Elementary algebra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Pergamon Press
1965
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | International series of monographs on pure and applied mathematics
75 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | XIX, 442 S. |
Internformat
MARC
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| 100 | 1 | |a Faddeev, Dmitrij K. |d 1907-1989 |e Verfasser |0 (DE-588)119125528 |4 aut | |
| 240 | 1 | 0 | |a Algebra dlja samoobrazovanija |
| 245 | 1 | 0 | |a Elementary algebra |c by D. K. Faddeyev and I. S. Sominskii |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1965 | |
| 300 | |a XIX, 442 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series of monographs on pure and applied mathematics |v 75 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Algebra | |
| 700 | 1 | |a Sominskij, Ilʹja Samuilovič |e Verfasser |0 (DE-588)1026251494 |4 aut | |
| 830 | 0 | |a International series of monographs on pure and applied mathematics |v 75 |w (DE-604)BV001888024 |9 75 | |
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Datensatz im Suchindex
| _version_ | 1804129461684142080 |
|---|---|
| adam_text | CONTENTS
Authors Preface xiii
Editor s Preface xix
CHAPTER I
The use of symbols in solving problems
§ 1. Introduction to symbolic notation 1
§ 2. The concept of an equation. Constructing an equation to express
the relationship between given quantities 4
§ 3. The sequence of operations 7
§ 4. The coefficient 12
§ 5. Powers. Raising to a power 14
§ 6. The laws of arithmetical operations 16
§ 7. Inverse operations 20
§ 8. Properties of arithmetical operations 21
§ 9. Equations in one unknown 22
§ 10. The notion of identity 24
§ 11. The principle underlying the solution of problems by means of
equations 25
§ 12. Solution of problems by means of equations 28
§ 13. Equations with symbolic coefficients 33
chapter n
Positive and negative numbers
§ 1. Definition of a negative number 35
§ 2. The subtraction of one positive number from a smaller one 38
§ 3. The use of negative numbers to describe a change in a variable
quantity 39
§ 4. The application of negative numbers to the measurement of
quantities varying in two opposite directions 41
§ 5. Representation of numbers as points on a straight line 42
§ 6. Addition of positive and negative numbers 43
§ 7. Properties of addition 45
§ 8. Subtraction 47
v
vi CONTENTS
§ 9. The algebraic sum 48
§ 10. The use of inequality signs 49
§ 11. Directed distances 51
§ 12. Multiplication of positive and negative numbers 54
§ 13. The fundamental property of zero 57.
§ 14. The multiplication of several numbers and raising a negative num¬
ber to a power 58
§ 15. Division 59
§ 16. The interpretation of a negative answer in the solution of a problem 61
§ 17. Graphical representation of the relationship between two variables 62
chapter in
Rearrangement of integral algebraic expressions
§ 1. The object of algebraic rearrangements 71
§ 2. Types of algebraic expressions 72
§ 3. Reduction of similar terms 73
§ 4. Addition and subtraction of polynomials 75
§ 5. Multiplication of powers of the same base and raising a power to a
power 76
§ 6. Multiplication of monomials 77
§ 7. Raising a monomial to a power 78
§ 8. Multiplication of a polynomial by a monomial 79
§ 9. Multiplication of a polynomial by a polynomial 80
§ 10. Multiplication of several polynomials 81
§ 11. Multiplication of polynomials containing only one letter 82
§ 12. Rapid multiplication by formulae 85
§ 13. Application of rapid multiplication formulae to mental calcula¬
tions 89
§ 14. Conclusions 91
CHAPTER IV
The factorization of polynomials
§ 1. The concept of factorization 94
§ 2. Taking a factor outside brackets 95
§ 3. The use of brackets in arranging a polynomial in powers of a single
symbol 97
§ 4. The method of grouping 99
§ 5. Splitting individual terms of a polynomial into similar terms 101
§ 6. The use of multiplication formulae 101
§ 7. More complicated examples 102
§ 8. Factorization of a quadratic trinomial 104
CONTENTS vii
CHAPTER V
The rearrangement of fractional algebraic expressions
§ 1. Characteristics of fractional expressions 107
§ 2. The basic property of a fraction 110
§ 3. Division of integral algebraic expressions 111
§ 4. Division of powers of the same base 112
§ 5. Division of monomials 113
§ 6. Division of a polynomial by a monomial 115
§ 7. The application of multiplication formulae to the division of a
polynomial by a polynomial 118
§ 8. General remarks on the division of a polynomial by a polynomial 119
§ 9. Division of polynomials involving a single letter . 121
§ 10. Simplification of algebraic fractions 125
§ 11. Simplification of an algebraic fraction with fractional coefficients 126
