Applied Calculus 4th Edition exhibits the same strengths from earlier editions including the "Rule of Four", an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.
The fourth edition gives readers the skills to apply calculus on the job. It highlights the applications' connection with real-world concerns. The problems take advantage of computers and graphing calculators to help them think mathematically. The applied exercises challenge them to apply the math they have learned in new ways. This develops their capacity for modeling in a way that the usual exercises patterned after similar solved examples cannot do. The material is also presented in a way to help business professionals decide when to use technology, which empowers them to learn what calculators/computers can and cannot do.
Contents
1 FUNCTIONS AND CHANGE
1.1 WHAT IS A FUNCTION?
1.2 LINEAR FUNCTIONS
1.3 AVERAGE RATE OF CHANGE AND RELATIVE CHANGE
1.4 APPLICATIONS OF FUNCTIONS TO ECONOMICS
1.5 EXPONENTIAL FUNCTIONS
1.6 THE NATURAL LOGARITHM
1.7 EXPONENTIAL GROWTH AND DECAY
1.8 NEW FUNCTIONS FROM OLD
1.9 PROPORTIONALITY AND POWER FUNCTIONS
1.10 PERIODIC FUNCTIONS
2 RATE OF CHANGE: THE DERIVATIVE
2.1 INSTANTANEOUS RATE OF CHANGE
2.2 THE DERIVATIVE FUNCTION
2.3 INTERPRETATIONS OF THE DERIVATIVE
2.4 THE SECOND DERIVATIVE
2.5 MARGINAL COST AND REVENUE
3 SHORT-CUTS TO DIFFERENTIATION
3.1 DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS
3.2 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
3.3 THE CHAIN RULE
3.4 THE PRODUCT AND QUOTIENT RULES
3.5 DERIVATIVES OF PERIODIC FUNCTIONS
4 USING THE DERIVATIVE
4.1 LOCAL MAXIMA AND MINIMA
4.2 INFLECTION POINTS
4.3 GLOBAL MAXIMA AND MINIMA
4.4 PROFIT, COST, AND REVENUE
4.5 AVERAGE COST
4.6 ELASTICITY OF DEMAND
4.7 LOGISTIC GROWTH
4.8 THE SURGE FUNCTION AND DRUG CONCENTRATION
5 ACCUMULATED CHANGE: THE DEFINITE INTEGRAL
5.1 DISTANCE AND ACCUMULATED CHANGE
5.2 THE DEFINITE INTEGRAL
5.3 THE DEFINITE INTEGRAL AS AREA
5.4 INTERPRETATIONS OF THE DEFINITE INTEGRAL
5.5 THE FUNDAMENTAL THEOREM OF CALCULUS
6 USING THE DEFINITE INTEGRAL
6.1 AVERAGE VALUE
6.2 CONSUMER AND PRODUCER SURPLUS
6.3 PRESENT AND FUTURE VALUE
6.4 INTEGRATING RELATIVE GROWTH RATES
7 ANTIDERIVATIVES
7.1 CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY
7.2 INTEGRATION BY SUBSTITUTION
7.3 USING THE FUNDAMENTAL THEOREM TO FIND DEFINITE INTEGRALS
7.4 INTEGRATION BY PARTS
7.5 ANALYZING ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY
8 PROBABILITY
8.1 DENSITY FUNCTIONS
8.2 CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY
8.3 THE MEDIAN AND THE MEAN
9 FUNCTIONS OF SEVERAL VARIABLES
9.1 UNDERSTANDING FUNCTIONS OF TWO VARIABLES
9.2 CONTOUR DIAGRAMS
9.3 PARTIAL DERIVATIVES
9.4 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY
9.5 CRITICAL POINTS AND OPTIMIZATION
9.6 CONSTRAINED OPTIMIZATION
10 MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS
10.1 MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION
10.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS
10.3 SLOPE FIELDS
10.4 EXPONENTIAL GROWTH AND DECAY
10.5 APPLICATIONS AND MODELING
10.6 MODELING THE INTERACTION OF TWO POPULATIONS
10.7 MODELING THE SPREAD OF A DISEASE
11 GEOMETRIC SERIES
11.1 GEOMETRIC SERIES
11.2 APPLICATIONS TO BUSINESS AND ECONOMICS
11.3 APPLICATIONS TO THE NATURAL SCIENCES
APPENDICES
A FITTING FORMULAS TO DATA
B COMPOUND INTEREST AND THE NUMBER
C SPREADSHEET PROJECTS
1. MALTHUS: POPULATION OUTSTRIPS FOOD SUPPLY
2. CREDIT CARD DEBT
3. CHOOSING A BANK LOAN
4. COMPARING HOME MORTGAGES
5. PRESENT VALUE OF LOTTERYWINNINGS
6. COMPARING INVESTMENTS
7. INVESTING FOR THE FUTURE: TUITION PAYMENTS
8. NEW OR USED?
9. VERHULST: THE LOGISTIC MODEL
10. THE SPREAD OF INFORMATION: A COMPARISON OF TWO MODELS
11. THE FLU IN WORLD WAR I
The fourth edition gives readers the skills to apply calculus on the job. It highlights the applications' connection with real-world concerns. The problems take advantage of computers and graphing calculators to help them think mathematically. The applied exercises challenge them to apply the math they have learned in new ways. This develops their capacity for modeling in a way that the usual exercises patterned after similar solved examples cannot do. The material is also presented in a way to help business professionals decide when to use technology, which empowers them to learn what calculators/computers can and cannot do.
