Functions Modeling Change: A Preparation for Calculus, 4th Edition
November 2010, ©2011
This text provides a strong foundation to precalculus that focuses on a small number of key topics thereby emphasizing depth of understanding rather than breath of coverage. It provides a solid way to motivate concepts and develop critical thinking skills. The new fourth edition emphasizes functions as models of change. It contains superior exercises and applications that motivate the concepts readers can use to fully grasp precalculus.
- Algebraic Skills Refreshers are introduced in two formats, both integrated with the text:
- Skills Refresher exercises are included at the start of many exercise sets, identified by S1, S2, etc.
- Skills Refresher sections are included at the end of some chapters.
- A new Chapter 3 on Quadratic Functions brings together and expands the material on quadratics in the former Sections 2.6 and 5.5.
- Section 4.4 on Compound Interest and Section 4.5 on the Number e have been reorganized to give instructors more flexibility in deciding how to introduce e.
- Limit Notation has been moved to the end of Section 5.3 to provide additional flexibility in how, or whether, limit notation is introduced.
- A new Section 6.5 on Combining Transformations investigates the effect of varying the order in which transformations are applied to functions and their graphs.
- The material on trigonometry in the former Chapters 6 and 7 has been expanded and reorganized into three chapters, allowing instructors to tailor their approach to the needs of their students.
- Chapter 7 defines the trigonometric functions in circles and triangles.
- Chapter 8 studies the behavior of the trigonometric functions and their graphs, and introduces trigonometric identities, polar coordinates, and complex numbers.
- Chapter 9 investigates trigonometric identities and their applications to modeling.
- Data and problems have been updated and revised as appropriate. Many new problems have been added.
- Exceptional Problems: Examples and problems based on real data help students create mathematical models to help them understand their world. An appropriate number of drill problems are included to assist students in learning techniques. The problems are varied and some are more challenging. Most cannot be done by following a template in the text.
- Allows for a broad range of teaching styles. This text is flexible enough for use in large lecture halls, small classes, or in group or lab settings.
- Focuses on fewer topics than is customary, but each topic is treated in greater depth. Only those topics essential to the study of calculus are included.
- Reflects the spirit of the standards established by the Mathematical Association of America (MAA) and the American Mathematical Association of Two-Year Colleges (AMATYC), and meets the recommendations of the National Council of Teachers of Mathematics (NCTM).
- Assumes technology has a place in modern mathematics. This text takes full advantage of technology when appropriate, although no specific technology is emphasised. It is important for students to learn how and when to use technology as a tool, as well as its limitations. However the focus of the text is on conceptual understanding not technology.
- The Rule of Four: Each function is represented symbolically, numerically, graphically, and verbally.
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