Applied Calculus for the Managerial, Life, and Social Sciences

by Tan, Soo T.

• ISBN13: 9780534378431
• ISBN10: 0534378439
• Edition: 5th
• Format: Hardcover
• Copyright: 2001-07-18
• Publisher: Brooks Cole

Summary

In this revision of his best-selling text, Soo Tan builds on the features that have made his texts best-sellers: a problem-solving approach, accurate mathematical development, a concise yet accessible writing style, and a wealth of interesting and appropriate applications. These features are combined with practical pedagogical tools to help students understand and comprehend the material. Tan also now includes innovative use of technology that is optional yet well integrated throughout the book.

Table of Contents

Preliminaries	2	(56)
Precalculus Review I	4	(10)
Precalculus Review II	14	(14)
The Cartesian Coordinate System	28	(9)
Straight Lines	37	(21)
Summary of Principal Formulas and Terms	55	(1)
Review Exercises	56	(2)
Functions, Limits, and the Derivative	58	(124)
Functions and Their Graphs	60	(21)
Using Technology: Graphing a Function	76	(5)
The Algebra of Functions	81	(9)
Portfolio: Michael Marchlik	86	(4)
Functions and Mathematical Models	90	(20)
Using Technology: Finding the Points of Intersection of Two Graphs and Modeling	104	(6)
Limits	110	(25)
Using Technology: Finding the Limit of a Function	130	(5)
One-Sided Limits and Continuity	135	(20)
Using Technology: Finding the Points of Discontinuity of a Function	150	(5)
The Derivative	155	(27)
Using Technology: Graphing a Function and Its Tangent Lines	176	(3)
Summary of Principal Formulas and Terms	179	(1)
Review Exercises	179	(3)
Differentiation	182	(94)
Basic Rules of Differentiation	184	(14)
Using Technology: Finding the Rate of Change of a Function	192	(6)
The Product and Quotient Rules	198	(13)
Using Technology: The Product and Quotient Rules	208	(3)
The Chain Rule	211	(13)
Using Technology: Finding the Derivative of a Composite Function	218	(6)
Marginal Functions in Economics	224	(16)
Higher-Order Derivatives	240	(9)
Using Technology: Finding the Second Derivative of a Function at a Given Point	246	(3)
Implicit Differentiation and Related Rates	249	(12)
Differentials	261	(15)
Portfolio: John Decker	262	(8)
Using Technology: Finding the Differential of a Function	270	(3)
Summary of Principal Formulas and Terms	273	(1)
Review Exercises	274	(2)
Applications of the Derivative	276	(96)
Applications of the First Derivative	278	(23)
Using Technology: Using the First Derivative to Analyze a Function	296	(5)
Applications of the Second Derivative	301	(20)
Using Technology: Finding the Inflection Points of a Function	318	(3)
Curve Sketching	321	(20)
Using Technology: Analyzing the Properties of a Function	334	(7)
Optimization I	341	(16)
Using Technology: Finding the Absolute Extrema of a Function	354	(3)
Optimization II	357	(15)
Summary of Principal Terms	369	(1)
Review Exercises	369	(3)
Exponential and Logarithmic Functions	372	(66)
Exponential Functions	374	(9)
Using Technology	380	(3)
Logarithmic Functions	383	(8)
Compound Interest	391	(14)
Portfolio: Misato Nakazaki	403	(2)
Differentiation of Exponential Functions	405	(12)
Using Technology	414	(3)
Differentiation of Logarithmic Functions	417	(8)
Exponential Functions as Mathematical Models	425	(13)
Summary of Principal Formulas and Terms	436	(1)
Review Exercises	437	(1)
Integration	438	(110)
Antiderivatives and the Rules of Integration	440	(15)
Integration by Substitution	455	(11)
Area and the Definite Integral	466	(11)
The Fundamental Theorem of Calculus	477	(14)
Using Technology: Evaluating Definite Integrals	488	(3)
Evaluating Definite Integrals	491	(12)
Using Technology: Evaluating Definite Integrals for Piecewise-Defined Functions	500	(3)
Area Between Two Curves	503	(16)
Using Technology: Finding the Area Between Two Curves	516	(3)
Applications of the Definite Integral to Business and Economics	519	(16)
Using Technology: Consumers' Surplus and Producers' Surplus	533	(2)
Volumes of Solids of Revolution	535	(13)
Summary of Principal Formulas and Terms	543	(1)
Review Exercises	544	(4)
Additional Topics in Integration	548	(48)
Integration by Parts	550	(7)
Integration Using Tables of Integrals	557	(8)
Numerical Integration	565	(17)
Portfolio: James H. Chesebro	580	(2)
Improper Integrals	582	(14)
Summary of Principal Formulas and Terms	593	(1)
Review Exercises	594	(2)
Calculus of Several Variables	596	(94)
Functions of Several Variables	598	(10)
Partial Derivatives	608	(18)
Using Technology: Finding Partial Derivatives at a Given Point	622	(4)
Maxima and Minima of Functions of Several Variables	626	(11)
The Method of Least Squares	637	(13)
Using Technology: Finding an Equation of a Least-Squares Line	646	(4)
Constrained Maxima and Minima and the Method of Lagrange Multipliers	650	(13)
Total Differentials	663	(6)
Double Integrals	669	(8)
Applications of Double Integrals	677	(13)
Summary of Principal Terms	687	(1)
Review Exercises	687	(3)
Differential Equations	690	(36)
Differential Equations	692	(7)
Separation of Variables	699	(7)
Applications of Separable Differential Equations	706	(10)
Approximate Solutions of Differential Equations	716	(10)
Summary of Principal Terms	724	(1)
Review Exercises	724	(2)
Probability and Calculus	726	(46)
Probability Distributions of Random Variables	728	(11)
Using Technology: Graphing a Histogram	736	(3)
Expected Value and Standard Deviation	739	(17)
Using Technology: Finding the Mean and Standard Deviation	754	(2)
Normal Distributions	756	(16)
Summary of Principal Formulas and Terms	769	(1)
Review Exercises	770	(2)
Taylor Polynomials and Infinite Series	772	(80)
Taylor Polynomials	774	(13)
Infinite Sequences	787	(9)
Infinite Series	796	(12)
Series with Positive Terms	808	(11)
Power Series and Taylor Series	819	(10)
More on Taylor Series	829	(10)
The Newton--Raphson Method	839	(13)
Summary of Principal Formulas and Terms	849	(1)
Review Exercises	850	(2)
Trigonometric Functions	852	(47)
Measurement of Angles	854	(6)
The Trigonometric Functions	860	(11)
Differentiation of Trigonometric Functions	871	(16)
Using Technology: Analyzing Trigonometric Functions	884	(3)
Integration of Trigonometric Functions	887	(12)
Using Technology: Evaluating Integrals of Trigonometric Functions	892	(4)
Summary of Principal Formulas and Terms	896	(1)
Review Exercises	897	(2)
Table	899	(4)
The Standard Normal Distribution	900	(3)
Answers to Odd-Numbered Exercises	903	(42)
Index	945