College Algebra Fifth Edition
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Size :29739 Ko
College Algebra
Schaum’s Outline Series
-------- Autors -------
Robert E. Moyer, PhD
Associate Professor of Mathematics
Southwest Minnesota State University (Retired)
Professor and Chairman,
Department of Mathematics & Physics
Fort Valley State University (Retired)
Murray R. Spiegel, PhD
Former Professor and Chairman, Mathematics Department
Rensselaer Polytechnic Institute, Hartford Graduate Center
------------------------
CONTENTS
CHAPTER 1- Fundamental Operations with Numbers 1
1.1 Four Operations 1
1.2 System of Real Numbers 2
1.3 Graphical Representation of Real Numbers 2
1.4 Properties of Addition and Multiplication of Real Numbers 3
1.5 Rules of Signs 3
1.6 Exponents and Powers 4
1.7 Operations with Fractions 4
Solved Problems 5
Supplementary Problems 9
CHAPTER 2- Fundamental Operations with Algebraic Expressions 12
2.1 Algebraic Expressions 12
2.2 Terms 12
2.3 Degree 13
2.4 Grouping 13
2.5 Computation with Algebraic Expressions 13
Solved Problems 16
Supplementary Problems 20
CHAPTER 3- Properties of Numbers 22
3.1 Sets of Numbers 22
3.2 Properties 22
3.3 Additional Properties 23
Solved Problems 23
Supplementary Problems 25
CHAPTER 4- Special Products 27
4.1 Special Products 27
4.2 Products Yielding Answers of the Form an ± bn 28
Solved Problems 28
Supplementary Problems 30
CHAPTER 5- Factoring 32
5.1 Factoring 32
5.2 Factorization Procedures 33
5.3 Greatest Common Factor 34
5.4 Least Common Multiple 34
Solved Problems 35
Supplementary Problems 39
CHAPTER 6- Fractions 41
6.1 Rational Algebraic Fractions 41
6.2 Operations with Algebraic Fractions 42
6.3 Complex Fractions 43
Solved Problems 44
Supplementary Problems 46
CHAPTER 7- Exponents 48
7.1 Positive Integral Exponent 48
7.2 Negative Integral Exponent 48
7.3 Roots 48
7.4 Rational Exponents 49
7.5 General Laws of Exponents 49
7.6 Scientific Notation 50
Solved Problems 50
Supplementary Problems 56
CHAPTER 8- Radicals 58
8.1 Radical Expressions 58
8.2 Laws for Radicals 58
8.3 Simplifying Radicals 58
8.4 Operations with Radicals 59
8.5 Rationalizing Binomial Denominators 60
Solved Problems 61
Supplementary Problems 65
CHAPTER 9- Simple Operations with Complex Numbers 67
9.1 Complex Numbers 67
9.2 Graphical Representation of Complex Numbers 67
9.3 Algebraic Operations with Complex Numbers 68
Solved Problems 69
Supplementary Problems 71
CHAPTER 10- Equations in General 73
10.1 Equations 73
10.2 Operations Used in Transforming Equations 73
10.3 Equivalent Equations 74
10.4 Formulas 74
10.5 Polynomial Equations 75
Solved Problems 75
Supplementary Problems 79
CHAPTER 11- Ratio, Proportion, and Variation 81
11.1 Ratio 81
11.2 Proportion 81
11.3 Variation 81
11.4 Unit Price 82
11.5 Best Buy 82
Solved Problems 83
Supplementary Problems 86
CHAPTER 12- Functions and Graphs 89
12.1 Variables 89
12.2 Relations 89
12.3 Functions 89
12.4 Function Notation 90
12.5 Rectangular Coordinate System 90
12.6 Function of Two Variables 91
12.7 Symmetry 91
12.8 Shifts 92
12.9 Scaling 93
12.10 Using a Graphing Calculator 93
Solved Problems 96
Supplementary Problems 106
CHAPTER 13- Linear Equations in One Variable 114
13.1 Linear Equations 114
13.2 Literal Equations 114
13.3 Word Problems 115
Solved Problems 116
Supplementary Problems 124
CHAPTER 14- Equations of Lines 128
14.1 Slope of a Line 128
14.2 Parallel and Perpendicular Lines 129
