Calculus with Applications

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

• ISBN13: 9780321228147
• ISBN10: 0321228146
• Edition: 8th
• Format: Hardcover
• Copyright: 2008-01-01
• Publisher: Addison Wesley

Summary

Widely known for incorporating interesting, relevant, and realistic applications, this text offers many real applications citing current data sources. There are a wide variety of opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts. MyMathLab, a complete online course, will be available with this text. For the first time, a comprehensive series of lectures on video will be available.

Table of Contents

Preface	ix
Index of Applications	xv
Algebra Reference	xix
Polynomials	xx
Factoring	xxiii
Rational Expressions	xxv
Equations	xxix
Inequalities	xxxv
Exponents	xl
Radicals	xlv
Linear Functions	1	(48)
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	49	(90)
Properties of Functions	50	(14)
Quadratic Functions; Translation and Reflection	64	(12)
Polynomials and Rational Functions	76	(14)
Exponential Functions	90	(13)
Logarithmic Functions	103	(14)
Applications: Growth and Decay; Mathematics of Finance	117	(22)
Review Exercises	129	(8)
Extended Application: Characteristics of the Monkeyface Prickleback	137	(2)
The Derivative	139	(72)
Limits	140	(18)
Continuity	158	(8)
Rates of Change	166	(12)
Definition of the Derivative	178	(19)
Graphical Differentiation	197	(14)
Review Exercises	205	(6)
Calculating the Derivative	211	(58)
Techniques for Finding Derivatives	212	(16)
Derivatives of Products and Quotients	228	(8)
The Chain Rule	236	(11)
Derivatives of Exponential Functions	247	(8)
Derivatives of Logarithmic Functions	255	(14)
Review Exercises	265	(4)
Graphs and the Derivative	269	(56)
Increasing and Decreasing Functions	270	(12)
Relative Extrema	282	(13)
Higher Derivatives, Concavity, and the Second Derivative Test	295	(15)
Curve Sketching	310	(15)
Review Exercises	320	(5)
Applications of the Derivative	325	(56)
Absolute Extrema	326	(9)
Applications of Extrema	335	(11)
Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand	346	(9)
Implicit Differentiation	355	(7)
Related Rates	362	(7)
Differentials: Linear Approximation	369	(12)
Review Exercises	376	(3)
Extended Application: A Total Cost Model for a Training Program	379	(2)
Integration	381	(78)
Antiderivatives	382	(12)
Substitution	394	(9)
Area and the Definite Integral	403	(14)
The Fundamental Theorem of Calculus	417	(11)
The Area Between Two Curves	428	(10)
Numerical Integration	438	(21)
Review Exercises	450	(6)
Extended Application: Estimating Depletion Dates for Minerals	456	(3)
Further Techniques and Applications of Integration	459	(38)
Integration by Parts	460	(9)
Volume and Average Value	469	(7)
Continuous Money Flow	476	(8)
Improper Integrals	484	(13)
Review Exercises	492	(3)
Extended Application: Estimating Learning Curves in Manufacturing with Integrals	495	(2)
Multivariable Calculus	497	(71)
Functions of Several Variables	498	(12)
Partial Derivatives	510	(12)
Maxima and Minima	522	(10)
Lagrange Multipliers	532	(8)
Total Differentials and Approximations	540	(6)
Double Integrals	546	(22)
Review Exercises	559	(5)
Extended Application: Using Multivariable Fitting to Create a Response Surface Design	564	(4)
Differential Equations	568	(44)
Solutions of Elementary and Separable Differential Equations	569	(13)
Linear First-Order Differential Equations	582	(6)
Euler's Method	588	(8)
Applications of Differential Equations	596	(16)
Review Exercises	606	(4)
Extended Application: Pollution of the Great Lakes	610	(2)
Probability and Calculus	612	(41)
Continuous Probability Models	613	(10)
Expected Value and Variance of Continuous Random Variables	623	(9)
Special Probability Density Functions	632	(21)
Review Exercises	645	(5)
Extended Application: Exponential Waiting Times	650	(3)
Sequences and Series	653	(56)
Geometric Sequences	654	(4)
Annuities: An Application of Sequences	658	(12)
Taylor Polynomials at 0	670	(9)
Infinite Series	679	(7)
Taylor Series	686	(10)
Newton's Method	696	(5)
L'Hospital's Rule	701	(8)
Review Exercises	706	(3)
The Trigonometric Functions	709	(40)
Definitions of the Trigonometric Functions	710	(16)
Derivatives of Trigonometric Functions	726	(12)
Integrals of Trigonometric Functions	738	(11)
Review Exercises	745	(4)
Extended Application: The Shortest Time and the Cheapest Path	749