Calculus A Short Course

by Gemignani, Michael C.

• ISBN13: 9780486438238
• ISBN10: 0486438236
• Format: Paperback
• Copyright: 2004-08-13
• Publisher: Dover Publications

Summary

This clearly written, well-illustrated text makes calculus understandable even for the rank beginner. It is geared toward undergraduate business and social science students rather than math majors; the only background necessary is high-school level algebra and a little familiarity with analytic geometry. Topics include sets, functions, and graphs; limits and continuity; special functions; the derivative and its uses; the definite integral and further methods and applications of integration; and the functions of several variables. User-friendly features include reviews at the end of each chapter and exercises on different levels; answers to more than half of the problems appear in the appendix. 1972 ed.

Table of Contents

Chapter 1 SETS, FUNCTIONS AND GRAPHS	3	(46)
1.1 Sets	3	(9)
1.2 Computations with Absolute Values and Inequalities	12	(8)
1.3 Functions. The Coordinate Plane	20	(7)
1.4 Graphs	27	(9)
1.5 Graphs of Inequalities. Graphs of Functions	36	(10)
Review	46	(3)
Chapter 2 LIMITS AND CONTINUITY	49	(22)
2.1 Limits	49	(9)
2.2 Operations with Functions. Continuity	58	(10)
Review	68	(3)
Chapter 3 SOME SPECIAL FUNCTIONS	71	(24)
3.1 The Power Function	71	(7)
3.2 The Exponential and Logarithmic Functions	78	(7)
3.3 Further Examples and Applications	85	(7)
Review	92	(3)
Chapter 4 THE DERIVATIVE	95	(26)
4.1 The Concept of the Derivative	95	(9)
4.2 Methods for Computing Derivatives	104	(8)
4.3 Composition of Functions. The Chain Rule	112	(7)
Review	119	(2)
Chapter 5 SOME USES OF THE DERIVATIVE	121	(42)
5.1 What the First Derivative Indicates About a Function	121	(9)
5.2 Obtaining More Information from the Derivative	130	(10)
5.3 Some Practical Applications of the Derivative	140	(11)
5.4 Further Uses of the Derivative	151	(9)
Review	160	(3)
Chapter 6 THE DEFINITE INTEGRAL	163	(36)
6.1 The Concept of the Definite Integral	163	(11)
6.2 The Fundamental Theorem of the Calculus	174	(8)
6.3 Substitution of Variable. Integration by Parts	182	(6)
6.4 Some Applications of the Definite Integral	188	(8)
Review	196	(3)
Chapter 7 FURTHER METHODS AND APPLICATIONS OF INTEGRATION	199	(22)
7.1 Improper Integrals	199	(9)
7.2 Numerical Methods of Integration	208	(10)
Review	218	(3)
Chapter 8 FUNCTIONS OF SEVERAL VARIABLES	221	(19)
8.1 Partial Differentiation	221	(6)
8.2 Maxima and Minima. Lagrangian Multipliers	227	(11)
Review	238	(2)
APPENDIX	240	(3)
ANSWERS TO SELECTED EXERCISES	243	(24)
INDEX	267