Syllabus

Chapter 1 – Functions and Change

1.1    What Is A Function?

1.3    Rates of Change

1.4    Applications of Functions to Economics

1.5    Exponential Functions

1.6    The Natural Logarithm

1.8    New Functions from Old

1.10  Periodic Functions

 

Chapter 2 – Rate of Change: The Derivative

2.1   Instantaneous Rate of Change

2.2   The Derivative Function

2.3   Interpretations of the Derivative

2.4   The Second Derivative

2.5  Marginal Cost and Revenue

 

Chapter 3 – Short-Cuts To Differentiation

3.1   Derivative Formulas for Powers and Polynomials

3.2   Exponential and Logarithmic Functions

3.3   The Chain Rule

3.4   The Product and Quotient Rules

3.5 Derivatives of Periodic Functions

 

Chapter 4 – Using the Derivative

4.1  Local Maxima and Minima

4.2   Inflection Points

4.3   Global Maxima and Minima

4.4  Profit, Cost, and Revenue

4.7  Logistic Growth

4.8  The Surge Function and Drug Concentration

 

Chapter 5 – Accumulated Change:  the Definite Integral

5.1   Accumulated Change

5.2   The Definite Integral

5.3   The Definite Integral as Area

5.4   Interpretations of the Definite Integral

5.5   The Fundamental Theorem of Calculus