Robert T Smith,
Millersville University Roland B Minton,
Roanoke College
ISBN: 0073383112 Copyright year: 2012
Table of Contents
Chapter 0: Preliminaries 0.1 The Real Numbers and the Cartesian Plane 0.2 Lines and Functions 0.3 Graphing Calculators and Computer Algebra Systems 0.4 Trigonometric Functions 0.5 Transformations of Functions Chapter 1: Limits and Continuity 1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve 1.2 The Concept of Limit 1.3 Computation of Limits 1.4 Continuity and its Consequences 1.5 Limits Involving Infinity; Asymptotes 1.6 The Formal Definition of the Limit 1.7 Limits and Loss-of-Significance Errors Chapter 2: Differentiation 2.1 Tangent Lines and Velocity 2.2 The Derivative 2.3 Computation of Derivatives: The Power Rule 2.4 The Product and Quotient Rules 2.5 The Chain Rule 2.6 Derivatives of the Trigonometric Functions 2.7 Implicit Differentiation 2.8 The Mean Value Theorem Chapter 3: Applications of Differentiation 3.1 Linear Approximations and Newton's Method 3.2 Maximum and Minimum Values 3.3 Increasing and Decreasing Functions 3.4 Concavity and the Second Derivative Test 3.5 Overview of Curve Sketching 3.6 Optimization 3.7 Related Rates 3.8 Rates of Change in Economics and the Sciences Chapter 4: Integration 4.1 Antiderivatives 4.2 Sums and Sigma Notation 4.3 Area 4.4 The Definite Integral 4.5 The Fundamental Theorem of Calculus 4.6 Integration by Substitution 4.7 Numerical Integration Chapter 5: Applications of the Definite Integral 5.1 Area Between Curves 5.2 Volume: Slicing, Disks, and Washers 5.3 Volumes by Cylindrical Shells 5.4 Arc Length and Surface Area 5.5 Projectile Motion 5.6 Applications of Integration to Physics and Engineering Chapter 6: Exponentials, Logarithms and other Transcendental Functions 6.1 The Natural Logarithm 6.2 Inverse Functions 6.3 The Exponential Function 6.4 The Inverse Trigonometric Functions 6.5 The Calculus of the Inverse Trigonometric Functions 6.6 The Hyperbolic Function Chapter 7: Integration Techniques 7.1 Review of Formulas and Techniques 7.2 Integration by Parts 7.3 Trigonometric Techniques of Integration 7.4 Integration of Rational Functions using Partial Fractions 7.5 Integration Tables and Computer Algebra Systems 7.6 Indeterminate Forms and L'Hopital's Rule 7.7 Improper Integrals 7.8 Probability Chapter 8: First-Order Differential Equations 8.1 Modeling with Differential Equations 8.2 Separable Differential Equations 8.3 Direction Fields and Euler's Method 8.4 Systems of First Order Equations Chapter 9: Infinite Series 9.1 Sequences of Real Numbers 9.2 Infinite Series 9.3 The Integral Test and Comparison Tests 9.4 Alternating Series 9.5 Absolute Convergence and the Ratio Test 9.6 Power Series 9.7 Taylor Series 9.8 Applications of Taylor Series 9.9 Fourier Series Chapter 10: Parametric Equations and Polar Coordinates 10.1 Plane Curves and Parametric Equations 10.2 Calculus and Parametric Equations 10.3 Arc Length and Surface Area in Parametric Equations 10.4 Polar Coordinates 10.5 Calculus and Polar Coordinates 10.6 Conic Sections 10.7 Conic Sections in Polar Coordinates Chapter 11: Vectors and the Geometry of Space 11.1 Vectors in the Plane 11.2 Vectors in Space 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Surfaces in Space Chapter 12: Vector-Valued Functions 12.1 Vector-Valued Functions 12.2 The Calculus Vector-Valued Functions 12.3 Motion in Space 12.4 Curvature 12.5 Tangent and Normal Vectors 12.6 Parametric Surfaces Chapter 13: Functions of Several Variables and Partial Differentiation 13.1 Functions of Several Variables 13.2 Limits and Continuity 13.3 Partial Derivatives 13.4 Tangent Planes and Linear Approximations 13.5 The Chain Rule 13.6 The Gradient and Directional Derivatives 13.7 Extrema of Functions of Several Variables 13.8 Constrained Optimization and LaGrange Multipliers Chapter 14: Multiple Integrals 14.1 Double Integrals 14.2 Area, Volume, and Center of Mass 14.3 Double Integrals in Polar Coordinates 14.4 Surface Area 14.5 Triple Integrals 14.6 Cylindrical Coordinates 14.7 Spherical Coordinates 14.8 Change of Variables in Multiple Integrals Chapter 15: Vector Calculus 15.1 Vector Fields 15.2 Line Integrals 15.3 Independence of Path and Conservative Vector Fields 15.4 Green's Theorem 15.5 Curl and Divergence 15.6 Surface Integrals 15.7 The Divergence Theorem 15.8 Stokes' Theorem 15.9 Applications of Vector Calculus Chapter 16: Second-Order Differential Equations 16.1 Second-Order Equations with Constant Coefficients 16.2 Nonhomogeneous Equations: Undetermined Coefficients 16.3 Applications of Second-Order Differential Equations 16.4 Power Series Solutions of Differential Equations Appendix A: Proofs of Selected Theorems Appendix B: Answers to Odd-Numbered Exercises
2012