Study Guide for Stewart/Redlin/Watson's Algebra and Trigonometry, 2nd / Edition 2

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Overview

This carefully crafted learning resource helps students develop their problem-solving skills while reinforcing their understanding with detailed explanations, worked-out examples, and practice problems. Students will also find listings of key ideas to master. Each section of the main text has a corresponding section in the Study Guide.

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Product Details

  • ISBN-13: 9780495013587
  • Publisher: Cengage Learning
  • Publication date: 1/12/2006
  • Edition description: Older Edition
  • Edition number: 2
  • Pages: 352
  • Product dimensions: 7.40 (w) x 9.20 (h) x 0.80 (d)

Meet the Author

James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning Brooks/Cole, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field is topology.

Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis.

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Table of Contents


Prerequisites     1
Modeling the Real World     1
Real Numbers     3
Integer Exponents     10
Rational Exponents and Radicals     13
Algebraic Expressions     16
Factoring     18
Rational Expressions     24
Equations and Inequalities     31
Basic Equations     31
Modeling with Equations     36
Quadratic Equations     40
Complex Numbers     44
Other Types of Equations     48
Inequalities     51
Absolute Value Equations and Inequalities     57
Coordinates and Graphs     59
The Coordinate Plane     59
Graphs of Equations in Two Variables     62
Graphing Calculators; Solving Equations and Inequalities Graphically     66
Lines     73
Modeling Variation     81
Functions     83
What is a Function?     83
Graphs of Functions     85
Increasing and Decreasing Functions; Average Rate of Change     91
Transformations of Functions     94
Quadratic Functions; Maxima and Minima     101
Combining Functions     106
One-to-One Functions and Their Inverses     111
Polynomial and Rational Functions     117
Polynomial Functions and Their Graphs     117
Dividing Polynomials     123
Real Zeros of Polynomials     125
Complex Zeros and the Fundamental Theorem of Algebra     131
Rational Functions     135
Exponential and Logarithmic Functions     141
Exponential Functions     141
Logarithmic Functions     145
Laws of Logarithms     148
Exponential and Logarithmic Equations     151
Modeling with Exponential and Logarithmic Functions     155
Trigonometric Functions of Angles     159
Angle Measure     159
Trigonometry of Right Triangles     163
Trigonometric Functions of Angles     166
The Law of Sines     171
The Law of Cosines     173
Trigonometric Functions of Real Numbers     177
The Unit Circle     177
Trigonometric Functions of Real Numbers     180
Trigonometric Graphs     183
More Trigonometric Graphs     186
Modeling Harmonic Motion     188
Analytic Trigonometry     191
Trigonometric Identities     191
Addition and Subtraction Formulas     194
Double-Angle, Half-Angle, and Product-Sum Formulas     197
Inverse Trigonometric Functions     201
Trigonometric Equations     204
Polar Coordinates and Vectors     209
Polar Coordinates     209
Graphs of Polar Equations     212
Polar Form of Complex Numbers; DeMoivre's Theorem     216
Vectors     221
The Dot Product     227
Systems of Equations and Inequalities     233
Systems of Equations     233
Systems of Linear Equations in Two Variables     237
Systems of Linear Equations in Several Variables     240
Systems of Linear Equations: Matrices     244
The Algebra of Matrices     251
Inverses of Matrices and Matrix Equations     256
Determinants and Cramer's Rule     263
Partial Fractions     268
Systems of Inequalities     273
Analytic Geometry     277
Parabolas     277
Ellipses     281
Hyperbolas     284
Shifted Conics     287
Rotation of Axes     292
Polar Equations of Conics      295
Plane Curves and Parametric Equations     298
Sequences and Series     301
Sequences and Summation Notation     301
Arithmetic Sequences     306
Geometric Sequences     308
Mathematics of Finance     310
Mathematical Induction     312
The Binomial Theorem     314
Counting and Probability     317
Counting Principles     317
Permutations and Combinations     319
Probability     324
Binomial Probability     328
Expected Value     330
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