Schaum's Outline of College Algebra

by Spiegel, Murray R.; Moyer, Robert E.

• ISBN13: 9780070602663
• ISBN10: 0070602662
• Edition: 2nd
• Format: Paperback
• Copyright: 1997-09-01
• Publisher: McGraw-Hill

Summary

Algebra, the foundation for all higher mathematics, is taught here both for beginners and for those who wish to review algebra for further work in math, science and engineering. This superior study guide­­the first edition sold more than 600,000 copies!­­includes the most current terminology, emphasis and technology. It treats many subjects more thoroughly than most texts, making it adaptable for any course and an excellent reference and bridge to further study. Also available as a Schaum's Electronic Tutor.

Table of Contents

PROBLEMS ALSO FOUND IN THE COMPANION SCHAUM'S ELECTRONIC TUTOR	x
Chapter 1 FUNDAMENTAL OPERATIONS WITH NUMBERS	1	(11)
1.1 Four Operations	1	(1)
1.2 System of Real Numbers	1	(1)
1.3 Graphical Representation of Real Numbers	2	(1)
1.4 Properties of Addition and Multiplication of Real Numbers	2	(1)
1.5 Rules of Signs	3	(1)
1.6 Exponents and Powers	3	(1)
1.7 Operations with Fractions	4	(8)
Chapter 2 FUNDAMENTAL OPERATIONS WITH ALGEBRAIC EXPRESSIONS	12	(10)
2.1 Algebraic Expressions	12	(1)
2.2 Terms	12	(1)
2.3 Degree	13	(1)
2.4 Grouping	13	(1)
2.5 Computation with Algebraic Expressions	13	(9)
Chapter 3 PROPERTIES OF NUMBERS	22	(5)
3.1 Sets of Numbers	22	(1)
3.2 Properties	22	(1)
3.3 Additional Properties	23	(4)
Chapter 4 SPECIAL PRODUCTS	27	(4)
4.1 Special Products	27	(1)
4.2 Products Yielding Answers of the Form a(n) plus or minus b(n)	27	(4)
Chapter 5 FACTORING	31	(10)
5.1 Factoring	31	(1)
5.2 Factorization Procedures	31	(2)
5.3 Greatest Common Factor	33	(1)
5.4 Least Common Multiple	33	(8)
Chapter 6 FRACTIONS	41	(7)
6.1 Rational Algebraic Fractions	41	(1)
6.2 Operations with Algebraic Fractions	42	(1)
6.3 Complex Fractions	43	(5)
Chapter 7 EXPONENTS	48	(10)
7.1 Positive Integral Exponent	48	(1)
7.2 Negative Integral Exponent	48	(1)
7.3 Roots	48	(1)
7.4 Rational Exponents	49	(1)
7.5 General Laws of Exponents	49	(1)
7.6 Scientific Notation	50	(8)
Chapter 8 RADICALS	58	(9)
8.1 Radical Expressions	58	(1)
8.2 Laws for Radicals	58	(1)
8.3 Simplifying Radicals	58	(1)
8.4 Operations with Radicals	59	(1)
8.5 Rationalizing Binomial Denominators	60	(7)
Chapter 9 SIMPLE OPERATIONS WITH COMPLEX NUMBERS	67	(6)
9.1 Complex Numbers	67	(1)
9.2 Graphical Representation of Complex Numbers	67	(1)
9.3 Algebraic Operations with Complex Numbers	68	(5)
Chapter 10 EQUATIONS IN GENERAL	73	(8)
10.1 Equations	73	(1)
10.2 Operations Used in Transforming Equations	73	(1)
10.3 Equivalent Equations	74	(1)
10.4 Formulas	74	(1)
10.5 Polynomial Equations	74	(7)
Chapter 11 RATIO, PROPORTION, AND VARIATION	81	(8)
11.1 Ratio	81	(1)
11.2 Proportion	81	(1)
11.3 Variation	81	(1)
11.4 Unit Price	82	(1)
11.5 Best Buy	82	(7)
Chapter 12 FUNCTIONS AND GRAPHS	89	(24)
12.1 Variables	89	(1)
12.2 Relations	89	(1)
12.3 Functions	89	(1)
12.4 Function Notation	90	(1)
12.5 Rectangular Coordinate System	90	(1)
12.6 Function of Two Variables	91	(1)
12.7 Symmetry	91	(1)
12.8 Shifts	92	(1)
12.9 Scaling	93	(1)
12.10 Using a Graphing Calculator	93	(20)
Chapter 13 LINEAR EQUATIONS IN ONE VARIABLE	113	(14)
13.1 Linear Equations	113	(1)
13.2 Literal Equations	113	(1)
13.3 Word Problems	113	(14)
Chapter 14 EQUATIONS OF LINES	127	(9)
14.1 Slope of a Line	127	(1)
14.2 Parallel and Perpendicular Lines	127	(1)
14.3 Slope-Intercept Form of Equation of a Line	128	(1)
14.4 Slope-Point Form of Equation of a Line	129	(1)
14.5 Two-Point Form of Equation of a Line	129	(1)
14.6 Intercept Form of Equation of a Line	130	(6)
Chapter 15 SIMULTANEOUS LINEAR EQUATIONS	136	(13)
15.1 Systems of Two Linear Equations	136	(1)
15.2 Systems of Three Linear Equations	137	(12)
Chapter 16 QUADRATIC EQUATIONS IN ONE VARIABLE	149	(18)
16.1 Quadratic Equations	149	(1)
