Calculus I — Teaching Materials

Textbook: Stewart Calculus, 8th Edition  ·  Sections 1.1 – 6.4

Chapter 1 — Functions and Limits

• 1.1 Four ways to represent a function
• 1.2 Mathematical models: a catalog of essential functions
• 1.3 New functions from old functions
• 1.4 Exponential functions
• 1.5 Inverse functions and logarithms

Chapter 2 — Limits and Derivatives

• 2.1 The tangent and velocity problems
• 2.2 The limit of a function
• 2.3 Calculating limits using the limit laws
• 2.4 The precise definition of a limit
• 2.5 Continuity
• 2.6 Limits at infinity; horizontal asymptotes
• 2.7 Derivatives and rates of change
• 2.8 The derivative as a function

Chapter 3 — Differentiation Rules

• 3.1 Derivatives of polynomials and exponential functions
• 3.2 The product and quotient rules
• 3.3 Derivatives of trigonometric functions
• 3.4 The chain rule
• 3.5 Implicit differentiation
• 3.6 Derivatives of logarithmic functions
• 3.7 Rates of change in the natural and social sciences
• 3.8 Exponential growth and decay
• 3.9 Related rates
• 3.10 Linear approximations and differentials
• 3.11 Hyperbolic functions

Chapter 4 — Applications of Differentiation

• 4.1 Maximum and minimum values
• 4.2 The mean value theorem
• 4.3 How derivatives affect the shape of a graph
• 4.4 Indeterminate forms and L'Hôpital's rule
• 4.5 Summary of curve sketching
• 4.6 Graphing with calculus and calculators
• 4.7 Optimization problems
• 4.8 Newton's method
• 4.9 Antiderivatives

Chapter 5 — Integrals

• 5.1 Areas and distances
• 5.2 The definite integral
• 5.3 The fundamental theorem of calculus
• 5.4 Indefinite integrals and the net change theorem
• 5.5 The substitution rule

Chapter 6 — Applications of Integration

• 6.1 Areas between curves
• 6.2 Volumes
• 6.3 Volumes by cylindrical shells
• 6.4 Work