: Publication

The formatting of PRECALCULUS:  A Rigorous, Yet Student Friendly, Approach resembles the structure of formal lecture notes. This structure was used to make the content easier to read. In addition to the clear writing style, the presentation of the material is highly detailed in order to add depth to the content. Throughout the text, there are more than 500 worked out examples to help with the homework exercises and to help explain the procedures. There is a wide variety of exercises, and examples, including a wide variety of difficulty levels. Almost all of the answers to the exercises can be found in the back of the text. Each chapter ends with a practice exam, which highlights the major concepts and procedures presented within that corresponding chapter. Also, the first seven exercises of each exam are similar, which reinforces basic concepts and shows that these basic concepts are among the themes running through the text. In addition to the function concept, which is the primary topic of the text, the related concept of an inverse function is used in every chapter to illustrate its importance. To illustrate the real-world importance of the theoretical material, we have included a wide variety of application topics, including: projectile motion, optimization, accounting, trigonometric, exponential growth, exponential decay, logistic growth, and logarithmic growth. To add depth to the content, we have included optional additional topics, including: the preimage function, the even-odd decomposition of a function, transformations of piecewise functions, a detailed discussion of the domain of a composition, limits, the conjugate of a radical of any index, rationalizing a radical expression with any conjugate, polynomial asymptotes and the derivative.

Chapter 1: Functions

1.1: An Introduction to Functions

1.2: Transformation of Function Graphs

1.3: Linear Functions

1.4: Quadratic Functions

1.5: Combinations of Functions

1.6: Piecewise – Defined Functions

1.7: Inverse Functions

1.8: Limits

1.9: Applications of Functions

Chapter 1 Exam

Chapter 2: Polynomial Functions

2.1: Polynomial Functions and Their Graphs

2.2: Polynomial Division

2.3: Zeros and Factors of Polynomial Functions

2.4: Factoring Polynomial Functions

2.5: Rational Functions

Chapter 2 Exam

Chapter 3: Trigonometry

3.1: The Measurement of an Angle

3.2: The Sine and Cosine Function

3.3: Graphing the Sine and Cosine Functions

3.4: The Remaining Trigonometric Functions

3.5: Special Trigonometric Identities

3.6: Proving Trigonometric Identities

3.7: Inverse Trigonometric Functions

3.8: Trigonometric Equations

3.9: Right Triangle Trigonometry and Applications

Chapter 3 Exam

Chapter 4: Exponential and Logarithmic Functions

4.1: Exponential Functions

4.2: Logarithmic Functions

4.3: Graphing Exponential and Logarithmic Functions

4.4: Exponential and Logarithmic Equations

4.5: Exponential and Logarithmic Modeling

Chapter 4 Exam

Appendix

A.1: Various Prerequisite and Related Topics

A.2: Summation and Product Notation

A.3: Partial Fraction Expansions

A.4: The Conjugate of a Radical

A.5: Other Functions

A.6: Symbols Glossary

Answers to Selected Exercises

Index

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Nick Goins received his B.S in mathematics from the University of Michigan – Dearborn and his M.A. in mathematics from the University of Toledo. He is a professor of mathematics at St. Clair County Community College. His primary mathematical interests include topology and real analysis in addition to teaching calculus courses. He is also the author of an upcoming calculus textbook. In his spare time, he enjoys traveling, cooking, reading and spending time with his wife and family.

 Jeff VanHamlin is a professor of Mathematics at St. Clair County Community College. Jeff’s first college experience was earning an A.S. at North Central Michigan Community College. He went on to earn a B.S. in mathematics and physics at Central Michigan University and an M.A. in mathematics at Oakland University. While enrolled at North Central he realized his calling was to teach at that the community college level. Jeff says teaching at a St. Clair CC allows for small class sizes which helps to bring a very engaging classroom setting. Also with a degree in physics, he is able to bring interesting and relevant real life problems into the classroom and ultimately to this book. Outside the classroom he enjoys building high end gaming computers and is also an avid golfer.