Worksheets and lessons
Chapter 0: PRE-CALCULUS
0.1 Functions
0.2 New functions from old
App B Trigonometry review
Inverse Functions
Review of exponents and logarithms
Exponentials and Logarithms
Chapter 1: LIMITS
Section 1.1: Intuitive view of limits
Sections 1.1-1.2: Computing limits
Section 1.3: Limits at Infinity
Section 1.4: Limits Done Rigorously
Epsilon-delta Definition of Limit
Section 1.5: Continuity
Section 1.6: Continuity of basic functions
Chapter 2: THE DERIVATIVE
Section 2.1: Tangent lines velocities, and instantaneous rates of change
Section 2.2: The Derivative Function
Section 2.3: Techniques
Section 2.4: Product and Quotient Rules
Product and Quotient Rules
Section 2.5: Derivatives of the six trigonometric functions
Derivatives of Trigonometric Functions
Section 2.6: The Chain Rule
Chapter 3: TOPICS IN DIFFERENTIATION
Implicit differentiation problems
The following also involves logs and exps.
Exercises: derivatives of trigonometric functions
L'Hospital's Rule
Chapter 4: THE DERIVATIVE IN GRAPHING AND APPLICATIONS
Using first and second derivatives
Answers
Section 4.3: Rational functions, cusps, etc.
Section 4.4
Section 4.4: Alternative exercises
Section 4.5: Applied Maximum and Minimum Problems
Section 4.5
Optimization
Optimal Can Design
Optimization worksheet
Optimization worksheet answers
Section 4.5 plus: Calculus in economics
Section 4.6: Rectilinear Motion
Section 4.7: Newton's Method
This is very interesting and useful, but not in the Calculus I syllabus.
Section 4.8: Rolle's Theorem; Mean-Value Theorem
Chapter 5: Integration
Section 5.1: Overview of the Area Problem
Approximating area by rectangles
Section 5.2: Antiderivatives and indefinite integrals
Section 5.3: Integration by substitution
Section 5.4: The Definition of Area as a Limit;Sigma Notation
Exercise 25
Section 5.5: The Definite (Riemann) Integral
Section 5.6: The Fundamental Theorem of Calculus!