14.3 Slope-Intercept Form of Equation of a Line 130
14.4 Slope-Point Form of Equation of a Line 130
14.5 Two-Point Form of Equation of a Line 130
14.6 Intercept Form of Equation of a Line 131
Solved Problems 131
Supplementary Problems 134
CHAPTER 15- Simultaneous Linear Equations 137
15.1 Systems of Two Linear Equations 137
15.2 Systems of Three Linear Equations 138
Solved Problems 139
Supplementary Problems 146
CHAPTER 16- Quadratic Equations in One Variable 150
16.1 Quadratic Equations 150
16.2 Methods of Solving Quadratic Equations 150
16.3 Sum and Product of the Roots 152
16.4 Nature of the Roots 152
16.5 Radical Equations 152
16.6 Quadratic-Type Equations 153
Solved Problems 153
Supplementary Problems 163
CHAPTER 17- Conic Sections 169
17.1 General Quadratic Equations 169
17.2 Conic Sections 170
17.3 Circles 170
17.4 Parabolas 171
17.5 Ellipses 173
17.6 Hyperbolas 177
17.7 Graphing Conic Sections with a Calculator 180
Solved Problems 180
Supplementary Problems 186
CHAPTER 18- Systems of Equations Involving Quadratics 191
18.1 Graphical Solution 191
18.2 Algebraic Solution 191
Solved Problems 193
Supplementary Problems 197
CHAPTER 19- Inequalities 199
19.1 Definitions 199
19.2 Principles of Inequalities 199
19.3 Absolute Value Inequalities 200
19.4 Higher Degree Inequalities 200
19.5 Linear Inequalities in Two Variables 202
19.6 Systems of Linear Inequalities 202
19.7 Linear Programming 203
Solved Problems 204
Supplementary Problems 210
CHAPTER 20- Polynomial Functions 214
20.1 Polynomial Equations 214
20.2 Zeros of Polynomial Equations 214
20.3 Solving Polynomial Equations 216
20.4 Approximating Real Zeros 218
Solved Problems 219
Supplementary Problems 231
CHAPTER 21- Rational Functions 235
21.1 Rational Functions 235
21.2 Vertical Asymptotes 235
21.3 Horizontal Asymptotes 235
21.4 Graphing Rational Functions 236
21.5 Graphing Rational Functions Using a Graphing Calculator 238
Solved Problems 238
Supplementary Problems 240
CHAPTER 22- Sequences and Series 245
22.1 Sequences 245
22.2 Arithmetic Sequences 245
22.3 Geometric Sequences 245
22.4 Infinite Geometric Series 246
22.5 Harmonic Sequences 246
22.6 Means 246
Solved Problems 247
Supplementary Problems 258
CHAPTER 23- Logarithms 263
23.1 Definition of a Logarithm 263
23.2 Laws of Logarithms 263
23.3 Common Logarithms 264
23.4 Using a Common Logarithm Table 264
23.5 Natural Logarithms 265
23.6 Using a Natural Logarithms Table 265
23.7 Finding Logarithms Using a Calculator 266
Solved Problems 267
Supplementary Problems 273
CHAPTER 24- Applications of Logarithms and Exponents 276
24.1 Introduction 276
24.2 Simple Interest 276
24.3 Compound Interest 277
24.4 Applications of Logarithms 278
24.5 Applications of Exponents 280
Solved Problems 280
Supplementary Problems 284
CHAPTER 25- Permutations and Combinations 288
25.1 Fundamental Counting Principle 288
25.2 Permutations 288
25.3 Combinations 289
25.4 Using a Calculator 290
Solved Problems 290
Supplementary Problems 300
CHAPTER 26- The Binomial Theorem 303
26.1 Combinatorial Notation 303
26.2 Expansion of (a + x)n 303
Solved Problems 304
Supplementary Problems 308
CHAPTER 27- Probability 310
27.1 Simple Probability 310
27.2 Compound Probability 310
27.3 Mathematical Expectation 311
27.4 Binomial Probability 311
27.5 Conditional Probability 311
Solved Problems 312
Supplementary Problems 320
CHAPTER 28- Determinants 323
28.1 Determinants of Second Order 323
