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**About this book :- **
** Schaum Differential and Integral Calculus (3E) ** written by
** Frank Ayres, Elliott Mendelson **.

This is another in the Schaum's series that is excellent for review, good as a supplement and almost impossible to use as a stand-alone learning tool. The problems are all suitable for the (re)study of differential and integral calculus, they are worked out in enough detail and the coverage of two semesters of calculus is essentially complete. If you have taken calculus and did well in the course, then there is no better way to perform a quick brushing up of your skills. Other than that, using this book is problematical. This third edition of the well-known calculus review book by Frank Ayres, Jr., has been thoroughly revised and includes many new features. Here are some of the more significant changes:

Analytic geometry, knowledge of which was presupposed in the first two editions, is now treated in detail from the beginning. Chapters 1 through 5 are completely new and introduce the reader to the basic ideas and results.

Exponential and logarithmic functions are now treated in two places.

They are first discussed briefly in Chapter 14, in the classical manner of earlier editions. Then, in Chapter 40, they are introduced and studied rigorously as is now customary in calculus courses. A thorough treatment of exponential growth and decay also is included in that chapter.

Terminology, notation, and standards of rigor have been brought up to date. This is especially true in connection with limits, continuity, the chain rule, and the derivative tests for extreme values.

Definitions of the trigonometric functions and information about the important trigonometric identities have been provided.

The chapter on curve tracing has been thoroughly revised, with the emphasis shifted from singular points to examples that occur more frequently in current calculus courses.

The purpose and method of the original text have nonetheless been preserved.

In particular, the direct and concise exposition typical of the Schaum Outline Series has been retained. The basic aim is to offer to students a collection of carefully solved problems that are representative of those they will encounter in elementary calculus courses (generally, the first two or three semesters of a calculus sequence). Moreover, since all fundamental concepts are defined and the most important theorems are proved, this book may be used as a text for a regular calculus course, in both colleges and secondary schools.

Each chapter begins with statements of definitions, principles, and theorems.

These are followed by the solved problems that form the core of the book. They give step-by-step practice in applying the principles and provide derivations of some of the theorems. In choosing these problems, we have attempted to anticipate the difficulties that normally beset the beginner. Every chapter ends with a carefully selected group of supplementary problems (with answers) whose solution is essential to the effective use of this book.

**Book Detail :- **
** Title: ** Schaum Differential and Integral Calculus (3E)
** Edition: ** 3rd
** Author(s): ** Frank Ayres, Elliott Mendelson
** Publisher: ** McGraw-Hill
** Series: ** Schaum's outline series
** Year: ** 1990
** Pages: ** 489
** Type: ** PDF
** Language: ** English
** ISBN: ** 9780070026629,0070026629
** Country: ** US
** Get this book from Amazon **

**About Author :- **

The author Frank Ayres, Jr. was a mathematics professor, best known as a famous author for the popular Schaum's Outlines series.

Ayres earned his bachelor of science degree from Washington College, Maryland and his master's and doctoral degrees from the University of Chicago.

He taught during 1921–4 at Ogden College and another four years at Texas A&M before coming to Dickinson College in 1928. He was promoted to associate professor in June, 1935. In 1943 he was named the Susan Powers Hoffman Professor of Mathematics. From 1938 until his retirement in June, 1958, he served as chairman of the mathematics department. Ayres was also an instructor in the Army Air Corps program at the College, 1943–44, and authored Basic Mathematics of Aviation, he wrote seven textbooks.

The author Elliott Mendelson is an American logician. He was a professor of mathematics at Queens College of the City University of New York,[1] and the Graduate Center, CUNY. He was Jr. Fellow, Society of Fellows, Harvard University.

Mendelson taught mathematics at the college level for more than 30 years, and is the author of books on logic, philosophy of mathematics, calculus, game theory and mathematical analysis.

**Other famous books of similar Author :- **

Here is list all books avaliable of this author.

** • Download PDF Schaum's Outlines Calculus (5E) by Frank Ayres, Elliott Mendelson ****
• Download PDF Schaum’s Outline Theory and Problems of Abstract Algebra (2E) by Frank Ayres, Lloyd Jaisingh
• Download PDF Schaum Differential and Integral Calculus (3E) by Frank Ayres, Elliott Mendelson
• Download PDF Schaum's Easy Outline Calculus Crash Course by Frank Ayres, Elliott Mendelson
• Download PDF Schaum's 3000 Solved Problems in Calculus by Elliot Mendelson
• Download PDF Schaum's Outline of Theory & Problems of Beginning Calculus (2E) by Elliott Mendelson
**

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**Book Contents :- **
** Schaum Differential and Integral Calculus (3E) ** written by
** Frank Ayres, Elliott Mendelson **
cover the following topics.

