Calculus for Life Sciences

CHAPTER 1

Modeling with Functions

1.1 Real Numbers and Functions

1.2 Data Fitting with Linear and Periodic Functions

1.3 Power Functions and Scaling Laws

1.4 Exponential Growth

1.5 Function Building

1.6 Inverse Functions and Logarithms

1.7 Sequences and Difference Equations

Review Questions

Group Projects

Figure 1.1 Mathematical models are used in Section 1.3 to identify Pocket Hercules as one of the all-time greatest weightlifters.

Preview

“Mathematicians do not study objects, but relations between objects.”

Henri Poincare, 1854–1912.

Although all readers taking a first course in calculus have a background in algebra, geometry, and trigonometry, the depth of exposure and choice of material covered can be quite variable. The material in this chapter is designed to provide a common framework upon which to build an introductory course in calculus for students who have a strong interest in the life sciences. In reviewing real numbers and functions, our intention is also to develop the notation we will use throughout the book. As students, you must become familiar with this notation if you want to be fluent in reading the mathematical text in this book. We also introduce data—and concepts around working with data—early on, because this component of the mathematical modeling process is critical to testing model predictions in the context of real-world problems (as discussed in ...