28.2 Cramer’s Rule 323
28.3 Determinants of Third Order 324
28.4 Determinants of Order n 326
28.5 Properties of Determinants 327
28.6 Minors 328
28.7 Value of a Determinant of Order n 328
28.8 Cramer’s Rule for Determinants of Order n 328
28.9 Homogenous Linear Equations 329
Solved Problems 329
Supplementary Problems 345
CHAPTER 29- Matrices 349
29.1 Definition of a Matrix 349
29.2 Operations with Matrices 349
29.3 Elementary Row Operations 351
29.4 Inverse of a Matrix 352
29.5 Matrix Equations 353
29.6 Matrix Solution of a System of Equations 354
Solved Problems 355
Supplementary Problems 359
CHAPTER 30- Mathematical Induction 362
30.1 Principle of Mathematical Induction 362
30.2 Proof by Mathematical Induction 362
Solved Problems 362
Supplementary Problems 366
CHAPTER 31- Partial Fractions 368
31.1 Rational Fractions 368
31.2 Proper Fractions 368
31.3 Partial Fractions 368
31.4 Identically Equal Polynomials 369
31.5 Fundamental Theorem 369
31.6 Finding the Partial Fraction Decomposition 370
Solved Problems 371
Supplementary Problems 373
CHAPTER 32- Solving Higher Degree Equations 375
32.1 The Iteration Method 375
32.2 The Bisection Method 377
32.3 The Approximation Method 377
Solved Problems 378
Supplementary Problems 381
CHAPTER 33- Algebra for Calculus 382
33.1 Introduction 382
33.2 Limit of a Sequence 382
33.3 Limit of a Series 382
33.4 Convergence and Divergence 383
33.5 Limit of a Function 384
33.6 Continuity 386
33.7 Derivatives 387
Solved Problems 388
Supplementary Problems 393
CHAPTER 34- Additional Problems 395
Solved Problems 395
Supplementary Problems 422
Answers to Supplementary Problems 432
APPENDIX A Table of Common Logarithms 439
APPENDIX B Table of Natural Logarithms 443
INDEX 447
Schaum’s Outline Series
-------- Autors -------
Robert E. Moyer, PhD
Associate Professor of Mathematics
Southwest Minnesota State University (Retired)
Professor and Chairman,
Department of Mathematics & Physics
Fort Valley State University (Retired)
Murray R. Spiegel, PhD
Former Professor and Chairman, Mathematics Department
Rensselaer Polytechnic Institute, Hartford Graduate Center
------------------------
CONTENTS
CHAPTER 1- Fundamental Operations with Numbers 1
1.1 Four Operations 1
1.2 System of Real Numbers 2
1.3 Graphical Representation of Real Numbers 2
1.4 Properties of Addition and Multiplication of Real Numbers 3
1.5 Rules of Signs 3
1.6 Exponents and Powers 4
1.7 Operations with Fractions 4
Solved Problems 5
Supplementary Problems 9
CHAPTER 2- Fundamental Operations with Algebraic Expressions 12
2.1 Algebraic Expressions 12
2.2 Terms 12
2.3 Degree 13
2.4 Grouping 13
2.5 Computation with Algebraic Expressions 13
Solved Problems 16
Supplementary Problems 20
CHAPTER 3- Properties of Numbers 22
3.1 Sets of Numbers 22
3.2 Properties 22
3.3 Additional Properties 23
Solved Problems 23
Supplementary Problems 25
CHAPTER 4- Special Products 27
4.1 Special Products 27
4.2 Products Yielding Answers of the Form an ± bn 28
Solved Problems 28
Supplementary Problems 30
CHAPTER 5- Factoring 32
5.1 Factoring 32
5.2 Factorization Procedures 33
5.3 Greatest Common Factor 34
5.4 Least Common Multiple 34
Solved Problems 35
Supplementary Problems 39
CHAPTER 6- Fractions 41
6.1 Rational Algebraic Fractions 41
6.2 Operations with Algebraic Fractions 42
6.3 Complex Fractions 43
Solved Problems 44
Supplementary Problems 46
CHAPTER 7- Exponents 48
7.1 Positive Integral Exponent 48
