### 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