Calculus: Single and Multivariable

Höfundar: Deborah Hughes-Hallett; Andrew M. Gleason; William G. McCallum (Útgáfa: 8)
Calculus: Single and Multivariable

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Calculus: Single and Multivariable, 8th Edition teaches calculus in a way that promotes critical thinking to reveal solutions to mathematical problems while highlighting the practical value of mathematics. From the Calculus Consortium based at Harvard University, this leading text reinforces the conceptual understanding students require to reduce complicated problems to simple procedures. In this new edition, the authors retain their emphasis on the Rule of Four--viewing problems graphically, numerically, symbolically, and verbally--with a special focus on introducing different perspectives for students with different learning styles.

The ideal textbook for promoting active learning in a 'flipped' classroom, Calculus engages students across multiple majors by providing a variety of problems with applications from the physical sciences, economics, health, biology, engineering, and economics. Throughout the text, the Consortium brings calculus to life with current and relevant examples and numerous opportunities to master key mathematical concepts and skills.

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Útgefandi
Wiley Global Education US
ISBN
9781119694298
Print ISBN
9781119696551
Format
ePub
Útgáfa
8
Höfundar
Deborah Hughes-Hallett; Andrew M. Gleason; William G. McCallum
Tungumál
English
Útgefið
01/2021
Prent takmörkun á líftíma
100

