Calculus: Single Variable, 6th Edition continues the effort to promote courses in which understanding and computation reinforce each other. The 6th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. For instructors wishing to emphasize the connection between calculus and other fields, the text includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics. In addition, new problems on the mathematics of sustainability and new case studies on calculus in medicine by David E. Sloane, MD have been added.
1 A LIBRARY OF FUNCTIONS
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 CONTINUITY
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
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
4 USING THE DERIVATIVE
4.1 USING FIRST AND SECOND DERIVATIVES
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
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
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
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
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
9 SEQUENCES AND SERIES
9.2 GEOMETRIC SERIES
9.3 CONVERGENCE OF SERIES
9.4 TESTS FOR CONVERGENCE
9.5 POWER SERIES AND INTERVAL OF CONVERGENCE
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
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
A ROOTS, ACCURACY, AND BOUNDS
B COMPLEX NUMBERS
C NEWTON’S METHOD
D VECTORS IN THE PLANE
ANSWERS TO ODD-NUMBERED PROBLEMS
- New Strengthen Your Understanding problems at the end of every section. These problems ask students to reflect on what they have learned by deciding “What is wrong?” with a statement and to “Give an example” of an idea.
- Updated Data and Models: For example, Section 11.7 follows the current debate on Peak Oil Production, underscoring the importance of mathematics in understanding the world’s economic and social? problems.
- Drill Exercises build student skill and confidence.
- Online Problems available in WileyPLUS or WeBWorK, for example. Many problems are randomized, providing students with expanded opportunities for practice with immediate feedback.
- Projects at the end of each chapter provide opportunities for a sustained investigation, often using skills from different parts of the course.
- ConcepTests promote active learning in the classroom. These can be used with or without clickers (personal response systems), and have been shown to dramatically improve student learning.
- Class Worksheets allow instructors to engage students in individual or group class-work. Samples are available in the Instructor’s Manual, and all are on the web at www.wiley.com/college/hughes-hallett
- Innovative and engaging problems. Under the approach called the “Rule of Four,” ideas are presented graphically, numerically, symbolically, and verbally, thereby encouraging students with a variety of learning styles to expand their knowledge.
- A Flexible Approach to Technology: Adaptable to courses having various levels of computer involvement, ranging from little or none to intensive. The book does not require any specific software or technology, though it has been used successfully with graphing calculators, graphing software, and computer algebra systems.
- Applied Problems for instructors wishing to emphasize the connection between calculus and other fields.