SCHAUM'S outlines Precalculus Second Edition Fred Safier Professor of Mathematics City College of San Francisco Schaum’s Outline Series New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto.
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Preface to the Second Edition 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 (Chapter 45) 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.
Preface to the First Edition Acourse in precalculus is designed to prepare college students for the level of algebraic skills and knowl- edge 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.
For more information about this title, click here Contents CHAPTER 1 Preliminaries 1 CHAPTER 2 Polynomials 7 CHAPTER 3 Exponents 15 CHAPTER 4 Rational and Radical Expressions 20 CHAPTER 5 Linear and Nonlinear Equations 29 CHAPTER 6 Linear and Nonlinear Inequalities 41 CHAPTER 7 Absolute Value in Equations and Inequalities 49 CHAPTER 8 Analytic Geometry 54 CHAPTER 9 Functions 68 CHAPTER 10 Linear Functions 79 CHAPTER 11 Transformations and Graphs 87 CHAPTER 12 Quadratic Functions 95 CHAPTER 13 Algebra of Functions;Inverse Functions 104 CHAPTER 14 Polynomial Functions 114 CHAPTER 15 Rational Functions 132 CHAPTER 16 Algebraic Functions;Variation 146 CHAPTER 17 Exponential Functions 154 CHAPTER 18 Logarithmic Functions 162 CHAPTER 19 Exponential and Logarithmic Equations 168 CHAPTER 20 Trigonometric Functions 176 CHAPTER 21 Graphs of Trigonometric Functions 187 CHAPTER 22 Angles 197 v.
vi Contents CHAPTER 23 Trigonometric Identities and Equations 211 CHAPTER 24 Sum,Difference,Multiple,and Half-Angle Formulas 220 CHAPTER 25 Inverse Trigonometric Functions 230 CHAPTER 26 Triangles 240 CHAPTER 27 Vectors 252 CHAPTER 28 Polar Coordinates;Parametric Equations 261 CHAPTER 29 Trigonometric Form of Complex Numbers 270 CHAPTER 30 Systems of Linear Equations 279 CHAPTER 31 Gaussian and Gauss-Jordan Elimination 287 CHAPTER 32 Partial Fraction Decomposition 294 CHAPTER 33 Nonlinear Systems of Equations 302 CHAPTER 34 Introduction to Matrix Algebra 309 CHAPTER 35 Matrix Multiplication and Inverses 313 CHAPTER 36 Determinants and Cramer’s Rule 322 CHAPTER 37 Loci;Parabolas 330 CHAPTER 38 Ellipses and Hyperbolas 337 CHAPTER 39 Rotation of Axes 349 CHAPTER 40 Conic Sections 356 CHAPTER 41 Sequences and Series 362 CHAPTER 42 The Principle of Mathematical Induction 368 CHAPTER 43 Special Sequences and Series 374 CHAPTER 44 Binomial Theorem 381 CHAPTER 45 Limits,Continuity,Derivatives 387 Index 399.
CHAPTER 1 Preliminaries The Sets of Numbers Used in Algebra The sets of numbers used in algebraare, in general, subsets of R,the set of real numbers.
2 CHAPTER 1 Preliminaries Inverse Laws For any real number a, there is a real number ⫺asuch that a⫹(⫺a) ⫽(⫺a) ⫹a⫽0.
3 CHAPTER 1 Preliminaries The number a is less than b,written a⬍b,if b⫺ais positive. Then b is greater than a,written b⬎a.If a is either less than or equal to b,this is written aⱕb.Then bis greater than or equal to a,written bⱖa.