Kaflar

  • Cover
  • Dedication
  • Title Page
  • Copyright
  • Preface
  • Acknowledgements
  • Chapter 1: FOUNDATION FOR CALCULUS: FUNCTIONS AND LIMITS
  • 1.1 FUNCTIONS AND CHANGE
  • 1.2 EXPONENTIAL FUNCTIONS
  • 1.3 NEW FUNCTIONS FROM OLD
  • 1.4 LOGARITHMIC FUNCTIONS
  • 1.5 TRIGONOMETRIC FUNCTIONS
  • 1.6 POWERS, POLYNOMIALS, AND RATIONAL FUNCTIONS
  • 1.7 INTRODUCTION TO LIMITS AND CONTINUITY
  • 1.8 EXTENDING THE IDEA OF A LIMIT
  • 1.9 FURTHER LIMIT CALCULATIONS USING ALGEBRA
  • 1.10 PREVIEW OF THE FORMAL DEFINITION OF A LIMIT
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 1
  • Notes
  • Chapter 2: KEY CONCEPT: THE DERIVATIVE
  • 2.1 HOW DO WE MEASURE SPEED?
  • 2.2 THE DERIVATIVE AT A POINT
  • 2.3 THE DERIVATIVE FUNCTION
  • 2.4 INTERPRETATIONS OF THE DERIVATIVE
  • 2.5 THE SECOND DERIVATIVE
  • 2.6 DIFFERENTIABILITY
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 2
  • Notes
  • Chapter 3: SHORT-CUTS TO DIFFERENTIATION
  • 3.1 POWERS AND POLYNOMIALS
  • 3.2 THE EXPONENTIAL FUNCTION
  • 3.3 THE PRODUCT AND QUOTIENT RULES
  • 3.4 THE CHAIN RULE
  • 3.5 THE TRIGONOMETRIC FUNCTIONS
  • 3.6 THE CHAIN RULE AND INVERSE FUNCTIONS
  • 3.7 IMPLICIT FUNCTIONS
  • 3.8 HYPERBOLIC FUNCTIONS
  • 3.9 LINEAR APPROXIMATION AND THE DERIVATIVE
  • 3.10 THEOREMS ABOUT DIFFERENTIABLE FUNCTIONS
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 3
  • Notes
  • Chapter 4: USING THE DERIVATIVE
  • 4.1 USING FIRST AND SECOND DERIVATIVES
  • 4.2 OPTIMIZATION
  • 4.3 OPTIMIZATION AND MODELING
  • 4.4 FAMILIES OF FUNCTIONS AND MODELING
  • 4.5 APPLICATIONS TO MARGINALITY
  • 4.6 RATES AND RELATED RATES
  • 4.7 L’HOPITAL’S RULE, GROWTH, AND DOMINANCE
  • 4.8 PARAMETRIC EQUATIONS
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 4
  • Notes
  • Chapter 5: KEY CONCEPT: THE DEFINITE INTEGRAL
  • 5.1 HOW DO WE MEASURE DISTANCE TRAVELED?
  • 5.2 THE DEFINITE INTEGRAL
  • 5.3 THE FUNDAMENTAL THEOREM AND INTERPRETATIONS
  • 5.4 THEOREMS ABOUT DEFINITE INTEGRALS
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 5
  • Notes
  • Chapter 6: CONSTRUCTING ANTIDERIVATIVES
  • 6.1 ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY
  • 6.2 CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY
  • 6.3 DIFFERENTIAL EQUATIONS AND MOTION
  • 6.4 SECOND FUNDAMENTAL THEOREM OF CALCULUS
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 6
  • Notes
  • Chapter 7: INTEGRATION
  • 7.1 INTEGRATION BY SUBSTITUTION
  • 7.2 INTEGRATION BY PARTS
  • 7.3 TABLES OF INTEGRALS
  • 7.4 ALGEBRAIC IDENTITIES AND TRIGONOMETRIC SUBSTITUTIONS
  • 7.5 NUMERICAL METHODS FOR DEFINITE INTEGRALS
  • 7.6 IMPROPER INTEGRALS
  • 7.7 COMPARISON OF IMPROPER INTEGRALS
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 7
  • Notes
  • Chapter 8: USING THE DEFINITE INTEGRAL
  • 8.1 AREAS AND VOLUMES
  • 8.2 APPLICATIONS TO GEOMETRY
  • 8.3 AREA AND ARC LENGTH IN POLAR COORDINATES
  • 8.4 DENSITY AND CENTER OF MASS
  • 8.5 APPLICATIONS TO PHYSICS
  • 8.6 APPLICATIONS TO ECONOMICS
  • 8.7 DISTRIBUTION FUNCTIONS
  • 8.8 PROBABILITY, MEAN, AND MEDIAN
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 8
  • Notes
  • Chapter 9: SEQUENCES AND SERIES
  • 9.1 SEQUENCES
  • 9.2 GEOMETRIC SERIES
  • 9.3 CONVERGENCE OF SERIES
  • 9.4 TESTS FOR CONVERGENCE
  • 9.5 POWER SERIES AND INTERVAL OF CONVERGENCE
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 9
  • Notes
  • Chapter 10: APPROXIMATING FUNCTIONS USING SERIES
  • 10.1 TAYLOR POLYNOMIALS
  • 10.2 TAYLOR SERIES
  • 10.3 FINDING AND USING TAYLOR SERIES
  • 10.4 THE ERROR IN TAYLOR POLYNOMIAL APPROXIMATIONS
  • 10.5 FOURIER SERIES
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 10
  • Notes
  • Chapter 11: DIFFERENTIAL EQUATIONS
