. After using this text a student should be well prepared for subsequent advanced courses in both algebra and linear differential equations as well as the many applications where linearity and its interplay with nonlinearity are significant. This second edition has been revised to clarify the concepts. Many exercises and illustrations have been included to make the text more usable for students.