Fred Safier - Schaums Outline of Precalculus

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This edition has been expanded by material on average rate of change, price/demand, polar form of complex numbers, conic sections in polar coordinates, and the algebra of the dot product. An entire chapter () is included as an introduction to differential calculus, which now appears in many precalculus texts.

More than 30 solved and more than 110 supplementary problems have been added. Thanks are due to Anya Kozorez and her staff at McGraw-Hill, and to Madhu Bhardwaj and her staff at International Typesetting and Composition. Also, the author would like to thank the users who sent him (mercifully few) corrections, in particular D. Mehaffey and B. DeRoes. Most of all he owes thanks once again to his wife Gitta, whose careful checking eliminated numerous errors.

Any further errors that users spot would be gratefully received at fsafier@ccsf.edu or fsafier@ccsf.cc.ca.us. Fred Safier

A course in precalculus is designed to prepare college students for the level of algebraic skills and knowledge that is expected in a calculus class. Such courses, standard at two-year and four-year colleges, review the material of algebra and trigonometry, emphasizing those topics with which familiarity is assumed in calculus. Key unifying concepts are those of functions and their graphs. The present book is designed as a supplement to college courses in precalculus. The material is divided into forty-four chapters, and covers basic algebraic operations, equations, and inequalities, functions and graphs, and standard elementary functions including polynomial, rational, exponential, and logarithmic functions.

Trigonometry is covered in , and the emphasis is on trigonometric functions as defined in terms of the unit circle. The course concludes with matrices, determinants, systems of equations, analytic geometry of conic sections, and discrete mathematics. Each chapter starts with a summary of the basic definitions, principles, and theorems, accompanied by elementary examples. The heart of the chapter consists of solved problems, which present the material in logical order and take the student through the development of the subject. The chapter concludes with supplementary problems with answers. These provide drill on the material and develop some ideas further.

The author would like to thank his friends and colleagues, especially F. Cerrato, G. Ling, and J. Morell, for useful discussions. Thanks are also due to the staff of McGraw-Hill and to the reviewer of the text for their invaluable help. Most of all he owes thanks to his wife Gitta, whose careful line-by-line checking of the manuscript eliminated numerous errors.

Any errors that remain are entirely his responsibility, and students and teachers who find errors are invited to send him email at fsafier@ccsf.cc.ca.us.

The sets of numbers used in algebra are, in general, subsets of R, the set of real numbers. Natural NumbersN
The counting numbers, e.g., 1, 2, 3, 4, IntegersZ
The counting numbers, together with their opposites and 0, e.g., 0, 1, 2, 3, 1, 2, 3, Rational NumbersQ
The set of all numbers that can be written as quotients a/b,, a and b integers, e.g., 3/17, 10/3, -5.13, Irrational NumbersH
All real numbers that are not rational numbers, e.g., , -/3, EXAMPLE 1.1 The number 5 is a member of the sets Z, Q,R. The number 156.73 is a member of the sets Q,R. The number 5 is a member of the sets H,R. There are two fundamental operations, addition and multiplication, that have the following properties (Next page