Lecture Notes

1     CHAPTER ONE

LIMITS AND DIFFERENTIATION 

1.1 A Dash of Limits

1.2 More on Limits

1.3 Continuity

1.4 The Intermediate Value Theorem

1.5 The Derivative

1.6 Rates of Change and Inc/Dec Functions

1.7 Simple Rules for Differentiation

1.8 Sums, Products and Quotients

1.9 The Chain Rule

1.10 Higher Order Derivatives

1.11 a) Exponential and Logarithmic Functions - 

1.11 b) Derivatives of Exponential and Logarithmic Functions

2     CHAPTER TWO

APPLICATIONS OF THE DERIVATIVE

2.1 Implicit Differentiation

2.2 Differentiating the Inverse 

2.3 Linear Approximations

2.4 Why We Use Elasticities

3     CHAPTER THREE

SINGLE-VARIABLE OPTIMIZATION 

3.1 Introduction 

3.2 Simple Test for Extreme Points 

3.3 Local Extreme Points 

3.4 The Extreme-Value Theorem

3.5 Business and Economic Models 

3.6 Inflection Points 

4     CHAPTER FOUR

INTEGRATION 

4.1 Indefinite Integrals 

4.2 Riemann Sums

4.3 Areas and Definite Integrals

4.4 Properties of Definite Integrals

4.5 Integration by Substitution

4.6 Integration by Parts

4.7 Indefinite Integrals of Integration

4.8 Business and Economic Applications

Course Review Materials 

More practice with derivatives (midterm review) 

More practice with evaluating integrals (final exam review)

 
last update: 1/9/10