Calculus : concepts and contexts

Description

Front Cover Context Title Page Copyright Page CONTENTS (with direct page links) Preface To the Student Diagnostic Tests A Preview of Calculus 1 Functions and Models 1.1 Four Ways to Represent a Function 1.2 Mathematical Models: A Catalog of Essential Functions 1.3 New Functions from Old Functions 1.4 Graphing Calculators and Computers 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms 1.7 Parametric Curves Laboratory Project Running Circles Around Circles Review Principles of Problem Solving 2 Limits and Derivatives 2.1 The Tangent and Velocity Problems 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.4 Continuity 2.5 Limits Involving Infinity 2.6 Derivatives and Rates of Change Writing Project Early Methods for Finding Tangents 2.7 The Derivative as a Function 2.8 What Does f' Say about f? Review Focus on Problem Solving 3 Differentiation Rules 3.1 Derivatives of Polynomials and Exponential Functions Applied Project Building a Better Roller Coaster 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule Laboratory Project Bézier Curves Applied Project Where Should a Pilot Start Descent? 3.5 Implicit Differentiation 3.6 Inverse Trigonometric Functions and Their Derivatives 3.7 Derivatives of Logarithmic Functions Discovery Project Hyperbolic Functions 3.8 Rates of Change in the Natural and Social Sciences 3.9 Linear Approximations and Differentials Laboratory Project Taylor Polynomials Review Focus on Problem Solving 4 Applications of Differentiation 4.1 Related Rates 4.2 Maximum and Minimum Values Applied Project The Calculus of Rainbows 4.3 Derivatives and the Shapes of Curves 4.4 Graphing with Calculus and Calculators 4.5 Indeterminate Forms and l’Hospital’s Rule Writing Project The Origins of l’Hospital’s Rule 4.6 Optimization Problems Applied Project The Shape of a Can 4.7 Newton’s Method 4.8 Antiderivatives Review Focus on Problem Solving 5 Integrals 5.1 Areas and Distances 5.2 The Definite Integral 5.3 Evaluating Definite Integrals Discovery Project Area Functions 5.4 The Fundamental Theorem of Calculus Writing Project Newton, Leibniz, and the Invention of Calculus 5.5 The Substitution Rule 5.6 Integration by Parts 5.7 Additional Techniques of Integration 5.8 Integration Using Tables and Computer Algebra Systems Discovery Project Patterns in Integrals 5.9 Approximate Integration 5.10 Improper Integrals Review Focus on Problem Solving 6 Applications of Integration 6.1 More About Areas 6.2 Volumes Discovery Project Rotating on a Slant 6.3 Volumes by Cylindrical Shells 6.4 Arc Length Discovery Project Arc Length Contest 6.5 Average Value of a Function Applied Project Where To Sit at the Movies 6.6 Applications to Physics and Engineering Discovery Project Complementary Coffee Cups 6.7 Applications to Economics and Biology 6.8 Probability Review Focus on Problem Solving 7 Differential Equations 7.1 Modeling with Differential Equations 7.2 Direction Fields and Euler’s Method 7.3 Separable Equations Applied Project How Fast Does a Tank Drain? Applied Project Which Is Faster, Going Up or Coming Down? 7.4 Exponential Growth and Decay Applied Project Calculus and Baseball 7.5 The Logistic Equation 7.6 Predator-Prey Systems Review Focus on Problem Solving 8 Infinite Sequences and Series 8.1 Sequences Laboratory Project Logistic Sequences 8.2 Series 8.3 The Integral and Comparison Tests; Estimating Sums 8.4 Other Convergence Tests 8.5 Power Series 8.6 Representations of Functions as Power Series 8.7 Taylor and Maclaurin Series Laboratory Project An Elusive Limit Writing Project How Newton Discovered the Binomial Series 8.8 Applications of Taylor Polynomials Applied Project Radiation from the Stars Review Focus on Problem Solving 9 Vectors and the Geometry of Space 9.1 Three-Dimensional Coordinate Systems 9.2 Vectors 9.3 The Dot Product 9.4 The Cross Product Discovery Project The Geometry of a Tetrahedron 9.5 Equations of Lines and Planes Laboratory Project Putting 3D in Perspective 9.6 Functions and Surfaces 9.7 Cylindrical and Spherical Coordinates Laboratory Project Families of Surfaces Review Focus on Problem Solving 10 Vector Functions 10.1 Vector Functions and Space Curves 10.2 Derivatives and Integrals of Vector Functions 10.3 Arc Length and Curvature 10.4 Motion in Space: Velocity and Acceleration Applied Project Kepler’s Laws 10.5 Parametric Surfaces Review Focus on Problem Solving 11 Partial Derivatives 11.1 Functions of Several Variables 11.2 Limits and Continuity 11.3 Partial Derivatives 11.4 Tangent Planes and Linear Approximations 11.5 The Chain Rule 11.6 Directional Derivatives and the Gradient Vector 11.7 Maximum and Minimum Values Applied Project Designing a Dumpster Discovery Project Quadratic Approximations and Critical Points 11.8 Lagrange Multipliers Applied Project Rocket Science Applied Project Hydro-Turbine Optimization Review Focus on Problem Solving 12 Multiple Integrals 12.1 Double Integrals over Rectangles 12.2 Iterated Integrals 12.3 Double Integrals over General Regions 12.4 Double Integrals in Polar Coordinates 12.5 Applications of Double Integrals 12.6 Surface Area 12.7 Triple Integrals Discovery Project Volumes of Hyperspheres 12.8 Triple Integrals in Cylindrical and Spherical Coordinates Applied Project Roller Derby Discovery Project The Intersection of Three Cylinders 12.9 Change of Variables in Multiple Integrals Review Focus on Problem Solving 13 Vector Calculus 13.1 Vector Fields 13.2 Line Integrals 13.3 The Fundamental Theorem for Line Integrals 13.4 Green’s Theorem 13.5 Curl and Divergence 13.6 Surface Integrals 13.7 Stokes’ Theorem Writing Project Three Men and Two Theorems 13.8 The Divergence Theorem 13.9 Summary Review Focus on Problem Solving Appendices A: Intervals, Inequalities, and Absolute Values B: Coordinate Geometry C: Trigonometry D: Precise Definitions of Limits E: A Few Proofs F: Sigma Notation G: Integration of Rational Functions by Partial Fractions H: Polar Coordinates I: Complex Numbers J: ANSWERS to Odd-Numbered Exercises ch01 ch02 ch03 ch04 ch05 ch06 ch07 ch08 ch09 ch10 ch11 ch12 ch13 app INDEX Quick Reference Pages Algebra & Geometry Trigonometry Special Functions Differentiation Rules Table of Integrals