Select Guide Rating

• CHAPTER 1 Limits and Continuity1.1 Limits (An Intuitive Approach)1.2 Computing Limits1.3 Limits at Infinity; End Behavior of a Function1.4 Limits (Discussed More Rigorously)1.5 Continuity1.6 Trigonometric Functions1.7 Inverse Trigonometric Functions1.8 Exponential and Logarithmic FunctionsCHAPTER 2 The Derivative2.1 Tangent Lines and Rates of Change2.2 The Derivative Function2.3 Introduction to Techniques of Differentiation2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 The Chain RuleCHAPTER 3 Differentiation3.1 Implicit Differentiation3.2 Derivatives of Logarithmic Functions3.3 Derivatives of Exponential and Inverse Trigonometric Functions3.4 Related Rates3.5 Local Linear Approximation; Differentials3.6 L'Hôpital's Rule; Indeterminate FormsCHAPTER 4 The Derivative in Graphing and Applications4.1 Analysis of Functions I: Increase, Decrease, and Concavity4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents4.4 Absolute Maxima and Minima4.5 Applied Maximum and Minimum Problems4.6 Rectilinear Motion4.7 Newton's Method4.8 Rolle's Theorem; Mean-Value TheoremCHAPTER 5 Integration5.1 An Overview of Area and Speed-Distance Problems5.2 The Indefinite Integral5.3 Integration by Substitution5.4 The Definition of Area as a Limit; Sigma Notation5.5 The Definite Integral5.6 The Fundamental Theorem of Calculus5.7 Rectilinear Motion Revisited Using Integration5.8 Average Value of a Function and its Applications5.9 Evaluating Definite Integrals by Substitution5.10 Logarithmic and Other Functions Defined by IntegralsCHAPTER 6 Applications of the Definite Integral6.1 Area Between Two Curves6.2 Volumes by Slicing; Disks and Washers6.3 Volumes by Cylindrical Shells6.4 Length of a Plane Curve6.5 Area of a Surface of Revolution6.6 Work6.7 Moments, Centers of Gravity, and Centroids6.8 Fluid Pressure and Force6.9 Hyperbolic Functions and Hanging CablesCHAPTER 7 Principles of Integral Evaluation7.1 An Overview of Integration Methods7.2 Integration by Parts7.3 Integrating Trigonometric Functions7.4 Trigonometric Substitutions7.5 Integrating Rational Functions by Partial Fractions7.6Using Computer Algebra Systems and Tables of Integrals7.7 Numerical Integration; Simpson's Rule7.8 Improper IntegralsCHAPTER 8 Mathematical Modeling with Differential Equations8.1 Modeling with Differential Equations8.2 Separation of Variables8.3 Slope Fields; Euler's Method8.4 First-Order Differential Equations and Applications8.5 Prey-Predator ModelCHAPTER 9 Parametric and Polar Curves; Conic Sections9.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves9.2 Polar Coordinates9.3 Tangent Lines, Arc Length, and Area for Polar Curves9.4 Conic Sections9.5 Rotation of Axes; Second-Degree Equations9.6 Conic Sections in Polar CoordinatesCHAPTER 10 Sequence and Infinite Series10.1 Sequences10.2 Monotone Sequences10.3 Infinite Series10.4 Convergence Tests10.5 The Comparison, Ratio, and Root Tests10.6 Alternating Series; Absolute and Conditional Convergence10.7 Maclaurin and Taylor Polynomials10.8 Maclaurin and Taylor Series; Power Series10.9 Convergence of Taylor Series10.10 Differentiating and Integrating Power Series; Modeling with Taylor SeriesCHAPTER 11 Three-dimensional Space; Vectors11.1 Rectangular Coordinates in 3-space; Spheres; Cylindrical Surfaces11.2 Vectors11.3 Dot Product; Projections11.4 Cross Product11.5 Parametric Equations of Lines11.6 Planes in 3-space11.7 Quadric Surfaces11.8 Cylindrical and Spherical CoordinatesCHAPTER 12 Vector-Valued Functions12.1 Introduction to Vector-Valued Functions12.2 Calculus of Vector-Valued Functions12.3 Change of Parameter; Arc Length12.4 Unit Tangent, Normal, and Binormal Vectors12.5 Curvature12.6 Motion Along a Curve12.7 Kepler's Laws of Planetary MotionCHAPTER 13 Partial Derivatives 13.1 Functions of Two or More Variables13.2 Limits and Continuity13.3 Partial Derivatives13.4 Differentiability, Differentials, and Local Linearity13.5 The Chain Rule13.6 Directional Derivatives and Gradients13.7 Tangent Planes and Normal Vectors13.8 Maxima and Minima of Functions of Two Variables13.9 Lagrange MultipliersCHAPTER 14 Multiple Integrals14.1 Double Integrals14.2 Double Integrals Over Nonrectangular Regions14.3 Double Integrals in Polar Coordinates14.4 Surface Area; Parametric Surfaces14.5 Triple Integrals14.6 Triple Integrals in Cylindrical and Spherical Coordinates14.7 Change of Variables in Multiple Integrals; Jacobians14.8Centers of Gravity Using Multiple IntegralsCHAPTER 15 Vector Calculus15.1 Vector Fields15.2 Line Integrals15.3 Independence of Path; Conservative Vector Fields15.4 Green's Theorem15.5 Surface Integrals15.6 Applications of Surface Integrals; Flux15.7 The Divergence Theorem15.8 Stokes' TheoremAPPENDICESA TRIGONOMETRY SUMMARYB FUNCTIONS (SUMMARY)C NEW FUNCTIONS FROM OLD (SUMMARY)D FAMILIES OF FUNCTIONS (SUMMARY)E Inverse Functions (SummaryREADY REFERENCE RR-1ANSWERS TO ODD-NUMBERED EXERCISES Ans-1INDEX Ind-1WEB APPENDICES (online only)Available for download at wwww.wiley.comA TRIGONOMETRY REVIEWB FUNCTIONSC NEW FUNCTIONS FROM OLDD FAMILIES OF FUNCTIONSE INVERSE FUNCTIONSF REAL NUMBERS, INTERVALS, AND INEQUALITIESG ABSOLUTE VALUEH COORDINATE PLANES, LINES, AND LINEAR FUNCTIONSI DISTANCE, CIRCLES, AND QUADRATIC EQUATIONSJ SOLVING POLYNOMIAL EQUATIONSK GRAPHING FUNCTIONS USING CALCULATORS ANDCOMPUTER ALGEBRA SYSTEMSL SELECTED PROOFSM EARLY PARAMETRIC EQUATIONS OPTIONN MATHEMATICAL MODELSO THE DISCRIMINANTP SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONSChapter Web Projects: Expanding the Calculus Horizon (online only)Available for download at www.wiley.comRobotics -- Chapter 2Railroad Design -- Chapter 7Iteration and Dynamical Systems -- Chapter 9Comet Collision -- Chapter 10Blammo the Human Cannonball -- Chapter 12Hurricane Modeling -- Chapter 15