Calculus M211

Jörg Endrullis
Indiana University Bloomington

Introduction and Overview
The Concept of Functions
Essential Functions
Introduction to Limits
Computing with Limits, Limit Laws
The Precise Definition of Limits
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
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)