Brief Calculus for Business, Social Sciences, and Life Sciences, Preliminary Edition

Table of Contents

1.1 How Do We Measure Change?
1.2 What's a Function?
1.3 Linear Functions
1.4 Applications of Linear Functions
1.5 Exponential Functions
1.6 Power Functions
1.7 Fitting Formulas to Data

2.1 Instantaneous Rate of Change
2.2 The Derivative
2.3 The Derivative Function
2.4 Interpretations of the Derivative
2.5 The Second Derivative
2.6 Marginal Cost and Revenue

3.1 Accumulated Change
3.2 The Definite Integral
3.3 The Definite Integral as Area
3.4 The Definite Integral as Average Value
3.5 Interpretations of the Definite Integral
3.6 The Fundamental Theorem of Calculus

4.1 The Number e
4.2 The Natural Logarithm
4.3 New Functions from Old; Polynomials
4.4 Periodic Functions
4.5 The Logistic Curve
4.6 The Surge Function

5.1 Derivative Formulas for Powers and Polynomials
5.2 Derivatives of Exponential and Logarithmic Functions
5.3 The Chain Rule
5.4 The Product Rule
5.5 Derivatives of Periodic Functions
5.6 Verifying Derivative Formulas
5.7 Finding Antiderivatives

6.1 Critical Points and Inflection Points
6.2 Optimization
6.3 More Optimization: Average Cost
6.4 Applications of Definite Integral
6.5 Consumer and Producer Surplus

7.1 Understanding Functions of Many Variables
7.2 Contour Diagrams
7.3 The Partial Derivative
7.4 Computing Partial Derivatives Algebraically
7.5 Critical Points and Optimization
7.6 LaGrange Multipliers

A. Roots and Accuracy
B. Notes on Compound Interest