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

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