Calculus 1 Class Notes, Thomas' Calculus, Early Transcendentals, 12th Edition

Copies of the classnotes are on the internet in PDF format as given below.

Introduction to Math Philosophy and Meaning.

Chapter 1: Functions.

• Section 1.1: Functions and Their Graphs. PDF.
• Section 1.3: Trigonometric Functions. PDF.
• Section 1.5: Exponential Functions. PDF.
• Section 1.6: Inverse Functions and Logarithms. PDF.
• Study Guide. PDF.

Chapter 2: Limits and Continuity.

• Section 2.1: Rates of Change and Tangents to Curves. PDF.
• Section 2.2: Limits of a Function and Limit Laws. PDF.
• Section 2.3: The Precise Definition of Limit. PDF.
• Section 2.4: One-Sided Limits. PDF.
• Section 2.5: Continuity. PDF.
• Section 2.6: Limits Involving Infinity; Asymptotes of Graphs. PDF.
• Study Guide. PDF.

Chapter 3: Differentiation.

• Section 3.1: Tangents and the Derivative at a Point. PDF.
• Section 3.2: The Derivative as a Function. PDF.
• Section 3.3: Differentiation Rules. PDF.
• Section 3.4: The Derivative as a Rate of Change. PDF.
• Section 3.5: Derivatives of Trigonometric Functions. PDF.
• Section 3.6: The Chain Rule. PDF.
• Section 3.7: Implicit Differentiation. PDF.
• Section 3.8: Derivatives of Inverse Functions and Logarithms. PDF.
• Section 3.9: Inverse Trigonometric Functions. PDF.
• Section 3.10: Related Rates. PDF.
• Section 3.11: Linearization and Differentials. PDF.
• Study Guide. PDF.

Chapter 4: Applications of Derivatives.

• Section 4.1: Extreme Values of Functions. PDF.
• Section 4.2: The Mean Value Theorem. PDF.
• Section 4.3: Monotone Functions and the First Derivative Test. PDF.
• Section 4.4: Concavity and Curve Sketching. PDF.
• Section 4.5: Indeterminate Forms and L'Hopital's Rule. PDF.
• Section 4.6: Applied Optimization. PDF.
• Section 4.7: Newton's Method. PDF.
• Section 4.8: Antiderviatives. PDF.
• Study Guide. PDF.

Chapter 5: Integration.

• Section 5.1: Area and Estimating with Finite Sums. PDF.
• Section 5.2: Sigma Notation and Limits of Finite Sums. PDF.
• Section 5.3: The Definite Integral. PDF.
• Section 5.4: The Fundamental Theorem of Calculus. PDF.
• Section 5.5: Indefinite Integrals and the Substitution Method. PDF.
• Section 5.6: Substitution and Area Between Curves. PDF.
• Study Guide. PDF.

Additional notes presented in class are also available:

• A "Quick Guide" to the use of the TI-89 in Calculus 1. PDF. PS.