Calculus with Applications : Brief Version

by Lial, Margaret L.; Greenwell, Raymond N.; Ritchey, Nathan P.

• ISBN13: 9780321067128
• ISBN10: 0321067126
• Edition: 7th
• Format: Hardcover
• Copyright: 2005-01-01
• Publisher: Addison Wesley

Summary

Calculus With Applications, Brief Version was written for the one-semester applied calculus course for students majoring in a variety of fields - business, econ, social science, and biological and physical science. Widely known for incorporating interesting, relevant, and realistic applications, this new edition now offers many more real applications citing current data sources. The new edition now offers more opportunitites for use of technology, allowing for increased visualization and a better understanding of difficult concepts. A dedicated Web site rounds out the teaching and learning package, offering extended applications from the book, skill mastery quizzes, and graphing calculator programs tied to the text.

Table of Contents

Preface	ix
Index of Applications	xv
Algebra Reference
Polynomials	xx
Factoring	xxiii
Rational Expressions	xxvi
Equations	xxix
Inequalities	xxxv
Exponents	xl
Radicals	xlv
Linear Functions
Slopes and Equations of Lines	2	(18)
Linear Functions and Applications	20	(10)
The Least Squares Line	30	(19)
Review Exercises	44	(3)
Extended Application: Using Extrapolation to Predict Life Expectancy	47	(2)
Nonlinear Functions
Properties of Functions	49	(13)
Quadratic Functions; Translation and Reflection	62	(11)
Polynomial and Rational Functions	73	(13)
Exponential Functions	86	(12)
Logarithmic Functions	98	(13)
Applications: Growth and Decay; Mathematics of Finance	111	(21)
Exponential and Logarithmic Functions Summary	122	(1)
Review Exercises	123	(7)
Extended Application: Characteristics of the Monkeyface Prickleback	130	(2)
The Derivative
Limits	132	(18)
Continuity	150	(7)
Rates of Change	157	(12)
Definition of the Derivative	169	(17)
Graphical Differentiation	186	(13)
Review Exercises	193	(6)
Calculating The Derivative
Techniques for Finding Derivatives	199	(15)
Derivatives of Products and Quotients	214	(8)
The Chain Rule	222	(10)
Derivatives of Exponential Functions	232	(8)
Derivatives of Logarithmic Functions	240	(13)
Rules for Derivatives Summary	247	(1)
Review Exercises	248	(5)
Graphs and the Derivative
Increasing and Decreasing Functions	253	(11)
Relative Extrema	264	(13)
Higher Derivatives, Concavity, and the Second Derivative Test	277	(14)
Curve Sketching	291	(15)
Review Exercises	301	(5)
Applications of the Derivative
Absolute Extrema	306	(9)
Applications of Extrema	315	(10)
Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand	325	(9)
Implicit Differentiation	334	(7)
Related Rates	341	(6)
Differentials: Linear Approximation	347	(12)
Review Exercises	354	(3)
Extended Application: A Total Cost Model for a Training Program	357	(2)
Integration
Antiderivatives	359	(12)
Substitution	371	(8)
Area and the Definite Integral	379	(14)
The Fundamental Theorem of Calculus	393	(10)
The Area Between Two Curves	403	(9)
Numerical Integration	412	(19)
Integration Summary	421	(2)
Review Exercises	423	(4)
Extended Application: Estimating Depletion Dates for Minerals	427	(4)
Further Techniques and Applications of Integration
Integration by Parts	431	(8)
Volume and Average Value	439	(7)
Continuous Money Flow	446	(8)
Improper Integrals	454	(12)
Review Exercises	460	(3)
Extended Application: Estimating Learning Curves in Manufacturing with Integrals	463	(3)
Multivariable Calculus
Functions of Several Variables	466	(11)
Partial Derivatives	477	(11)
Maxima and Minima	488	(9)
Lagrange Multipliers	497	(9)
Total Differentials and Approximations	506	(5)
Double Integrals	511
Review Exercises	524	(4)
Extended Application: Using Multivariable Fitting to Create a Response Surface Design	528
Tables
Formulas from Geometry	1	(1)
Integrals	2	(1)
Answers to Selected Exercises	3	(30)
Photo Acknowledgments	33
Index	1