1. Functions
1.1 Â Â Functions and Their Graphs
1.2 Â Â Combining Functions; Shifting and Scaling Graphs
1.3 Â Â Trigonometric Functions
1.4 Â Â Graphing with Software
1.5 Â Â Exponential Functions
1.6 Â Â Inverse Functions and Logarithms
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2. Â Â Limits and ContinuityÂ
2.1 Â Â Rates of Change and Tangent Lines to Curves
2.2 Â Â Limit of a Function and Limit Laws
2.3 Â Â The Precise Definition of a Limit
2.4 Â Â One-Sided Limits
2.5 Â Â Continuity
2.6 Â Â Limits Involving Infinity; Asymptotes of Graphs
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
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3. Â Â Derivatives
3.1 Â Â Tangent Lines and the Derivative at a Point
3.2 Â Â The Derivative as a Function
3.3 Â Â Differentiation Rules
3.4 Â Â The Derivative as a Rate of Change
3.5 Â Â Derivatives of Trigonometric Functions
3.6 Â Â The Chain Rule
3.7 Â Â Implicit Differentiation
3.8 Â Â Derivatives of Inverse Functions and Logarithms
3.9 Â Â Inverse Trigonometric Functions
3.10 Related Rates
3.11 Linearization and Differentials
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
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4. Â Â Applications of Derivatives
4.1 Â Â Extreme Values of Functions on Closed Intervals
4.2 Â Â The Mean Value Theorem
4.3 Â Â Monotonic Functions and the First Derivative Test
4.4 Â Â Concavity and Curve Sketching
4.5   Indeterminate Forms and L’Hôpital’s Rule
4.6 Â Â Applied Optimization
4.7   Newton’s Method
4.8 Â Â Antiderivatives
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
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5. Â Â Integrals
5.1 Â Â Area and Estimating with Finite Sums
5.2 Â Â Sigma Notation and Limits of Finite Sums
5.3 Â Â The Definite Integral
5.4 Â Â The Fundamental Theorem of Calculus
5.5 Â Â Indefinite Integrals and the Substitution Method
5.6 Â Â Definite Integral Substitutions and the Area Between Curves
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
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6. Â Â Applications of Definite Integrals
6.1 Â Â Volumes Using Cross-Sections
6.2 Â Â Volumes Using Cylindrical Shells
6.3 Â Â Arc Length
6.4 Â Â Areas of Surfaces of Revolution
6.5 Â Â Work
6.6 Â Â Moments and Centers of Mass
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
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7. Â Â Integrals and Transcendental Functions
7.1 Â Â The Logarithm Defined as an Integral
7.2 Â Â Exponential Change and Separable Differential Equations
7.3 Â Â Hyperbolic Functions
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
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8. Â Â Techniques of Integration Â
8.1 Â Â Integration by Parts
8.2 Â Â Trigonometric Integrals
8.3 Â Â Trigonometric Substitutions
8.4 Â Â Integration of Rational Functions by Partial Fractions