Larson, Ron : The Pennsylvania State University, The Behrend College
Hostetler, Robert P. : The Pennsylvania State University, The Behrend College
Edwards, Bruce H. : University of Florida
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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 Fitting Models to Data
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
Section Project: Graphs and Limits of Trigonometric Functions 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 The Product and Quotient Rules and Higher-Order Derivatives 2.4 The Chain Rule 2.5 Implicit Differentiation
Section Project: Optical Illusions
2.6 Related Rates
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
Section Project: Rainbows
3.4 Concavity and the Second Derivative Test 3.5 Limits at Infinity 3.6 A Summary of Curve Sketching 3.7 Optimization Problems
Section Project: Connecticut River
3.8 Newton's Method 3.9 Differentials
P.S. Problem Solving 4. Integration
4.1 Antiderivatives and Indefinite Integration 4.2 Area 4.3 Reimann Sums and Definite Integrals 4.4 The Fundamental Theorem of Calculus
Section Project: Demonstrating the Fundamental Theorem
4.5 Integration by Substitution 4.6 Numerical Integration
P.S. Problem Solving 5. Logarithmic, Exponential, and Other Transcendental Functions
5.1 The Natural Logarithmic Function and Differentiation 5.2 The Natural Logarithmic Function and Integration 5.3 Inverse Functions 5.4 Exponential Functions: Differentiation and Integration 5.5 Bases Other Than e and Applications
Section Project: Using Graphing Utilities to Estimate Slope
5.6 Differential Equations: Growth and Decay 5.7 Differential Equations: Separation of Variables 5.8 Inverse Trigonometric Functions and Differentiation 5.9 Inverse Trigonometric Functions and Integration 5.10 Hyperbolic Functions
Section Project: St. Louis Arch P.S. Problem Solving 6. Applications of Integration
6.1 Area of a Region Between Two Curves 6.2 Volume: The Disc Method 6.3 Volume: The Shell Method
Section Project: Saturn's Oblateness
6.4 Arc Length and Surfaces of Revolution 6.5 Work
Section Project: Tidal Energy
6.6 Moments, Centers of Mass, and Centroids 6.7 Fluid Pressure and Fluid Force
P.S. Problem Solving 7. Integration Techniques, L'Hôpital's Rule, and Improper Integrals
7.1 Basic Integration Rules 7.2 Integration by Parts 7.3 Trigonometric Integrals
Section Project: Power Lines
7.4 Trigonometric Substitution 7.5 Partial Fractions 7.6 Integration by Tables and Other Integration Techniques 7.7 Indeterminant Forms and L'Hôpital's Rule 7.8 Improper Integrals
P.S. Problem Solving 8. Infinite Series
8.1 Sequences 8.2 Series and Convergence
Section Project: Cantor's Disappearing Table
8.3 The Integral Test and p-Series
Section Project: The Harmonic Series
8.4 Comparisons of Series
Section Project: Solera Method
8.5 Alternating Series 8.6 The Ratio and Root Tests 8.7 Taylor Polynomials and Approximations 8.8 Power Series 8.9 Representation of Functions by Power Series 8.10 Taylor and Maclaurin Series
P.S. Problem Solving 9. Conics, Parametric Equations, and Polar Coordinates
9.1 Conics and Calculus 9.2 Plane Curves and Parametric Equations
9.3 Parametric Equations and Calculus 9.4 Polar Coordinates and Polar Graphs
9.5 Area and Arc Length in Polar Coordinates 9.6 Polar Equations of Conics and Kepler's Laws
P.S. Problem Solving 10. Vectors and the Geometry of Space
10.1 Vectors in the Plane 10.2 Space Coordinates and Vectors in Space 10.3 The Dot Product of Two Vectors 10.4 The Cross Product of Two Vectors in Space 10.5 Lines and Planes in Space
10.6 Surfaces in Space 10.7 Cylindrical and Spherical Coordinates
Section Project P.S. Problem Solving 11. Vector-Valued Functions
11.1 Vector-Valued Functions
11.2 Differentiation and Integration of Vector-Valued Functions 11.3 Velocity and Acceleration
11.4 Tangent Vectors and Normal Vectors 11.5 Arc Length and Curvature
P.S. Problem Solving 12. Functions of Several Variables
12.1 Introduction to Functions of Several Variables 12.2 Limits and Continuity 12.3 Partial Derivatives
12.4 Differentials 12.5 Chain Rules for Functions of Several Variables 12.6 Directional Derivatives and Gradients 12.7 Tangent Planes and Normal Lines
12.8 Extrema of Functions of Two Variables 12.9 Applications of Extrema of Functions of Two Variables
12.10 Lagrange Multipliers
P.S. Problem Solving 13. Multiple Integration
13.1 Iterated Integrals and Area in the Plane 13.2 Double Integrals and Volume 13.3 Change of Variables: Polar Coordinates 13.4 Center of Mass and Moments of Inertia
13.5 Surface Area
13.6 Triple Integrals and Applications 13.7 Triple Integrals in Cylindrical and Spherical Coordinates
13.8 Change of Variables: Jacobians
P.S. Problem Solving 14. Vector Analysis
14.1 Vector Fields 14.2 Line Integrals 14.3 Conservative Vector Fields and Independence of Path 14.4 Green's Theorem 14.5 Parametric Surfaces 14.6 Surface Integrals 14.7 Divergence Theorem 14.8 Stoke's Theorem
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