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Algebra for College Students / Edition 4

Algebra for College Students / Edition 4

by R. David Gustafson


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Product Details

ISBN-13: 9780534251888
Publisher: Brooks/Cole
Publication date: 01/28/1995
Series: Mathematics Series
Edition description: Older Edition
Pages: 650
Product dimensions: 8.12(w) x 9.44(h) x 1.44(d)

Table of Contents

Chapter 1Basic Concepts1
1.1The Real Number System2
1.2Arithmetic and Properties of Real Numbers13
1.4Scientific Notation38
1.5Solving Equations45
1.6Using Equations to Solve Problems55
1.7More Applications of Equations66
Chapter Summary74
Chapter Test78
Chapter 2Graphs, Equations of Lines, and Functions80
2.1Graphing Linear Equations81
2.2Slope of a Nonvertical Line96
2.3Writing Equations of Lines106
2.4Introduction to Functions118
2.5Graphs of Other Functions128
Chapter Summary139
Chapter Test143
Cumulative Review Exercises143
Chapter 3Systems of Equations145
3.1Solutions by Graphing146
3.2Solution by Elimination154
3.3Solutions of Three Equations in Three Variables169
3.4Solution by Matrices178
3.5Solution by Determinants186
Chapter Summary197
Chapter Test198
Chapter 4Inequalities200
4.1Linear Inequalities201
4.2Equations and Inequalities with Absolute Values211
4.3Linear Inequalities in Two Variables223
4.4Systems of Inequalities231
4.5Linear Programming237
Chapter Summary247
Chapter Test250
Cumulative Review Exercises251
Chapter 5Polynomials and Polynomial Functions253
5.1Polynomials and Polynomial Functions254
5.2Adding and Subtracting Polynomials263
5.3Multiplying Polynomials268
5.4The Greatest Common Factor and Factoring by Grouping278
5.5The Difference of Two Squares; the Sum and Difference of Two Cubes287
5.6Factoring Trinomials294
5.7Summary of Factoring Techniques305
5.8Solving Equations by Factoring308
Chapter Summary318
Chapter Test322
Chapter 6Rational Expressions323
6.1Rational Functions and Simplifying Rational Expressions324
6.2Proportion and Variation335
6.3Multiplying and Dividing Rational Expressions348
6.4Adding and Subtracting Rational Expressions356
6.5Complex Fractions365
6.6Equations Containing Rational Expressions374
6.7Dividing Polynomials384
Chapter Summary392
Chapter Test395
Cumulative Review Exercises396
Chapter 7Radicals and Rational Exponents398
7.1Radical Expressions399
7.2Applications of Radicals411
7.3Rational Exponents418
7.4Simplifying and Combining Radical Expressions426
7.5Multiplying and Dividing Radical Expressions435
7.6Radical Equations443
Chapter Summary452
Chapter Test456
Chapter 8Quadratic Functions and Inequalities458
8.1Completing the Square and the Quadratic Formula459
8.2Graphs of Quadratic Functions470
8.3Complex Numbers481
8.4The Discriminant and Equations That Can Be Written in Quadratic Form491
8.5Quadratic and Other Nonlinear Inequalities497
Chapter Summary506
Chapter Test509
Cumulative Review Exercises510
Chapter 9More Functions and Operations on Functions512
9.1Symmetry and Stretchings of Graphs513
9.2Piecewise-Defined Functions and the Greatest Integer Function522
9.3More Rational Functions527
9.4Partial Fractions541
9.5Algebra and Composition of Functions548
9.6Inverses of Functions555
Chapter Summary566
Chapter Test569
Chapter 10Exponential and Logarithmic Functions571
10.1Exponential Functions572
10.2Base-e Exponential Functions584
10.3Logarithmic Functions591
10.4Base-e Logarithms600
10.5Properties of Logarithms606
10.6Exponential and Logarithmic Equations615
Chapter Summary626
Chapter Test630
Cumulative Review Exercises632
Chapter 11Solving Polynomial Equations633
11.1The Remainder and Factor Theorems; Synthetic Division634
11.2Descartes' Rule of Signs and Bounds on Roots643
11.3Rational Roots of Polynomial Equations650
11.4Irrational Roots of Polynomial Equations658
Chapter Summary664
Chapter Test667
Chapter 12Conic Sections and Quadratic Systems668
12.1The Circle669
12.2The Parabola678
12.3The Ellipse686
12.4The Hyperbola696
12.5Solving Simultaneous Second-Degree Equations705
Chapter Summary713
Chapter Test717
Cumulative Review Exercises719
Chapter 13Natural Number Functions and Probability721
13.1The Binomial Theorem722
13.2Sequences, Series, and Summation Notation729
13.3Arithmetic Sequences736
13.4Geometric Sequences742
13.5Mathematical Induction750
13.6Permutations and Combinations756
13.8Computation of Compound Probabilities772
13.9Odds and Mathematical Expectation778
Chapter Summary782
Chapter Test787
Cumulative Review Exercises788
Appendix IMatrix Algebra1
I.1Matrix Algebra1
I.2Matrix Inversion9
Appendix IITables15
Table APowers and Roots15
Table BBase-10 Logarithms16
Table CBase-e Logarithms17
Appendix IIIAnswers to Selected Exercises19

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