ABSOLUTE VALUE; LINEAR COORDINATE SYSTEMS;

INEQUALITIES

THE RECTANGULAR COORDINATE SYSTEM

LINES

CIRCLES

EQUATIONS AND THEIR GRAPHS

FUNCTIONS

LIMITS

CONTINUITY

THE DERIVATIVE

RULES FOR DIFFERENTIATING FUNCTIONS

IMPLICIT DIFFERENTIATION

TANGENTS AND NORMALS

MAXIMUM AND MINIMUM VALUES

APPLIED PROBLEMS INVOLVING MAXIMA AND MINIMA

RECTILINEAR AND CIRCULAR MOTION

RELATED RATES

DIFFERENTIATION OF TRIGONOMETRIC FUNCTIONS

DIFFERENTIATION OF INVERSE TRIGONOMETRIC FUNCTIONS

DIFFERENTIATION OF EXPONENTIAL AND LOGARITHMIC

FUNCTIONS

DIFFERENTIATION OF HYPERBOLIC FUNCTIONS

PARAMETRIC REPRESENTATION OF CURVES

CURVATURE

PLANE VECTORS

CURVILINEAR MOTION

POLAR COORDINATES

THE LAW OFTHE MEAN

INDETERMINATE FORMS

DIFFERENTIALS

CURVE TRACING

FUNDAMENTAL INTEGRATION FORMULAS

INTEGRATION BY PARTS

TRIGONOMETRIC INTEGRALS

TRIGONOMETRIC SUBSTITUTIONS

INTEGRATION BY PARTIAL FRACTIONS

MISCELLANEOUS SUBSTITUTIONS

INTEGRATION OF HYPERBOLIC FUNCTIONS

APPLICATIONS OF INDEFINITE INTEGRALS

THE DEFINITE INTEGRAL

PLANE AREAS BY INTEGRATION

EXPONENTIAL AND LOGARITHMIC FUNCTIONS; EXPONENTIAL

GROWTH AND DECAY

VOLUMES OF SOLIDS OF REVOLUTION

VOLUMES OF SOLIDS WITH KNOWN CROSS SECTIONS

CENTROIDS OF PLANE AREAS AND SOLIDS OF REVOLUTION

MOMENTS OF INERTIA OF PLANE AREAS AND SOLIDS OF EVOLUTION

FLUID PRESSURE

WORK

LENGTH OF ARC

AREAS OF A SURFACE OF REVOLUTION

CENTROIDS AND MOMENTS OF INERTIA OF ARCS AND

SURFACES OF REVOLUTION

PLANE AREA AND CENTROID OF AN AREA IN POLAR

COORDINATES

LENGTH AND CENTROID OF AN ARC AND AREA OF A

SURFACE OF REVOLUTION IN POLAR COORDINATES

IMPROPER INTEGRALS

INFINITE SEQUENCES AND SERIES

TESTS FOR THE CONVERGENCE AND DIVERGENCE OF POSITIVE SERIES

SERIES WITH NEGATIVE TERMS

COMPUTATIONS WITH SERIES

POWER SERIES

SERIES EXPANSION O F FUNCTIONS

MACLAURIN'S AND TAYLOR'S FORMULAS WITH REMAINDERS COMPUTATIONS USING POWER SERIES

APPROXIMATE INTEGRATION

PARTIAL DERIVATIVES

TOTAL DIFFERENTIALS AND TOTAL DERIVATIVES

IMPLICIT FUNCTIONS

SPACE VECTORS

SPACE CURVES AND SURFACE

DIRECTIONAL DERIVATIVES; MAXIMUM AND MINIMUM VALUES

VECTOR DIFFERENTIATION AND INTEGRATION

DOUBLE AND ITERATED INTEGRALS

CENTROIDS AND MOMENTS OF INERTIA OF PLANE AREAS

VOLUME UNDER A SURFACE BY DOUBLE INTEGRATION

AREA OF A CURVED SURFACE BY DOUBLE INTEGRATION

TRIPLE INTEGRALS

MASSES O F VARIABLE DENSITY

DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS OF ORDER TWO

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