1 FUNCTIONS AND CHANGE
1.1 WHAT IS A FUNCTION?
1.2 LINEAR FUNCTIONS
1.3 AVERAGE RATE OF CHANGE AND RELATIVE CHANGE
1.4 APPLICATIONS OF FUNCTIONS TO ECONOMICS
1.5 EXPONENTIAL FUNCTIONS
1.6 THE NATURAL LOGARITHM
1.7 EXPONENTIAL GROWTH AND DECAY
1.8 NEW FUNCTIONS FROM OLD
1.9 PROPORTIONALITY AND POWER FUNCTIONS
1.10 PERIODIC FUNCTIONS
2 RATE OF CHANGE: THE DERIVATIVE
2.1 INSTANTANEOUS RATE OF CHANGE
2.2 THE DERIVATIVE FUNCTION
2.3 INTERPRETATIONS OF THE DERIVATIVE
2.4 THE SECOND DERIVATIVE
2.5 MARGINAL COST AND REVENUE
3 SHORT-CUTS TO DIFFERENTIATION
3.1 DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS
3.2 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
3.3 THE CHAIN RULE
3.4 THE PRODUCT AND QUOTIENT RULES
3.5 DERIVATIVES OF PERIODIC FUNCTIONS
4 USING THE DERIVATIVE
4.1 LOCAL MAXIMA AND MINIMA
4.2 INFLECTION POINTS
4.3 GLOBAL MAXIMA AND MINIMA
4.4 PROFIT, COST, AND REVENUE
4.5 AVERAGE COST
4.6 ELASTICITY OF DEMAND
4.7 LOGISTIC GROWTH
4.8 THE SURGE FUNCTION AND DRUG CONCENTRATION
5 ACCUMULATED CHANGE: THE DEFINITE INTEGRAL
5.1 DISTANCE AND ACCUMULATED CHANGE
5.2 THE DEFINITE INTEGRAL
5.3 THE DEFINITE INTEGRAL AS AREA
5.4 INTERPRETATIONS OF THE DEFINITE INTEGRAL
5.5 THE FUNDAMENTAL THEOREM OF CALCULUS
6 USING THE DEFINITE INTEGRAL
6.1 AVERAGE VALUE
6.2 CONSUMER AND PRODUCER SURPLUS
6.3 PRESENT AND FUTURE VALUE
6.4 INTEGRATING RELATIVE GROWTH RATES
7 ANTIDERIVATIVES
7.1 CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY
7.2 INTEGRATION BY SUBSTITUTION
7.3 USING THE FUNDAMENTAL THEOREM TO FIND DEFINITE INTEGRALS
7.4 INTEGRATION BY PARTS
7.5 ANALYZING ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY
8 PROBABILITY
8.1 DENSITY FUNCTIONS
8.2 CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY
8.3 THE MEDIAN AND THE MEAN
9 FUNCTIONS OF SEVERAL VARIABLES
9.1 UNDERSTANDING FUNCTIONS OF TWO VARIABLES
9.2 CONTOUR DIAGRAMS
9.3 PARTIAL DERIVATIVES
9.4 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY
9.5 CRITICAL POINTS AND OPTIMIZATION
9.6 CONSTRAINED OPTIMIZATION
10 MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS
10.1 MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION
10.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS
10.3 SLOPE FIELDS
10.4 EXPONENTIAL GROWTH AND DECAY
10.5 APPLICATIONS AND MODELING
10.6 MODELING THE INTERACTION OF TWO POPULATIONS
10.7 MODELING THE SPREAD OF A DISEASE
11 GEOMETRIC SERIES
11.1 GEOMETRIC SERIES
11.2 APPLICATIONS TO BUSINESS AND ECONOMICS
11.3 APPLICATIONS TO THE NATURAL SCIENCES
APPENDICES
A FITTING FORMULAS TO DATA
B COMPOUND INTEREST AND THE NUMBER
C SPREADSHEET PROJECTS
1. MALTHUS: POPULATION OUTSTRIPS FOOD SUPPLY
2. CREDIT CARD DEBT
3. CHOOSING A BANK LOAN
4. COMPARING HOME MORTGAGES
5. PRESENT VALUE OF LOTTERYWINNINGS
6. COMPARING INVESTMENTS
7. INVESTING FOR THE FUTURE: TUITION PAYMENTS
8. NEW OR USED?
9. VERHULST: THE LOGISTIC MODEL
10. THE SPREAD OF INFORMATION: A COMPARISON OF TWO MODELS
11. THE FLU IN WORLD WAR I
Book Details
- Paperback: 560 pages
- Publisher: Wiley; 4 edition
- Language: English
- ISBN-10: 0470170522
- ISBN-13: 978-0470170526
- Product Dimensions: 10.2 x 8.1 x 0.9 inches