Calculus. Concepts and Contexts

Description

Cover Contents Preface To the Student About the Author Diagnostic Tests A Preview of Calculus Chapter 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 Exponential Functions 1.5 Inverse Functions and Logarithms 1.6 Parametric Curves 1 Review Principles of Problem Solving Chapter 2: Limits 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 2.7 The Derivative as a Function 2 Review Focus on Problem Solving Chapter 3: Differentiation Rules 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Inverse Trigonometric Functions and Their Derivatives 3.7 Derivatives of Logarithmic Functions 3.8 Rates of Change in the Natural and Social Sciences 3.9 Linear Approximations and Differentials 3 Review Focus on Problem Solving Chapter 4: Applications of Differentiation 4.1 Related Rates 4.2 Maximum and Minimum Values 4.3 Derivatives and the Shapes of Curves 4.4 Graphing with Calculus and Technology 4.5 Indeterminate Forms and L'Hospital's Rule 4.6 Optimization Problems 4.7 Newton's Method 4.8 Antiderivatives 4 Review Focus on Problem Solving Chapter 5: Integrals 5.1 Areas and Distances 5.2 The Definite Integral 5.3 Evaluating Definite Integrals 5.4 The Fundamental Theorem 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 5.9 Approximate Integration 5.10 Improper Integrals 5 Review Focus on Problem Solving Chapter 6: Applications of Integration 6.1 More about Areas 6.2 Volumes 6.3 Volumes by Cylindrical Shells 6.4 Arc Length 6.5 Average Value of a Function 6.6 Applications to Physics and Engineering 6.7 Applications to Economics and Biology 6.8 Probability 6 Review Focus on Problem Solving Chapter 7: Differential Equations 7.1 Modeling with Differential Equations 7.2 Slope Fields and Euler's Method 7.3 Separable Equations 7.4 Exponential Growth and Decay 7.5 The Logistic Equation 7.6 Predator-Prey Systems 7 Review Focus on Problem Solving Chapter 8: Infinite Sequences and Series 8.1 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 8.8 Applications of Taylor Polynomials 8 Review Focus on Problem Solving Chapter 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 9.5 Equations of Lines and Planes 9.6 Functions and Surfaces 9.7 Cylindrical and Spherical Coordinates 9 Review Focus on Problem Solving Chapter 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 10.5 Parametric Surfaces 10 Review Focus on Problem Solving Chapter 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 11.8 Lagrange Multipliers 11 Review Focus on Problem Solving Chapter 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 12.8 Triple Integrals in Cylindrical and Spherical Coordinates 12.9 Change of Variables in Multiple Integrals 12 Review Focus on Problem Solving Chapter 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 13.8 The Divergence Theorem 13.9 Summary 13 Review Focus on Problem Solving Appendixes Appendix A: Intervals, Inequalities, and Absolute Values Appendix B: Coordinate Geometry Appendix C: Trigonometry Appendix D: Precise Definitions of Limits Appendix E: A Few Proofs Appendix F: Sigma Notation Appendix G: Integration of Rational Functions by Partial Fractions Appendix H: Polar Coordinates Appendix I: Complex Numbers Appendix J: Answers to Odd-Numbered Exercises Index