CONTENTS

Preview of Modeling and Calculus

What is mathematical modeling?

What is calculus?

1 Modeling with Functions

1.1 Real Numbers and Functions

Real numbers

Functions

1.2 Data Fitting with Linear and Periodic Functions

Linear functions

Fitting linear functions to data

Periodic and trigonometric functions

1.3 Power Functions and Scaling Laws

Power functions and their properties

Proportionality and geometric similarity

Allometric scaling

1.4 Exponential Growth

Exponential growth and exponential functions

Exponential decay

The number e

1.5 Function Building

Shifting, reflecting, and stretching

Adding, subtracting, multiplying and dividing

Composing

1.6 Inverse Functions and Logarithms

Inverse functions

Logarithms

The logarithmic scale

1.7 Sequences and Difference Equations

Sequences

Difference equations

Cobwebbing

Group Projects

2 Limits and Derivatives

2.1 Rates of Change and Tangent Lines

Rates of change

Velocity

Tangent lines

2.2 Limits

Introduction to Limits

One-sided limits

Limits: A formal perspective (optional)

2.3 Limit Laws and Continuity

Properties of limits

Continuity at a point

Intermediate value theorem

2.4 Asymptotes and Infinity

Horizontal asymptotes

Vertical asymptotes

Infinite limits at infinity

2.5 Sequential Limits

Sequential limits and continuity

Asymptotic behavior of difference equations

2.6 Derivative at a Point

Slopes of tangent lines

Instantaneous rates of change

Differentiability and continuity

2.7 Derivatives as Functions

Notational alternatives

Mean ...

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