Calculus I

Lecture Notes:

• Chapter 0.1: Review of Functions (complete)

• Appendix B: Trigonometry Review (complete)

• Chapter 0.2: New Functions From Old (complete)

• Chapter 0.4: Inverse Functions (complete)

• Chapter 0.5: Exponential and Logarithmic Functions (complete)

• Chapter 1.1: Limits: An Intuitive Approach (preprinted)
• Chapter 1.1: Limits: An Intuitive Approach (in-class notes; complete)

• Chapter 1.2: Computing Limits

• Chapter 1.3: Limits at Infinty (complete)

• Chapter 1.5: Continuity (complete)

• Chapter 1.6: Continuity of Trigonometric Functions (complete)

• Chapter 2.1: Tangent Lines and Rates of Change (preprinted)
• Chapter 2.1: Tangent Lines and Rates of Change (in-class notes, complete)
• Here is a good applet that illustrates the concepts of secant and tangent lines.

• Chapter 2.2: The Derivative (preprinted)
• Chapter 2.2: The Derivative (in-class notes, complete)
• Here is a good applet that illustrates the relationship between the graph of f(x) and f'(x).

• Chapters 2.3 & 2.4: Techniques of Differentiation (Derivative "Short-cuts")

• Chapter 2.5: Derivatives of Trigonometric Functions

• Chapter 2.6: The Chain Rule

• Chapter 3.1: Implicit Differentiation

• Chapter 3.2: Derivatives of Logarithmic Functions

• Chapter 3.3: Derivatives of Exponential and Inverse Trigonometric Functions

• Chapter 3.4: Related Rates (preprinted)
• Chapter 3.4: Related Rates (in-class notes)

• Chapter 3.5: Local Linear Approximations

• Chapter 3.6: Indeterminate Forms

• Chapter 4.1: Analysis of Functions (Increase, Decrease, Concavity)

• Chapter 4.2 (Part One): Relative Extrema

• Chapters 4.2 (Part Two), 4.3: Curve Sketching (preprinted)
• Chapters 4.2 (Part Two), 4.3: Curve Sketching (in-class notes)
• Curve Sketching Assigned Problems: First and Second Derivatives

• Chapter 4.4: Absolute Extrema

• Chapter 4.5: Applied Maximum & Minimum Problems (preprinted)
• Chapter 4.5: Applied Maximum & Minimum Problems (in-class notes)