7.2 Negative Integral Exponent 48
7.3 Roots 48
7.4 Rational Exponents 49
7.5 General Laws of Exponents 49
7.6 Scientific Notation 50
Solved Problems 50
Supplementary Problems 56
CHAPTER 8- Radicals 58
8.1 Radical Expressions 58
8.2 Laws for Radicals 58
8.3 Simplifying Radicals 58
8.4 Operations with Radicals 59
8.5 Rationalizing Binomial Denominators 60
Solved Problems 61
Supplementary Problems 65
CHAPTER 9- Simple Operations with Complex Numbers 67
9.1 Complex Numbers 67
9.2 Graphical Representation of Complex Numbers 67
9.3 Algebraic Operations with Complex Numbers 68
Solved Problems 69
Supplementary Problems 71
CHAPTER 10- Equations in General 73
10.1 Equations 73
10.2 Operations Used in Transforming Equations 73
10.3 Equivalent Equations 74
10.4 Formulas 74
10.5 Polynomial Equations 75
Solved Problems 75
Supplementary Problems 79
CHAPTER 11- Ratio, Proportion, and Variation 81
11.1 Ratio 81
11.2 Proportion 81
11.3 Variation 81
11.4 Unit Price 82
11.5 Best Buy 82
Solved Problems 83
Supplementary Problems 86
CHAPTER 12- Functions and Graphs 89
12.1 Variables 89
12.2 Relations 89
12.3 Functions 89
12.4 Function Notation 90
12.5 Rectangular Coordinate System 90
12.6 Function of Two Variables 91
12.7 Symmetry 91
12.8 Shifts 92
12.9 Scaling 93
12.10 Using a Graphing Calculator 93
Solved Problems 96
Supplementary Problems 106
CHAPTER 13- Linear Equations in One Variable 114
13.1 Linear Equations 114
13.2 Literal Equations 114
13.3 Word Problems 115
Solved Problems 116
Supplementary Problems 124
CHAPTER 14- Equations of Lines 128
14.1 Slope of a Line 128
14.2 Parallel and Perpendicular Lines 129
14.3 Slope-Intercept Form of Equation of a Line 130
14.4 Slope-Point Form of Equation of a Line 130
14.5 Two-Point Form of Equation of a Line 130
14.6 Intercept Form of Equation of a Line 131
Solved Problems 131
Supplementary Problems 134
CHAPTER 15- Simultaneous Linear Equations 137
15.1 Systems of Two Linear Equations 137
15.2 Systems of Three Linear Equations 138
Solved Problems 139
Supplementary Problems 146
CHAPTER 16- Quadratic Equations in One Variable 150
16.1 Quadratic Equations 150
16.2 Methods of Solving Quadratic Equations 150
16.3 Sum and Product of the Roots 152
16.4 Nature of the Roots 152
16.5 Radical Equations 152
16.6 Quadratic-Type Equations 153
Solved Problems 153
Supplementary Problems 163
CHAPTER 17- Conic Sections 169
17.1 General Quadratic Equations 169
17.2 Conic Sections 170
17.3 Circles 170
17.4 Parabolas 171
17.5 Ellipses 173
17.6 Hyperbolas 177
17.7 Graphing Conic Sections with a Calculator 180
Solved Problems 180
Supplementary Problems 186
CHAPTER 18- Systems of Equations Involving Quadratics 191
18.1 Graphical Solution 191
18.2 Algebraic Solution 191
Solved Problems 193
Supplementary Problems 197
CHAPTER 19- Inequalities 199
19.1 Definitions 199
19.2 Principles of Inequalities 199
19.3 Absolute Value Inequalities 200
19.4 Higher Degree Inequalities 200
19.5 Linear Inequalities in Two Variables 202
19.6 Systems of Linear Inequalities 202
19.7 Linear Programming 203
Solved Problems 204
Supplementary Problems 210
CHAPTER 20- Polynomial Functions 214
20.1 Polynomial Equations 214
20.2 Zeros of Polynomial Equations 214
20.3 Solving Polynomial Equations 216
20.4 Approximating Real Zeros 218
Solved Problems 219
Supplementary Problems 231
CHAPTER 21- Rational Functions 235
21.1 Rational Functions 235
21.2 Vertical Asymptotes 235
