Schaum’s 3,000 Solved Problems in Calculus

Book Preface

To the Student

This collection of solved problems covers elementary and intermediate calculus, and much of advanced calculus. We have aimed at presenting the broadest range of problems that you are likely to encounter—the old chestnuts, all the current standard types, and some not so standard.
Each chapter begins with very elementary problems. Their difficulty usually increases as the chapter progresses, but there is no uniform pattern.

It is assumed that you have available a calculus textbook, including tables for the trigonometric, logarithmic, and exponential functions. Our ordering of the chapters follows the customary order found in many textbooks, but as no two textbooks have exactly the same sequence of topics, you must expect an occasional discrepancy from the order followed in your course.

The printed solution that immediately follows a problem statement gives you all the details of one way to solve the problem. You might wish to delay consulting that solution until you have outlined an attack in your own mind. You might even disdain to read it until, with pencil and paper, you have solved the problem yourself (or failed gloriously). Used thus, 3000 Solved Problems in Calculus can almost serve as a supplement to any course in calculus, or even as an independent refresher course.

CONTENTS
Chapter 1 INEQUALITIES
Chapter 2 ABSOLUTE VALUE
Chapter 3 LINES
Chapter 4 CIRCLES
Chapter 5 FUNCTIONS AND THEIR GRAPHS
Chapter 6 LIMITS
Chapter 7 CONTINUITY
Chapter 8 THE DERIVATIVE
Chapter 9 THE CHAIN RULE
Chapter 10 TRIGONOMETRIC FUNCTIONS AND THEIR DERIVATIVES
Chapter 11 ROLLE’S THEOREM, THE MEAN VALUE THEOREM, AND THE SIGN OF THE DERIVATIVE
Chapter 12 HIGHER-ORDER DERIVATIVES AND IMPLICIT DIFFERENTIATION
Chapter 13 MAXIMA AND MINIMA
Chapter 14 RELATED RATES
Chapter 15 CURVE SKETCHING (GRAPHS)
Chapter 16 APPLIED MAXIMUM AND MINIMUM PROBLEMS
Chapter 17 RECTILINEAR MOTION
Chapter 18 APPROXIMATION BY DIFFERENTIALS
Chapter 19 ANTIDERIVATIVES (INDEFINITE INTEGRALS)
Chapter 20 THE DEFINITE INTEGRAL AND THE FUNDAMENTAL THEOREM OF CALCULUS
Chapter 21 AREA AND ARC LENGTH
Chapter 22 VOLUME
Chapter 23 THE NATURAL LOGARITHM
Chapter 24 EXPONENTIAL FUNCTIONS
Chapter 25 L’HOPITAL’S RULE
Chapter 26 EXPONENTIAL GROWTH AND DECAY
Chapter 27 INVERSE TRIGONOMETRIC FUNCTIONS
Chapter 28 INTEGRATION BY PARTS
Chapter 29 TRIGONOMETRIC INTEGRANDS AND SUBSTITUTIONS
Chapter 30 INTEGRATION OF RATIONAL FUNCTIONS: THE METHOD OF PARTIAL FRACTIONS
Chapter 31 INTEGRALS FOR SURFACE AREA, WORK, CENTROIDS
Surface Area of a Solid of Revolution / Work / Centroid of a Planar Region /
Chapter 32 IMPROPER INTEGRALS
Chapter 33 PLANAR VECTORS
Chapter 34 PARAMETRIC EQUATIONS, VECTOR FUNCTIONS, CURVILINEAR MOTION
Parametric Equations of Plane Curves / Vector-Valued Functions /
Chapter 35 POLAR COORDINATES
Chapter 36 INFINITE SEQUENCES
Chapter 37 INFINITE SERIES
Chapter 38 POWER SERIES
Chapter 39 TAYLOR AND MACLAURIN SERIES
Chapter 40 VECTORS IN SPACE. LINES AND PLANES
Chapter 41 FUNCTIONS OF SEVERAL VARIABLES
Multivariate Functions and Their Graphs / Cylindrical and Spherical Coordinates /
Chapter 42 PARTIAL DERIVATIVES
Chapter 43 DIRECTIONAL DERIVATIVES AND THE GRADIENT. EXTREME VALUES
Chapter 44 MULTIPLE INTEGRALS AND THEIR APPLICATIONS
Chapter 45 VECTOR FUNCTIONS IN SPACE. DIVERGENCE AND CURL. LINE INTEGRALS
Chapter 46 DIFFERENTIAL EQUATIONS