  • 11.1 WHAT IS A DIFFERENTIAL EQUATION?
  • 11.2 SLOPE FIELDS
  • 11.3 EULER’S METHOD
  • 11.4 SEPARATION OF VARIABLES
  • 11.5 GROWTH AND DECAY
  • 11.6 APPLICATIONS AND MODELING
  • 11.7 THE LOGISTIC MODEL
  • 11.8 SYSTEMS OF DIFFERENTIAL EQUATIONS
  • 11.9 ANALYZING THE PHASE PLANE
  • 11.10 SECOND-ORDER DIFFERENTIAL EQUATIONS: OSCILLATIONS
  • 11.11 LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 11
  • Notes
  • Chapter 12: FUNCTIONS OF SEVERAL VARIABLES
  • 12.1 FUNCTIONS OF TWO VARIABLES
  • 12.2 GRAPHS AND SURFACES
  • 12.3 CONTOUR DIAGRAMS
  • 12.4 LINEAR FUNCTIONS
  • 12.5 FUNCTIONS OF THREE VARIABLES
  • 12.6 LIMITS AND CONTINUITY
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 12
  • Notes
  • Chapter 13: A FUNDAMENTAL TOOL: VECTORS
  • 13.1 DISPLACEMENT VECTORS
  • 13.2 VECTORS IN GENERAL
  • 13.3 THE DOT PRODUCT
  • 13.4 THE CROSS PRODUCT
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 13
  • Notes
  • Chapter 14: DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES
  • 14.1 THE PARTIAL DERIVATIVE
  • 14.2 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY
  • 14.3 LOCAL LINEARITY AND THE DIFFERENTIAL
  • 14.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE
  • 14.5 GRADIENTS AND DIRECTIONAL DERIVATIVES IN SPACE
  • 14.6 THE CHAIN RULE
  • 14.7 SECOND-ORDER PARTIAL DERIVATIVES
  • 14.8 DIFFERENTIABILITY
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 14
  • Notes
  • Chapter 15: OPTIMIZATION: LOCAL AND GLOBAL EXTREMA
  • 15.1 CRITICAL POINTS: LOCAL EXTREMA AND SADDLE POINTS
  • 15.2 OPTIMIZATION
  • 15.3 CONSTRAINED OPTIMIZATION: LAGRANGE MULTIPLIERS
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 15
  • Notes
  • Chapter 16: INTEGRATING FUNCTIONS OF SEVERAL VARIABLES
  • 16.1 THE DEFINITE INTEGRAL OF A FUNCTION OF TWO VARIABLES
  • 16.2 ITERATED INTEGRALS
  • 16.3 TRIPLE INTEGRALS
  • 16.4 DOUBLE INTEGRALS IN POLAR COORDINATES
  • 16.5 INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES
  • 16.6 APPLICATIONS OF INTEGRATION TO PROBABILITY
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 16
  • Notes
  • Chapter 17: PARAMETERIZATION AND VECTOR FIELDS
  • 17.1 PARAMETERIZED CURVES
  • 17.2 MOTION, VELOCITY, AND ACCELERATION
  • 17.3 VECTOR FIELDS
  • 17.4 THE FLOW OF A VECTOR FIELD
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 17
  • Notes
  • Chapter 18: LINE INTEGRALS
  • 18.1 THE IDEA OF A LINE INTEGRAL
  • 18.2 COMPUTING LINE INTEGRALS OVER PARAMETERIZED CURVES
  • 18.3 GRADIENT FIELDS AND PATH-INDEPENDENT FIELDS
  • 18.4 PATH-DEPENDENT VECTOR FIELDS AND GREEN’S THEOREM
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 18
  • Notes
  • Chapter 19: FLUX INTEGRALS AND DIVERGENCE
  • 19.1 THE IDEA OF A FLUX INTEGRAL
  • 19.2 FLUX INTEGRALS FOR GRAPHS, CYLINDERS, AND SPHERES
  • 19.3 THE DIVERGENCE OF A VECTOR FIELD
  • 19.4 THE DIVERGENCE THEOREM
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 19
  • Notes
  • Chapter 20: THE CURL AND STOKES’ THEOREM
  • 20.1 THE CURL OF A VECTOR FIELD
  • 20.2 STOKES’ THEOREM
  • 20.3 THE THREE FUNDAMENTAL THEOREMS
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 20
  • Notes
  • Chapter 21: PARAMETERS, COORDINATES, AND INTEGRALS
  • 21.1 COORDINATES AND PARAMETERIZED SURFACES
  • 21.2 CHANGE OF COORDINATES IN A MULTIPLE INTEGRAL
  • 21.3 FLUX INTEGRALS OVER PARAMETERIZED SURFACES
  • REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 21
  • Notes
  • APPENDICES
  • A: ROOTS, ACCURACY, AND BOUNDS
  • B: COMPLEX NUMBERS
  • C: NEWTON’S METHOD
  • D: VECTORS IN THE PLANE
  • E: DETERMINANTS
  • READY REFERENCE
  • INDEX
  • Differentiation Formulas and A Short Table of Indefinite Integrals
  • End User License Agreement