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Ideal for the single-variable, one-, or two-semester calculus course, Calculus of a Single Variable, 7/e, contains the first 9 chapers of Calculus with Analytic Geometry, 7/e. For a description, see Larson et al., Calculus with Analytic Geometry, 7/e.
Author Bio
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
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
Section Project
9.3 Parametric Equations and Calculus
9.4 Polar Coordinates and Polar Graphs
Section Project
9.5 Area and Arc Length in Polar Coordinates
9.6 Polar Equations of Conics and Kepler's Laws
P.S. Problem Solving
Ron Larson, Robert P. Hostetler and Bruce H. Edwards
ISBN13: 978-0618149162Ideal for the single-variable, one-, or two-semester calculus course, Calculus of a Single Variable, 7/e, contains the first 9 chapers of Calculus with Analytic Geometry, 7/e. For a description, see Larson et al., Calculus with Analytic Geometry, 7/e.
Author Bio
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
Table of Contents
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
Section Project
9.3 Parametric Equations and Calculus
9.4 Polar Coordinates and Polar Graphs
Section Project
9.5 Area and Arc Length in Polar Coordinates
9.6 Polar Equations of Conics and Kepler's Laws
P.S. Problem Solving