Calculus M211

Introduction and Overview

The Concept of Functions

Essential Functions

Introduction to Limits

Computing with Limits, Limit Laws

The Precise Definition of Limits

Continuity

Limits at Infinity

Review 1

Introduction to Derivatives

Derivatives as Functions

Derivatives of Basic Functions

Differentiation Rules

Derivatives of Trigonometric Functions

Implicit Differentiation

Logarithmic Differentiation

Related Rates

Exponential Growth and Decay

Review 2

Linear Approximation and Differentials

Minima and Maxima

The Mean Value Theorem

Derivatives and the Shape of Graphs

L'Hospital's Rule

Curve Sketching

Optimization

Newtons Method

Introduction to Integrals

The Area Problem

The Definite Integral

The Fundamental Theorem of Calculus

The Indefinite Integral

The Area Between Curves

Review 3

The Substitution Rule for Integration

The Average Value of Functions (the Mean Value Theorem for Integrals)