Basic concepts of college algebra and trigonometry / M.N. Manougian

Includes index.

Some Basic Concepts -- Algebraic Expressions -- Equations in One Variable -- Cartesian product and Complex Numbers -- Functions -- The Exponential and Logarithmic Functions -- Matrices, Determinants, and Systems of Equations and Inequalities -- Polynomial Functions -- Selected Topics.

The main purpose of this text is to prepare students for further study in mathematics, the sciences, engineering, and other disciplines. It exposes them to the basic concepts of algebra with an emphasis on practical applications. It is assumed that students who use this text have had the equivalent of one year of high school geometry and at least one year of high school algebra or a college course in beginning algebra. In writing this book every effort was made to maintain an informal presentation with a proper balance between intuition and rigor. Mathematical concepts are introduced with simple examples, many of which illustrate the applicability of algebra to real-world situations. Following precise mathematical formulations, many worked-out examples are given to illustrate the concepts presented. Techniques and drills are emphasized throughout the text. Each section begins with a statement of objectives and is concluded with exercises containing numerous problems ranging from the elementary to the more challenging. The problems are designed to help the students' understanding of the concepts discussed in each of the sections. Following each chapter is a review emphasizing the main ideas discussed in the chapter. These serve as self-tests. In order to help students in their learning process, other features are also included. In each section, students are asked to respond to simple questions under the heading Self-test. The answers to these questions are provided in the margin for instant feedback. This feature is used to ensure student understanding of the material discussed and to prepare them for the exercises. The marginal column is also used for illustrations, notes, and remarks as well as for pinpointing some common mistakes. Finally, for better understanding and general interest, historical developments of some of the concepts and biographical sketches of some of the famous mathematicians who contributed to the development of mathematics are presented. The book is designed for a one-semester course of three to five credits or for an equivalent course in the quarter system. Instructors may want to create a syllabus and set their own pace. Various syllabi may be devised for a one-quarter or a one-semester course.