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Full Description
Applied Calculus 5th Edition is praised for the creative and varied conceptual and modeling problems which motivate and challenge students. The 5th Edition of this market leading text 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. Updated data and fresh applications throughout the book are designed to build student confidence with basic concepts and to reinforce skills. As in the previous edition, a Pre-test is included for students whose skills may need a refresher prior to taking the course.
Contents
1 FUNCTIONS AND CHANGE 1 1.1 WHAT IS A FUNCTION? 2 1.2 LINEAR 1.6 THE NATURAL LOGARITHM 46 1.7 EXPONENTIAL GROWTH AND DECAY 51 1.8 NEW FUNCTIONS FROM OLD 60 1.9 PROPORTIONALITY AND POWER FUNCTIONS 65 1.10 PERIODIC FUNCTIONS 71 REVIEW PROBLEMS 78 STRENGTHEN YOUR MARGINAL COST AND REVENUE 119 REVIEW PROBLEMS 125 STRENGTHEN YOUR UNDERSTANDING 130 PROJECTS: ESTIMATING TEMPERATURE OF A YAM; TEMPERATURE POLYNOMIALS 138 3.2 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 145 3.3 THE CHAIN RULE 150 3.4 THE PRODUCT AND QUOTIENT RULES 156 3.5 DERIVATIVES OF PERIODIC FUNCTIONS 161 REVIEW PROBLEMS 165 STRENGTHEN YOUR ALTITUDE; RELATIVE GROWTH RATES: POPULATION, GDP, AND GDP PER CAPITA; KEELING 4 USING THE DERIVATIVE 175 4.1 LOCAL MAXIMA AND MINIMA 176 4.2 INFLECTION POINTS 183 4.3 GLOBAL MAXIMA AND MINIMA 189 4.4 PROFIT, 4.7 LOGISTIC GROWTH 213 4.8 THE SURGE FUNCTION AND DRUG CONCENTRATION 221 REVIEW PROBLEMS 228 STRENGTHEN YOUR UNDERSTANDING 235 PROJECTS: ACCUMULATED CHANGE: THE DEFINITE INTEGRAL 241 5.1 DISTANCE AND ACCUMULATED CHANGE 242 5.2 THE DEFINITE INTEGRAL 250 5.3 THE DEFINITE INTEGRAL AS REVIEW PROBLEMS 276 STRENGTHEN YOUR UNDERSTANDING 281 PROJECTS: CARBON ANTIDERIVATIVES AND APPLICATIONS 291 6.1 ANALYZING ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY 292 6.2 ANTIDERIVATIVES AND THE INDEFINITE 302 6.4 APPLICATION: CONSUMER AND PRODUCER SURPLUS 306 6.5 APPLICATION: 7.1 DENSITY FUNCTIONS 332 7.2 CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY 336 7.3 THE MEDIAN AND THE MEAN 343 REVIEW PROBLEMS 348 STRENGTHEN YOUR UNDERSTANDING 350 PROJECTS: TRIANGULAR PROBABILITY DERIVATIVES 369 8.4 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY 376 8.5 CRITICAL POINTS AND OPTIMIZATION 381 8.6 CONSTRAINED OPTIMIZATION 387 REVIEW PROBLEMS 394 STRENGTHEN YOUR UNDERSTANDING 399 PROJECTS: A HEATER IN A ROOM, OPTIMIZING RELATIVE PRICES FOR ADULTS AND CHILDREN, MAXIMIZING PRODUCTION AND MINIMIZING COST: DUALITY 401 FOCUS ON THEORY 403 DERIVING THE FORMULA FOR A REGRESSION LINE 403 9 MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS 409 9.1 MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION 410 9.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS 414 9.3 SLOPE FIELDS 418 9.4 EXPONENTIAL GROWTH AND DECAY 424 9.5 APPLICATIONS AND MODELING 430 9.6 MODELING THE 445 REVIEW PROBLEMS 450 STRENGTHEN YOUR UNDERSTANDING 452 PROJECTS: PROBLEMS 479 STRENGTHEN YOUR UNDERSTANDING 480 PROJECTS: DO YOU HAVE INTEREST AND THE NUMBER e 492 C SPREADSHEET PROJECTS 497 1. MALTHUS: POPULATION OUTSTRIPS FOOD SUPPLY 497 2. CREDIT CARD DEBT 498 3. CHOOSING A BANK LOAN 499 4. COMPARING HOME MORTGAGES 500 5. PRESENT PROBLEMS 507 PRETEST 535 INDEX 539
