Calculus : with CalcChat and CalcView

Front Cover Title Page Copyright Page CONTENTS Preface P. Preparation for Calculus P.1 Graphs and Models P.2 Linear Models and Rates of Change P.3 Functions and Their Graphs P.4 Review of Trigonometric Functions Review Exercises P.S. Problem Solving 1. Limits and Their Properties 1.1 A Preview of Calculus 1.2 Finding Limits Graphically and Numerically 1.3 Evaluating Limits Analytically 1.4 Continuity and One-Sided Limits 1.5 Infinite Limits Review Exercises P.S. Problem Solving 2. Differentiation 2.1 The Derivative and the Tangent Line Problem 2.2 Basic Differentiation Rules and Rates of Change 2.3 Product and Quotient Rules and Higher-Order Derivatives 2.4 The Chain Rule 2.5 Implicit Differentiation 2.6 Related Rates Review Exercises P.S. Problem Solving 3. Applications of Differentiation 3.1 Extrema on an Interval 3.2 Rolle's Theorem and the Mean Value Theorem 3.3 Increasing and Decreasing Functions and the First Derivative Test 3.4 Concavity and the Second Derivative Test 3.5 Limits at Infinity 3.6 A Summary of Curve Sketching 3.7 Optimization Problems 3.8 Newton's Method 3.9 Differentials Review Exercises P.S. Problem Solving 4. Integration 4.1 Antiderivatives and Indefinite Integration 4.2 Area 4.3 Riemann Sums and Definite Integrals 4.4 The Fundamental Theorem of Calculus 4.5 Integration by Substitution Review Exercises P.S. Problem Solving 5. Logarithmic, Exponential, and Other Transcendental Functions 5.1 The Natural Logarithmic Function: Differentiation 5.2 The Natural Logarithmic Function: Integration 5.3 Inverse Functions 5.4 Exponential Functions: Differentiation and Integration 5.5 Bases Other than e and Applications 5.6 Indeterminate Forms and L'Hopital's Rule 5.7 Inverse Trigonometric Functions: Differentiation 5.8 Inverse Trigonometric Functions: Integration 5.9 Hyperbolic Functions Review Exercises P.S. Problem Solving 6. Differential Equations 6.1 Slope Fields and Euler's Method 6.2 Growth and Decay 6.3 Separation of Variables and the Logistic Equation 6.4 First-Order Linear Diffferrenttiiall Equattiions Review Exercises P.S. Problem Solving 7. Applications of Integration 7.1 Area of a Region Between Two Curves 7.2 Volume: The Disk Method 7.3 Volume: The Shell Method 7.4 Arc Length and Surfaces of Revolution 7.5 Work 7.6 Moments, Centers of Mass, and Centroids 7.7 Fluid Pressure and Fluid Force Review Exercises P.S. Problem Solving 8. Integration Techniques and Improper Integrals 8.1 Basic Integration Rules 8.2 Integration by Parts 8.3 Trigonometric Integrals 8.4 Trigonometric Substitution 8.5 Partial Fractions 8.6 Numerical Integration 8.7 Integration by Tables and Other Integration Techniques 8.8 Improper Integrals Review Exercises P.S. Problem Solving 9. Infinite Series 9.1 Sequences 9.2 Series and Convergence 9.3 The Integral Test and p-Series 9.4 Comparisons of Series 9.5 Alternating Series 9.6 The Ratio and Root Tests 9.7 Taylor Polynomials and Approximations 9.8 Power Series 9.9 Representation of Functions by Power Series 9.10 Taylor and Maclaurin Series Review Exercises P.S. Problem Solving 10. Conics, Parametric Equations, and Polar Coordinates 10.1 Conics and Calculus 10.2 Plane Curves and Parametric Equations 10.3 Parametric Equations and Calculus 10.4 Polar Coordinates and Polar Graphs 10.5 Area and Arc Length in Polar Coordinates 10.6 Polar Equations of Conics and Kepler's Laws Review Exercises P.S. Problem Solving 11. Vectors and the Geometry of Space 11.1 Vectors in the Plane 11.2 Space Coordinates and Vectors in Space 11.3 The Dot Product of Two Vectors 11.4 The Cross Product of Two Vectors in Space 11.5 Lines and Planes in Space 11.6 Surfaces in Space 11.7 Cylindrical and Spherical Coordinates Review Exercises P.S. Problem Solving 12. Vector-Valued Functions 12.1 Vector-Valued Functions 12.2 Differentiation and Integration of Vector-Valued Functions 12.3 Velocity and Acceleration 12.4 Tangent Vectors and Normal Vectors 12.5 Arc Length and Curvature Review Exercises P.S. Problem Solving 13. Functions of Several Variables 13.1 Introduction to Functions of Several Variables 13.2 Limits and Continuity 13.2 Exercises 13.3 Partial Derivatives 13.4 Differentials 13.5 Chain Rules for Functions of Several Variables 13.6 Directional Derivatives and Gradients 13.7 Tangent Planes and Normal Lines 13.8 Extrema of Functions of Two Variables 13.9 Applications of Extrema 13.10 Lagrange Multipliers Review Exercises P.S. Problem Solving 14. Multiple Integration 14.1 Iterated Integrals and Area in the Plane 14.2 Double Integrals and Volume 14.3 Change of Variables: Polar Coordinates 14.4 Center of Mass and Moments of Inertia 14.5 Surface Area 14.6 Triple Integrals and Applications 14.7 Triple Integrals in Other Coordinates 14.8 Change of Variables: Jacobians Review Exercises P.S. Problem Solving 15. Vector Analysis 15.1 Vector Fields 15.2 Line Integrals 15.3 Conservative Vector Fields and Independence of Path 15.4 Green's Theorem 15.5 Parametric Surfaces 15.6 Surface Integrals 15.7 Divergence Theorem 15.8 Stokes's Theorem Review Exercises P.S. Problem Solving APPENDICES A: Proofs of Selected Theorems B: Integration Tables ANSWERS to Odd-Numbered Exercises P. P.1 P.2 P.3 P.4 R PS 1. 1.1 1.2 1.3 1.4 1.5 R PS 2. 2.1 2.2 2.3 2.4 2.5 2.6 R - PS 3. 3.1 - 3.2 3.3 3.4 3.5 3.6 3.7 3.8 - 3.9 R PS 4. 4.1 4.2 4.3 4.4 4.5 R PS 5. 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 - R PS 6. 6.1 6.2 6.3 6.4 - R PS 7. 7.1 7.2 7.3 7.4 7.5 7.6 7.7 R PS 8. 8.1 8.2 8.3 - 8.4 8.5 8.6 8.7 8.8 - R PS 9. 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 R PS 10. 10.1 10.2 10.3 10.4 10.5 10.6 R PS 11. 11.1 11.2 11.3 - 11.4 11.5 11.6 11.7 R PS 12. 12.1 12.2 12.3 12.4 12.5 R PS 13. 13.1 13.2 - 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 R PS 14. 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 R PS 15. 15.1 - 15.2 15.3 - 15.4 15.5 15.6 15.7 - 15.8 - R - PS INDEX A B C D E F G H - I J - K - L M - N O P Q R S T U - V - W X - Y - Z Index of Applications Index of Applications (cont'd) Useful Formulas Algebra Formulas from Geometry Trigonometry Derivatives & Integrals