Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 3. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | PART I Functions An Introduction C R Functions Are Lurking Everywhere FUNCTIONS ARE EVERYWHERE Each of us attempts to make sense out of his or her environment this is a fundamental human endeavor. We think about the variables characterizing our world we measure these variables and observe how one variable affects another. For instance a child in his flrst years of life names and categorizes objects people and sensations and looks for predictable relationships. As a child discovers that a certain phenomenon precipitates a predictable outcome the child learns. The child learns that the position of a switch determines whether a lamp is on or off and that the position of a faucet determines the flow of water into a sink. The novice musician learns that hitting a piano key produces a note and that which key is hit determines which note is heard. The deterministic relationship between the piano key hit and the resulting note is characteristic of the input-output relationship that is the object of our study in this flrst chapter. 1 2 CHAPTER 1 Functions Are Lurking Everywhere Mathematical modeling involves constructing mathematical machines that mimic important characteristics of commonly occurring phenomena. Chemists biologists environmental scientists economists physicists engineers computer scientists students and parents all search for relationships between measurable A chemist might be interested in the relationship between the temperature and the pressure of a gas an environmental scientist in the relationship between use of pesticides and mortality rate of songbirds a physician in the relationship between the radius of a blood vessel and blood pressure an economist in the relationship between the quantity of an item purchased and its price a grant manager in the relationship between funds allocated to a program and results achieved. A thermometer manufacturer must know the relationship between the temperature and the volume of a gram of mercury in .
