### Math 221, Section 006, Fall 2010 topics

- Chapter 1: Functions
- § 1.1-1.3
- Chapter 2: Limits and Continuity
- §2.2: Limits
- §2.4: One-sided limits
- §2.5: Continuity
- §2.6: Limits involving ∞; Asymptotes of Graphs
- Chapter 3: Differentiation
- §2.1, 3.1: Tangents and Derivative at a point
- §3.2: The Derivative as a Function
- §3.3: Differentiation Rules
- §3.4: The Derivative as a Rate of Change
- §3.5: Derivatives of Trigonometric Functions
- §3.6: The Chain Rule
- §3.7 Implicit Differentiation
- §3.8: Related Rates
- §3.9: Linearization and Differentials
- Chapter 4: Applications of Derivatives
- §4.1: Extreme Values of Functions
- §4.2: The Mean Value Theorem
- §4.3: Monotonic Functions and the First Derivative Test
- §4.4: Concavity and Curve Sketching
- §4.5: Applied Optimization Problems
- §4.6: Newton's Method
- §4.7: Antiderivatives
- Chapter 5: Integration
- §5.1: Estimating with Finite Sums
- §5.2: Sigma Notation and Limits of Finite Sums
- §5.3: The Definite Integral
- §5.4: The Fundamental Theorem of Calculus
- §5.5 Indefinite Integrals and the Substitution Method
- §5.6 Substitution and Area Between Curves
- Chapter 6: Applications of Definite Integrals
- §6.1, §6.2: Volumes by slices and shells
- §6.3: Lengths of Plane Curves
- §6.4: Surface Area
- §6.5: Work, and force from fluid pressure
- §6.6: Moments and Centers of Mass
- Chapter 7: Transcendental Functions
- §7.1: Inverse Functions and Their Derivatives
- §7.2 and §7.3: Natural Logarithms and Exponentials
- §7.4: Exponential Change and Separable Differential
- §7.5: Indeterminate Forms and L'Hopital's Rule
- §7.6: Relative Rates of Growth
- §7.7: Inverse Trigonometric Functions
- §7.8: Hyperbolic Functions