21.3 Horizontal Asymptotes 235
21.4 Graphing Rational Functions 236
21.5 Graphing Rational Functions Using a Graphing Calculator 238
Solved Problems 238
Supplementary Problems 240
CHAPTER 22- Sequences and Series 245
22.1 Sequences 245
22.2 Arithmetic Sequences 245
22.3 Geometric Sequences 245
22.4 Infinite Geometric Series 246
22.5 Harmonic Sequences 246
22.6 Means 246
Solved Problems 247
Supplementary Problems 258
CHAPTER 23- Logarithms 263
23.1 Definition of a Logarithm 263
23.2 Laws of Logarithms 263
23.3 Common Logarithms 264
23.4 Using a Common Logarithm Table 264
23.5 Natural Logarithms 265
23.6 Using a Natural Logarithms Table 265
23.7 Finding Logarithms Using a Calculator 266
Solved Problems 267
Supplementary Problems 273
CHAPTER 24- Applications of Logarithms and Exponents 276
24.1 Introduction 276
24.2 Simple Interest 276
24.3 Compound Interest 277
24.4 Applications of Logarithms 278
24.5 Applications of Exponents 280
Solved Problems 280
Supplementary Problems 284
CHAPTER 25- Permutations and Combinations 288
25.1 Fundamental Counting Principle 288
25.2 Permutations 288
25.3 Combinations 289
25.4 Using a Calculator 290
Solved Problems 290
Supplementary Problems 300
CHAPTER 26- The Binomial Theorem 303
26.1 Combinatorial Notation 303
26.2 Expansion of (a + x)n 303
Solved Problems 304
Supplementary Problems 308
CHAPTER 27- Probability 310
27.1 Simple Probability 310
27.2 Compound Probability 310
27.3 Mathematical Expectation 311
27.4 Binomial Probability 311
27.5 Conditional Probability 311
Solved Problems 312
Supplementary Problems 320
CHAPTER 28- Determinants 323
28.1 Determinants of Second Order 323
28.2 Cramer’s Rule 323
28.3 Determinants of Third Order 324
28.4 Determinants of Order n 326
28.5 Properties of Determinants 327
28.6 Minors 328
28.7 Value of a Determinant of Order n 328
28.8 Cramer’s Rule for Determinants of Order n 328
28.9 Homogenous Linear Equations 329
Solved Problems 329
Supplementary Problems 345
CHAPTER 29- Matrices 349
29.1 Definition of a Matrix 349
29.2 Operations with Matrices 349
29.3 Elementary Row Operations 351
29.4 Inverse of a Matrix 352
29.5 Matrix Equations 353
29.6 Matrix Solution of a System of Equations 354
Solved Problems 355
Supplementary Problems 359
CHAPTER 30- Mathematical Induction 362
30.1 Principle of Mathematical Induction 362
30.2 Proof by Mathematical Induction 362
Solved Problems 362
Supplementary Problems 366
CHAPTER 31- Partial Fractions 368
31.1 Rational Fractions 368
31.2 Proper Fractions 368
31.3 Partial Fractions 368
31.4 Identically Equal Polynomials 369
31.5 Fundamental Theorem 369
31.6 Finding the Partial Fraction Decomposition 370
Solved Problems 371
Supplementary Problems 373
CHAPTER 32- Solving Higher Degree Equations 375
32.1 The Iteration Method 375
32.2 The Bisection Method 377
32.3 The Approximation Method 377
Solved Problems 378
Supplementary Problems 381
CHAPTER 33- Algebra for Calculus 382
33.1 Introduction 382
33.2 Limit of a Sequence 382
33.3 Limit of a Series 382
33.4 Convergence and Divergence 383
33.5 Limit of a Function 384
33.6 Continuity 386
33.7 Derivatives 387
Solved Problems 388
Supplementary Problems 393
CHAPTER 34- Additional Problems 395
Solved Problems 395
Supplementary Problems 422
Answers to Supplementary Problems 432
APPENDIX A Table of Common Logarithms 439
APPENDIX B Table of Natural Logarithms 443
INDEX 447
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