Overview


This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculus unclear. It is not an ordinary textbook. It is, instead, an examination of the most important aspects of integral and differential calculus in terms of the 756 questions most likely to occur to the technical reader. It provides a very easily followed presentation and may also be used as either an introductory or ...
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Calculus Refresher

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Overview


This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculus unclear. It is not an ordinary textbook. It is, instead, an examination of the most important aspects of integral and differential calculus in terms of the 756 questions most likely to occur to the technical reader. It provides a very easily followed presentation and may also be used as either an introductory or supplementary textbook.
The first part of this book covers simple differential calculus, with constants, variables, functions, increments, derivatives, differentiation, logarithms, curvature of curves, and similar topics. The second part covers fundamental ideas of integration (inspection, substitution, transformation, reduction) areas and volumes, mean value, successive and partial integration, double and triple integration. In all cases the author stresses practical aspects rather than theoretical, and builds upon such situations as might occur.
A 50-page section illustrates the application of calculus to specific problems of civil and nautical engineering, electricity, stress and strain, elasticity, industrial engineering, and similar fields. 756 questions answered. 566 problems to measure your knowledge and improvement; answers. 36 pages of useful constants, formulae for ready reference. Index.
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Product Details

  • ISBN-13: 9780486138602
  • Publisher: Dover Publications
  • Publication date: 5/11/2012
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 431
  • Sales rank: 478,844
  • File size: 70 MB
  • Note: This product may take a few minutes to download.

Table of Contents

SECTION I SIMPLE DIFFERENTIAL CALCULUS
I CONSTANTS
VARIABLES
FUNCTIONS
INCREMENTS
II LIMITS
III DERIVATIVES
IV DIFFERENTIATION
ELEMENTARY RULES
ALGEBRAIC
V DIFFERENTIATION BY SUBSTITUTION
VI INVERSE FUNCTIONS
VII DIFFERENTIATION
ELEMENTARY RULES
TRIGONOMETRIC
VIII GEOMETRICAL MEANING OF DIFFERENTIATION
IX TANGENT
NORMAL
SUBTANGENT
SUBNORMAL
X MAXIMA AND MINIMA
XI DIFFERENTIALS
XII SPLITTING FRACTIONS TO AID DIFFERENTIATION
XIII TYPES OF GROWTH
XIV EPSILON = e
EXPONENTIAL FUNCTIONS
XV LOGARITHMS
XVI DIFFERENTIATION OF LOGARITHMIC FUNCTIONS
XVII CONDITIONS OF LOGARITHMIC OR ORGANIC GROWTH
XVIII PARTIAL DIFFERENTIATION
XIX CURVATURE OF CURVES
SECTION II SIMPLE INTEGRAL CALCULUS
XX INTEGRATION
FUNDAMENTAL IDEAS
XXI INTEGRATION
THE INVERSE OF DIFFERENTIATION
XXII INTEGRATION BY FUNDAMENTAL FORMULAS
XXIII INTEGRATION BY INSPECTION
XXIV INTEGRATION BY SUBSTITUTION
XXV INTEGRATION OF TRIGONOMETRIC FUNCTIONS BY TRANSFORMATION AND REDUCTION
XXVI INTEGRATION BY PARTS
XXVII INTEGRATION BY FRACTIONS
XXVIII PLANE AREAS BY INTEGRATION
DEFINITE INTEGRAL
DIFFERENTIAL OF AN AREA
LIMIT OF A SUM
XXIX MEAN VALUE
XXX LENGTH OF AN ARC
XXXI AREAS OF SURFACES
VOLUMES BY SINGLE INTEGRATION
XXXII SUCCESSIVE AND PARTIAL INTEGRATION
XXXIII PLANE AREAS BY DOUBLE INTEGRATION
XXXIV VOLUMES BY TRIPLE INTEGRATION
XXXV CENTER OF GRAVITY
XXXVI MOMENT OF INERTIA
XXXVIII INTRODUCTION TO DIFFERENTIAL EQUATIONS
SECTION III APPLICATIONS OF CALCULUS
XXXVIII APPLICATIONS OF CALCULUS
APPENDIX A-ANSWERS TO PROBLEMS
"APPENDIX B-USEFUL FORMULAS, NOTATIONS, AND TABLES"
INDEX
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