Brief Calculus

by LARSON

• ISBN13: 9780395916858
• ISBN10: 0395916852
• Edition: 5th
• Format: Paperback
• Copyright: 1998-08-08
• Publisher: Brooks Cole

Summary

This text comprises Chapters 0–7 of Larson and Edwards' Calculus: An Applied Approach, 6/e. For a complete description of this text's features, refer to the entry for that text.

Table of Contents

A Word from the Authors (Preface)	vii
Features	ix
A Plan for You as a Student	xx
A Precalculus Review	0-1
The Real Line and Order	0-2
Absolute Value and Distance on the Real Line	0-8
Exponents and Radicals	0-13
Factoring Polynomials	0-19
Fractions and Rationalization	0-25
Functions, Graphs, and Limits	1	(80)
The Cartesian Plane and the Distance Formula	2	(9)
Graphs of Equations	11	(13)
Lines in the Plane and Slope	24	(12)
Functions	36	(13)
Limits	49	(12)
Continuity	61	(20)
Differentiation	81	(90)
The Derivative and the Slope of a Graph	82	(11)
Some Rules for Differentiation	93	(12)
Rates of Change: Velocity and Marginals	105	(15)
The Product and Quotient Rules	120	(11)
The Chain Rule	131	(9)
Higher-Order Derivatives	140	(7)
Implicit Differentiation	147	(7)
Related Rates	154	(17)
Applications of the Derivative	171	(86)
Increasing and Decreasing Functions	172	(9)
Extrema and the First-Derivative Test	181	(10)
Concavity and the Second-Derivative Test	191	(10)
Optimization Problems	201	(9)
Business and Economics Applications	210	(10)
Asymptotes	220	(11)
Curve Sketching: A Summary	231	(9)
Differentials and Marginal Analysis	240	(17)
Exponential and Logarithmic Functions	257	(56)
Exponential Functions	258	(11)
Derivatives of Exponential Functions	269	(8)
Logarithmic Functions	277	(9)
Derivatives of Logarithmic Functions	286	(9)
Exponential Growth and Decay	295	(18)
Integration and Its Applications	313	(70)
Antiderivatives and Indefinite Integrals	314	(11)
The General Power Rule	325	(8)
Exponential and Logarithmic Integrals	333	(7)
Area and the Fundamental Theorem of Calculus	340	(11)
The Area of a Region Bounded by Two Graphs	351	(9)
The Definite Integral as the Limit of a Sum	360	(7)
Volumes of Solids of Revolution	367	(16)
Techniques of Integration	383	(68)
Integration by Substitution	384	(8)
Integration by Parts and Present Value	392	(10)
Partial Fractions and Logistics Growth	402	(10)
Integration Tables and Completing the Square	412	(10)
Numerical Integration	422	(10)
Improper Integrals	432	(19)
Functions of Several Variables	451	(1)
The Three-Dimensional Coordinate System	452	(8)
Surfaces in Space	460	(10)
Functions of Several Variables	470	(9)
Partial Derivatives	479	(11)
Extrema of Functions of Two Variables	490	(1)
Lagrange Multipiers	500	(10)
Least Squares Regression Analysis	510	(10)
Double Integrals and Area in the Plane	520	(8)
Applications of Double Integrals	528
Appendices	A1
Appendix A Alternate Introduction to the Fundamental Theorem of Calculus	A2
Appendix B Formulas, Properties, and Measurements	A12
Appendix C Graphing Utility Programs	A37
Answers to Selected Exercises	A49
Index	A117