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For full description, see Larson et al., Calculus with Analytic Geometry, 6/e.
Note: Each chapter contains review exercises.
P. Preparation for Calculus
1. Graphs and Models
2. Linear Models and Rates of Change
3. Functions and their Graphs
4. Fitting Models to Data
1. Limits and Their Properties
1. A Preview of Calculus
2. Finding Limits Graphically and Numerically
3. Evaluating Limits Analytically
4. Continuity and One-Sided Limits
5. Infinite Limits
2. Differentiation
1. The Derivative and the Tangent Line Problem
2. Basic Differentiation Rules and Rates of Change
3. The Product and Quotient Rules and Higher-Order Derivatives
4. The Chain Rule
5. Implicit Differentiation
6. Related Rates
3. Applications of Differentiation
1. Extrema on an Interval
2. Rolle's Theorem and the Mean Value Theorem
3. Increasing and Decreasing Functions and the First Derivative Test
4. Concavity and the Second Derivative Test
5. Limits at Infinity
6. A Summary of Curve Sketching
7. Optimization Problems
8. Newton's Method
9. Differentials
10. Business and Economics Applications
4. Integration
1. Antiderivatives and Indefinite Integration
2. Area
3. Riemann Sums and Definite Integrals
4. The Fundamental Theorem of Calculus
5. Integration by Substitution
6. Numerical Integration
5. Logarithmic, Exponential, and Other Transcendental Functions
1. The Natural Logarithmic Function and Differentiation
2. The Natural Logarithmic Function and Integration
3. Inverse Functions
4. Exponential Functions: Differentiation and Integration
5. Bases Other than e and Applications
6. Differential Equations: Growth and Decay
7. Differential Equations: Separation of Variables
8. Inverse Trigonometric Functions and Differentiation
9. Inverse Trigonometric Functions and Integration
10. Hyperbolic Functions
6. Applications of Integration
1. Area of a Region Between Two Curves
2. Volume: The Disc Method
3. Volume: The Shell Method
4. Arc Length and Surfaces of Revolution
5. Work
6. Moments, Centers of Mass, and Centroids
7. Fluid Pressure and Fluid Force
7. Integration Techniques, L'Hopital's Rule, and Improper Integrals
1. Basic Integration Rules
2. Integration by Parts
3. Trigonometric Integrals
4. Trigonometric Substitution
5. Partial Fractions
6. Integration by Tables and Other Integration Techniques
7. Indeterminate Forms and L'Hopital's Rule
8. Improper Integrals
8. Infinite Series
1. Sequences
2. Series and Convergence
3. The Integral Test and p-Series
4. Comparisons of Series
5. Alternating Series
6. The Ratio and Root Tests
7. Taylor Polynomials and Approximations
8. Power Series
9. Representation of Functions by Power Series
10. Taylor and Maclaurin Series
9. Conics, Parametric Equations, and Polar Coordinates
1. Conics and Calculus
2. Plane Curves and Parametric Equations
3. Parametric Equations and Calculus
4. Polar Coordinates and Polar Graphs
5. Area and Arc Length in Polar Coordinates
6. Polar Equations of Conics and Kepler's Laws
Ron Larson, Robert P. Hostetler and Bruce H. Edwards
ISBN13: 978-0395885789For full description, see Larson et al., Calculus with Analytic Geometry, 6/e.
Table of Contents
Note: Each chapter contains review exercises.
P. Preparation for Calculus
1. Graphs and Models
2. Linear Models and Rates of Change
3. Functions and their Graphs
4. Fitting Models to Data
1. Limits and Their Properties
1. A Preview of Calculus
2. Finding Limits Graphically and Numerically
3. Evaluating Limits Analytically
4. Continuity and One-Sided Limits
5. Infinite Limits
2. Differentiation
1. The Derivative and the Tangent Line Problem
2. Basic Differentiation Rules and Rates of Change
3. The Product and Quotient Rules and Higher-Order Derivatives
4. The Chain Rule
5. Implicit Differentiation
6. Related Rates
3. Applications of Differentiation
1. Extrema on an Interval
2. Rolle's Theorem and the Mean Value Theorem
3. Increasing and Decreasing Functions and the First Derivative Test
4. Concavity and the Second Derivative Test
5. Limits at Infinity
6. A Summary of Curve Sketching
7. Optimization Problems
8. Newton's Method
9. Differentials
10. Business and Economics Applications
4. Integration
1. Antiderivatives and Indefinite Integration
2. Area
3. Riemann Sums and Definite Integrals
4. The Fundamental Theorem of Calculus
5. Integration by Substitution
6. Numerical Integration
5. Logarithmic, Exponential, and Other Transcendental Functions
1. The Natural Logarithmic Function and Differentiation
2. The Natural Logarithmic Function and Integration
3. Inverse Functions
4. Exponential Functions: Differentiation and Integration
5. Bases Other than e and Applications
6. Differential Equations: Growth and Decay
7. Differential Equations: Separation of Variables
8. Inverse Trigonometric Functions and Differentiation
9. Inverse Trigonometric Functions and Integration
10. Hyperbolic Functions
6. Applications of Integration
1. Area of a Region Between Two Curves
2. Volume: The Disc Method
3. Volume: The Shell Method
4. Arc Length and Surfaces of Revolution
5. Work
6. Moments, Centers of Mass, and Centroids
7. Fluid Pressure and Fluid Force
7. Integration Techniques, L'Hopital's Rule, and Improper Integrals
1. Basic Integration Rules
2. Integration by Parts
3. Trigonometric Integrals
4. Trigonometric Substitution
5. Partial Fractions
6. Integration by Tables and Other Integration Techniques
7. Indeterminate Forms and L'Hopital's Rule
8. Improper Integrals
8. Infinite Series
1. Sequences
2. Series and Convergence
3. The Integral Test and p-Series
4. Comparisons of Series
5. Alternating Series
6. The Ratio and Root Tests
7. Taylor Polynomials and Approximations
8. Power Series
9. Representation of Functions by Power Series
10. Taylor and Maclaurin Series
9. Conics, Parametric Equations, and Polar Coordinates
1. Conics and Calculus
2. Plane Curves and Parametric Equations
3. Parametric Equations and Calculus
4. Polar Coordinates and Polar Graphs
5. Area and Arc Length in Polar Coordinates
6. Polar Equations of Conics and Kepler's Laws