§ 12. Addition and subtraction of algebraic fractions 127
§ 13. Multiplication of algebraic fractions 130
§ 14. Division of algebraic fractions 131
§ 15. Simplification of fractions in which the numerator and denomina¬
tor are algebraic sums of fractions 132
§ 16. General conclusions 134
CHAPTER VI
Proportion and proportionality
1. Definitions 136
§ 2. The principal property of a proportion 136
§ 3. Finding the unknown member of a proportion 137
§ 4. Transposing the terms of a proportion 138
§ 5. Derived proportions 139
§ 6. A set of equal ratios 141
§ 7. Proportionality 142
CHAPTER VII
Equations and inequalities of the first degree
in one unknown
§ 1. Two properties of equations 145
§ 2. The concept of equivalence of equations 149
§ 3. Some transformations of an equation which can lead to loss or gain
of solutions 150
§ 4. Solving equations 152
§ 5. The number of solutions to an equation of the first degree in one
unknown 154
Viii CONTENTS
§ 6. Equations with the unknown in a denominator 155
§ 7. Solving problems by means of equations. The idea of analysing
problems 156
§ 8. The use of equations to solve problems in general form 164
§ 9. The notion of inequality 165
§ 10. Properties of inequalities 166
§11. The solution of inequalities of the first degree in one unknown 169
chapter vm
Systems of equations
§ 1. Systems of two equations of the first degree in two unknowns 172
§ 2. One equation of the first degree in two unknowns 174
§ 3. Graphical solution of systems of equations 178
§ 4. The number of solutions of a system of two equations of the first
degree in two unknowns 180
§ 5. The method of comparison 182
§ 6. Properties of derived equations 187
§ 7. The method of addition and subtraction 190
§ 8. The method of substitution 194
§ 9. Solving systems of equations of the first degree in two unknowns
with symbolic coefficients 197
§ 10. Solution of problems by means of a system of two equations of the
first degree in two unknowns 198
§11. Systems of three equations of the first degree in three unknowns 200
§ 12. The solution of a system of three equations of the first degree in
three unknowns 202
§ 13. The number of solutions of a system of three equations of the first
degree in three unknowns 207
CHAPTER IX
Extracting a square root
§ 1. Definition of the operation of root extraction 209
§ 2. The arithmetical value of a square root 209
§ 3. Approximate calculation of a root 211
§ 4. Extracting a square root graphically 213
§ 5. The use of graphs for the approximate solution of equations and
systems of two equations in two unknowns 216
CONTENTS ix
CHAPTER X
Powers, roots and irrational numbers
§ 1. Properties of powers with integral indices 219
§ 2. The square of the sum of several terms 221
§ 3. Some properties of powers 223
§ 4. The root to any power of a number 225
§ 5. The impossibility of expressing the root of any rational positive
number by a combination of rational numbers 227
§ 6. The connexion between root extraction and the measurement of
distances 228
§ 7. The measurement of lengths. Definition of irrational and real num¬
bers 229
§ 8. Representation of real numbers on the number axis. Inequalities 234
§ 9. Addition of real numbers 235
§ 10. Extracting the root of products, fractions and powers 237
§ 11. Multiplication and division of roots 239
§ 12. Raising a root to a power and extracting the root of a root 240
§ 13. Removing a rational factor from under the root sign. Putting a
rational factor under the root sign 242
§ 14. Similar radicals and their addition 244
§ 15. Rationalizing a denominator 244
CHAPTER XI
Quadratic equations
and equations reducing to quadratics
§ 1. Integral algebraic equations and their classification 247
§ 2. Incomplete quadratic equations 249
§ 3. The reduced quadratic equation 250
§ 4. The general quadratic equation 253
§ 5. Some problems giving rise to quadratic equations 255
§ 6. Connexion between the coefficients and roots of a quadratic
equation 259
§ 7. Factorizing a quadratic trinomial 260
§ 8. Forming a quadratic equation from given roots 261
§ 9. Examples and applications 262
§ 10. Investigation of the roots of a quadratic equation according to the
coefficients and discriminant 265
§ 11. Biquadratic equations 266
§ 12. Some equations reducing to quadratics by the introduction
of a new unknown 268
X CONTENTS
§ 13. Transformation of equations 269
§ 14. Fractional algebraic equations 273
§ 15. Irrational equations 277
CHAPTER XII
Functions and their graphs
§ 1. Functional relationship 280
§ 2. Plane rectangular system of coordinates 283
§ 3. The graph of a function 284
§ 4. Direct proportionality 290
§ 5. Linear functions 293
