Basic College AlgebraPDF|Epub|txt|kindle电子书版本网盘下载

Basic College AlgebraPDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

0 SOME BASIC CONCEPTS1

0．1．Introductory remarks1

0．2．Sets and subsets5

0．3．On the logical method11

1 NUMERICAL SYSTEMS19

1．1．Natural numbers19

1．2．Systems of numeration．Decimal scale20

1．3．Addition of natural numbers22

1．4．Multiplication of natural numbers26

1．5．Multiples and divisors31

1．6．Prime and composite numbers32

1．7．Greatest common divisor and least common multiple34

1．8．Number bases37

1．9．Rational fractions41

1．10．Operations on fractions42

1．11．Decimal representation of fractions47

1．12．Concepts of irrational numbers49

1．13．Summary52

2 THE SYSTEM OF REAL NUMBERS55

2．1．Introduction55

2．2．Field properties of real numbers59

2．3．Summary62

3 OPERATIONS ON SIGNED NUMBERS65

3．1．Some order properties of real numbers65

3．2．Addition of signed numbers68

3．3．Subtraction of signed numbers71

3．4．Multiplication of signed numbers73

3．5．Powers of signed numbers75

3．6．Summary77

4 ALGEBRAIC EXPRESSIONS81

4．1．Constants，variables，and parameters81

4．2．Algebraic expressions82

4．3．Degree of a polynomial84

4．4．Numerical value of an algebraic expression85

4．5．Ratio and proportion88

4．6．Summary93

5 FUNDAMENTAL OPERATIONS ON POLYNOMIALS95

5．1．Introduction95

5．2．Addition of polynomials95

5．3．Subtraction of polynomials96

5．4．Multiplication of polynomials99

5．5．Division of polynomials101

5．6．Factoring polynomials106

5．7．Special products108

5．8．Simple types of factoring110

5．9．Special devices112

5．10．Factoring the general quadratic trinomial114

5．11．Summary116

6 RATIONAL FRACTIONS119

6．1．Definitions119

6．2．Reduction of fractions119

6．3．Addition and subtraction of fractions121

6．4．Multiplication and division of fractions125

6．5．Complex fractions127

6．6．Summary130

7 EXPONENTS AND RADICALS133

7．1．Introduction133

7．2．Rational exponents133

7．3．Laws for radicals137

7．4．Operations with radicals140

7．5．Real exponents143

7．6．Irrational algebraic expressions146

7．7．Summary149

8 RELATIONS AND FUNCTIONS155

8．1．Some properties of complete ordered fields—the real number system155

8．2．Geometric representations of the real numbers157

8．3．Coordinates of points on a line160

8．4．On the language of sets163

8．5．Cartesian coordinates of points in a plane165

8．6．Relations166

8．7．Identities and equations170

8．8．Linear equations171

8．9．Functions178

8．10．Variation182

8．11．Summary186

9 COMPLEX NUMBERS189

9．1．Introduction189

9．2．Equality of complex numbers190

9．3．Operations on complex numbers191

9．4．Absolute value of complex numbers197

9．5．Square roots of complex numbers200

9．6．Geometric representation of complex numbers203

9．7．Euclidean coordinate geometry205

9．8．Summary208

10 ALGEBRAIC EQUATIONS211

10．1．Introduction211

10．2．Transformation of equations212

10．3．Solution of linear equations220

10．4．Solution of quadratic equations223

10．5．Some properties of the roots of quadratic equations226

10．6．Equations of higher degree232

10．7．Summary232

11 MATRICES，DETERMINANTS，AND SYSTEMS OF LINEAR EQUATIONS237

11．1．Matrices237

11．2．Different types of matrices238

11．3．Equality of matrices and operations on matrices240

11．4．Systems of equations246

11．5．Solution of a system of linear equations by addition and subtraction249

11．6．Systems of linear equations in matrix form254

11．7．The inverse of a square matrix258

11．8．Determinants261

11．9．A formula for the inverse of a square matrix．Cramer＇s rule265

11．10．Summary270

12 PROPERTIES OF POLYNOMIALS IN ONE VARIABLE275

12．1．Introduction275

12．2．Theorem of the remainder276

12．3．Divisibility277

12．4．Factored form of the polynomial279

12．5．Polynomial identities282

12．6．Method of undetermined coefficients283

12．7．Synthetic division285

12．8．Polynomials expressed as polynomials in x—k289

12．9．Summary291

13 SOLUTION OF REAL NUMERICAL POLYNOMIAL EQUATIONS295

13．1．Introduction295

13．2．Upper and lower bounds of the roots295

13．3．Descartes＇ rule of signs297

13．4．Graphs of polynomials299

13．5．Locating real roots303

13．6．Rational roots of an equation307

13．7．Irrational roots．Horner＇s method311

13．8．Summary316

14 SYSTEMS OF HIGHER DEGREE EQUATIONS319

14．1．Introduction319

14．2．Method of adjunction322

14．3．Graphical interpretation326

14．4．Problems involving systems of equations332

14．5．Summary336

15 INEQUALITIES339

15．1．Introduction339

15．2．Absolute inequalities339

15．3．Conditional inequalities342

15．4．Summary349

16 SEQUENCES AND SERIES353

16．1．Introduction353

16．2．Arithmetic progressions354

16．3．Harmonic progressions357

16．4．Geometric progressions358

16．5．Infinite geometric series361

16．6．Summary365

17 APPROXIMATIONS AND LOGARITHMS369

17．1．Introduction369

17．2．Intervals370

17．3．Absolute and relative errors in approximations372

17．4．Trustworthy and significant digits374

17．5．Determination of the trustworthy digits of an approximation376

17．6．Precision and accuracy of approximations379

17．7．On the arithmetic of approximations380

17．8．General method of calculation with approximations380

17．9．Logarithms384

17．10．Common logarithms—base 10388

17．11．Some uses of common logarithms391

17．12．Change of base of logarithms394

APPENDIX：ON THE FOUNDATIONS OF ARITHMETIC401

A．1 Introduction401

A．2 Undefined elements401

A．3 Assumptions403

A．4 Some fundamental definitions405

A．5 Mathematical induction408

A．6 Exhaustion of a set409

A．7 Properties of equivalent sets410

A．8 Fundamental sequence412

A．9 Cardinal and ordinal numbers413

A．10 Equality and inequality of natural numbers414

A．11 Addition of sets414

A．12 Properties of set addition415

A．13 Addition of numbers416

A．14 Product of two sets417

A．15 Multiplication of numbers418

A．16 Peano＇s postulates for natural numbers419

ANSWERS423

INDEX453