Open Educational Resources
Document Type
Textbook
Publication Date
2023
Abstract
This text, our third edition, contains notes for a course in precalculus as it is taught at New York City College of Technology, CUNY, where it is offered under the course number MAT 1375. Our approach is calculator-based. As of the third edition of this text, we use the Desmos graphing calculator to analyze and solve many of the examples studied in this course. An introduction to the Desmos graphing calculator appears in Chapter 4. Moreover, we are very grateful to be able to include in this edition many wonderful illustrations of the cartoon characters featured on the cover of this edition. These characters and images were created by Kate Poirier and provide a charming visualization of the course content. Our course in precalculus has the overarching theme of “functions.” This means that many of the often more algebraic topics studied in prior courses are revisited under this new function theoretic point of view. However, in order to keep this text as self-contained as possible, we will recall all of the results necessary to follow the core of the course even if we assume that the student has familiarity with the formula or topic at hand. Below is an outline of the topics of this course:
- Part I: Functions and graphs
- Part II: Polynomials and rational functions
- Part III: Exponential and logarithmic functions
- Part IV: Trigonometric functions
- Part V: Vectors, complex numbers, and sequences
After an introduction to the abstract notion of a function and its graph, we study polynomials, rational functions, exponential functions, logarithmic functions, and trigonometric functions. Throughout, we will always assign particular importance to the corresponding graph of the discussed function which will be analyzed with the help of the Desmos graphing calculator. In the f ifth and last part of the course, we deviate from the above theme and collect more algebraically oriented topics that will be needed in calculus or other advanced mathematics courses or even other science courses. The fifth part includes a discussion of the 2-dimensional real vector space R2, the algebra of complex numbers (in particular complex numbers in polar form), and sequences and series with focus on the arithmetic and geometric series. The generalized binomial theorem is discussed in an appendix. The topics in this book are organized into 25 chapters, each corresponding to one course lesson. Each chapter ends with a list of exercises the student is expected to be able to solve. Answers to all exercises are provided at the end of the book. We cannot overstate the importance of completing these exercises for a successful completion of this course. These 25 lessons, together with four scheduled exams and one review session give a total of 30 class sessions, which is the number of regularly scheduled class meetings in one semester. Each of the five parts also ends with a review of the topics discussed. This may be used as a review for any of the exams during the semester.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.
All handouts and slides as zipped file
Comments
The textbook for MAT 1375 Precalculus is: Precalculus, Third Edition (3.0), by Thomas Tradler and Holly Carley and is posted on City Tech's Open Lab at Textbook – MAT 1375 Precalculus (cuny.edu). Additional course materials include: a course outline for the third edition and handouts and slides that follow the lessons from the third edition.
A printed version of the textbook (via print on demand) is available from www.lulu.com.
The course outline, handouts, and slides are appended to this record as supplementary files.