16.2 Methods of Solving Quadratic Equations	149	(1)
16.3 Sum and Product of the Roots	150	(1)
16.4 Nature of the Roots	151	(1)
16.5 Radical Equations	151	(1)
16.6 Quadratic-Type Equations	151	(16)
Chapter 17 CONIC SECTIONS	167	(21)
17.1 General Quadratic Equations	167	(1)
17.2 Conic Sections	167	(1)
17.3 Circles	168	(1)
17.4 Parabolas	169	(2)
17.5 Ellipses	171	(4)
17.6 Hyperbolas	175	(2)
17.7 Graphing Conic Sections with a Calculator	177	(11)
Chapter 18 SYSTEMS OF EQUATIONS INVOLVING QUADRATICS	188	(7)
18.1 Graphical Solution	188	(1)
18.2 Algebraic Solution	188	(7)
Chapter 19 INEQUALITIES	195	(15)
19.1 Definitions	195	(1)
19.2 Principles of Inequalities	195	(1)
19.3 Absolute Value Inequalities	196	(1)
19.4 Higher Degree Inequalities	196	(1)
19.5 Linear Inequalities in Two Variables	197	(1)
19.6 Systems of Linear Inequalities	198	(1)
19.7 Linear Programming	199	(11)
Chapter 20 POLYNOMIAL FUNCTIONS	210	(21)
20.1 Polynomial Equations	210	(1)
20.2 Zeros of Polynomial Equations	210	(1)
20.3 Solving Polynomial Equations	211	(2)
20.4 Approximating Real Zeros	213	(18)
Chapter 21 RATIONAL FUNCTIONS	231	(10)
21.1 Rational Functions	231	(1)
21.2 Vertical Asymptotes	231	(1)
21.3 Horizontal Asymptotes	231	(1)
21.4 Graphing Rational Functions	232	(1)
21.5 Graphing Rational Functions Using a Graphing Calculator	233	(8)
Chapter 22 SEQUENCES AND SERIES	241	(18)
22.1 Sequences	241	(1)
22.2 Arithmetic Sequences	241	(1)
22.3 Geometric Sequences	241	(1)
22.4 Infinite Geometric Series	242	(1)
22.5 Harmonic Sequences	242	(1)
22.6 Means	242	(17)
Chapter 23 LOGARITHMS	259	(15)
23.1 Definition of a Logarithm	259	(1)
23.2 Laws of Logarithms	259	(1)
23.3 Common Logarithms	259	(1)
23.4 Using a Common Logarithm Table	260	(1)
23.5 Natural Logarithms	261	(1)
23.6 Using a Natural Logarithm Table	261	(2)
23.7 Finding Logarithms Using a Calculator	263	(11)
Chapter 24 APPLICATIONS OF LOGARITHMS AND EXPONENTS	274	(13)
24.1 Introduction	274	(1)
24.2 Simple Interest	274	(1)
24.3 Compound Interest	274	(2)
24.4 Applications of Logarithms	276	(1)
24.5 Applications of Exponents	277	(10)
Chapter 25 PERMUTATIONS AND COMBINATIONS	287	(16)
25.1 Fundamental Counting Principle	287	(1)
25.2 Permutations	287	(1)
25.3 Combinations	288	(1)
25.4 Using a Calculator	289	(14)
Chapter 26 THE BINOMIAL THEOREM	303	(8)
26.1 Combinatorial Notation	303	(1)
26.2 Expansion of (a + x)(n)	303	(8)
Chapter 27 PROBABILITY	311	(14)
27.1 Simple Probability	311	(1)
27.2 Compound Probability	311	(1)
27.3 Mathematical Expectation	312	(1)
27.4 Binomial Probability	312	(1)
27.5 Conditional Probability	312	(13)
Chapter 28 DETERMINANTS AND SYSTEMS OF LINEAR EQUATIONS	325	(10)
28.1 Determinants of Second Order	325	(1)
28.2 Cramer's Rule	325	(1)
28.3 Determinants of Third Order	326	(9)
Chapter 29 DETERMINANTS OF ORDER n	335	(18)
29.1 Inversion	335	(1)
29.2 Determinants of Order n	335	(1)
29.3 Properties of Determinants	336	(1)
29.4 Minors	337	(1)
29.5 Value of a Determinant	337	(1)
29.6 Cramer's Rule	338	(1)
29.7 Homogeneous Linear Equations	338	(15)
Chapter 30 MATRICES	353	(13)
30.1 Definition of a Matrix	353	(1)
30.2 Operations with Matrices	353	(2)
30.3 Elementary Row Operations	355	(1)
30.4 Inverse of a Matrix	356	(1)
30.5 Matrix Equations	357	(1)
30.6 Matrix Solution of a System of Equations	357	(9)
Chapter 31 MATHEMATICAL INDUCTION	366	(6)
31.1 Principle of Mathematical Induction	366	(1)
31.2 Proof by Mathematical Induction	366	(6)
Chapter 32 PARTIAL FRACTIONS	372	(7)
32.1 Rational Fractions	372	(1)
32.2 Proper Fractions	372	(1)
32.3 Partial Fractions	372	(1)
32.4 Identically Equal Polynomials	372	(1)
32.5 Fundamental Theorem	373	(1)
32.6 Finding the Partial Fraction Decomposition	374	(5)
Appendix A TABLE OF COMMON LOGARITHMS	379	(3)
Appendix B TABLE OF NATURAL LOGARITHMS	382	(3)
Appendix C SAMPLE SCREENS FROM THE COMPANION SCHAUM'S ELECTRONIC TUTOR	385	(16)
INDEX	401