§ 6. The geometrical meaning of an equation of the first degree in two
unknowns 296
§ 7. Quadratic functions 297
§ 8. Analysis of the graph of a quadratic function 302
§ 9. Inverse proportionality 305
CHAPTER XIII
Systems of equations of higher degree
§ 1. System of two equations of the first and second degree in two un¬
knowns 308
§ 2. Some systems of equations soluble in special ways 309
§ 3. Graphical solution of equations in one unknown 312
§ 4. Graphical solution of a system of two equations in two unknowns 315
§ 5. Finding the root of an equation or solving a system of non linear
equations by successive approximations 319
CHAPTER XIV
Sequences of numbers
§ 1. Basic definitions 321
§ 2. The arithmetic progression 324
§ 3. The geometric progression 329
CHAPTER XV
Generalization of the concept of index of a power
§ 1. Introduction 333
§ 2. The concept of a power with zero or negative index 333
§ 3. The concept of a power with a fractional index 335
CONTENTS XI
§ 4. The concept of a power with a negative fractional index 336
§ 5. Operations on powers with rational indices 337
CHAPTER XVI
Inequalities
§ 1. Fundamental properties of inequalities 341
§ 2. Proof of inequalities 344
§ 3. Equivalent inequalities 351
§ 4. The solution of inequalities and systems of inequalities of the first
degree in one unknown 354
§ 5. Solution of an inequality of the second degree in one unknown 358
CHAPTER XVII
Equations of higher degrees
§ 1. Equations of the «th degree in one unknown 361
§ 2. Division of a polynomial in x by x — a 361
§ 3. Forming an equation of the «th degree from its roots 364
§ 4. The fundamental theorem of algebra and some of its consequences 365
§ 5. Solution of equations of higher degrees 366
SUPPLEMENT
True and false statements 368
APPENDIX I
Operations with real numbers
§ 1. Addition and subtraction of real numbers 380
§ 2. Multiplication and division of real numbers 381
§ 3. Raising to a power and extracting a root 383
appendix n
Complex numbers
§ 1. Extension of the number concept 385
§ 2. Definition of a complex number 390
§ 3. Properties of complex numbers 392
§ 4. Properties of zero 394
§ 5. Geometrical representation of complex numbers 395
xii CONTENTS
§ 6. Complex numbers in trigonometrical form 395
§ 7. Extracting the square root of a negative number 396
§ 8. Some applications of complex numbers 396
APPENDIX III
Analysis of equations
§ 1. The object of analysing equations 399
§ 2. The analysis of an equation of the first degree in one unknown 399
§ 3. The analysis of a system of two equations of the first degree in two
unknowns 401
APPENDIX IV
The rational roots of an equation
§ 1. Calculation of rational roots of equations with integer coefficients 409
Answers and solutions 413
Other Titles in the Series 441
|
| any_adam_object | 1 |
| author | Faddeev, Dmitrij K. 1907-1989 Sominskij, Ilʹja Samuilovič |
| author_GND | (DE-588)119125528 (DE-588)1026251494 |
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| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
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| language | English |
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| physical | XIX, 442 S. |
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| publisher | Pergamon Press |
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| series2 | International series of monographs on pure and applied mathematics |
| spelling | Faddeev, Dmitrij K. 1907-1989 Verfasser (DE-588)119125528 aut Algebra dlja samoobrazovanija Elementary algebra by D. K. Faddeyev and I. S. Sominskii 1. ed. Oxford [u.a.] Pergamon Press 1965 XIX, 442 S. txt rdacontent n rdamedia nc rdacarrier International series of monographs on pure and applied mathematics 75 Aus dem Russ. übers. Algebra Sominskij, Ilʹja Samuilovič Verfasser (DE-588)1026251494 aut International series of monographs on pure and applied mathematics 75 (DE-604)BV001888024 75 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009979866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Faddeev, Dmitrij K. 1907-1989 Sominskij, Ilʹja Samuilovič Elementary algebra International series of monographs on pure and applied mathematics Algebra |
| title | Elementary algebra |
| title_alt | Algebra dlja samoobrazovanija |
| title_auth | Elementary algebra |
| title_exact_search | Elementary algebra |
| title_full | Elementary algebra by D. K. Faddeyev and I. S. Sominskii |
| title_fullStr | Elementary algebra by D. K. Faddeyev and I. S. Sominskii |
| title_full_unstemmed | Elementary algebra by D. K. Faddeyev and I. S. Sominskii |
| title_short | Elementary algebra |
| title_sort | elementary algebra |
| topic | Algebra |
| topic_facet | Algebra |
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