Verfügbarkeit: Elementary algebra | Technische Universität München

Elementary algebra:

Gespeichert in:

Bibliographische Detailangaben
Beteiligte Personen:	Faddeev, Dmitrij K. 1907-1989 (VerfasserIn), Sominskij, Ilʹja Samuilovič (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Oxford [u.a.] Pergamon Press 1965
Ausgabe:	1. ed.
Schriftenreihe:	International series of monographs on pure and applied mathematics 75
Schlagwörter:	Algebra
Links:	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
Beschreibung:	Aus dem Russ. übers.
Umfang:	XIX, 442 S.

Internformat

MARC


LEADER	00000nam a2200000 cb4500
001	BV014726685
003	DE-604
005	20210419
007	t\|
008	020916s1965 xx \|\|\|\| 00\|\|\| eng d
035			\|a (OCoLC)1473538
035			\|a (DE-599)BVBBV014726685
040			\|a DE-604 \|b ger \|e rakwb
041	0		\|a eng
049			\|a DE-91 \|a DE-29T \|a DE-188
050		0	\|a QA152
082	0		\|a 512
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
856	4	2	\|m HBZ Datenaustausch \|q application/pdf \|u 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 \|3 Inhaltsverzeichnis
943	1		\|a oai:aleph.bib-bvb.de:BVB01-009979866

Datensatz im Suchindex

DE-BY-TUM_call_number	0024 58 A 287-75
DE-BY-TUM_katkey	1303263
DE-BY-TUM_location	Mag
DE-BY-TUM_media_number	TEMP2666200
_version_	1821932539073265664
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
author_facet	Faddeev, Dmitrij K. 1907-1989 Sominskij, Ilʹja Samuilovič
author_role	aut aut
author_sort	Faddeev, Dmitrij K. 1907-1989
author_variant	d k f dk dkf i s s is iss
building	Verbundindex
bvnumber	BV014726685
callnumber-first	Q - Science
callnumber-label	QA152
callnumber-raw	QA152
callnumber-search	QA152
callnumber-sort	QA 3152
callnumber-subject	QA - Mathematics
ctrlnum	(OCoLC)1473538 (DE-599)BVBBV014726685
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.
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01408nam a2200361 cb4500</leader><controlfield tag="001">BV014726685</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210419 </controlfield><controlfield tag="007">t\|</controlfield><controlfield tag="008">020916s1965 xx \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1473538</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014726685</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA152</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Faddeev, Dmitrij K.</subfield><subfield code="d">1907-1989</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)119125528</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Algebra dlja samoobrazovanija</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elementary algebra</subfield><subfield code="c">by D. K. Faddeyev and I. S. Sominskii</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford [u.a.]</subfield><subfield code="b">Pergamon Press</subfield><subfield code="c">1965</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIX, 442 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">International series of monographs on pure and applied mathematics</subfield><subfield code="v">75</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Aus dem Russ. übers.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sominskij, Ilʹja Samuilovič</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1026251494</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">International series of monographs on pure and applied mathematics</subfield><subfield code="v">75</subfield><subfield code="w">(DE-604)BV001888024</subfield><subfield code="9">75</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009979866</subfield></datafield></record></collection>
id	DE-604.BV014726685
illustrated	Not Illustrated
indexdate	2024-12-20T11:06:59Z
institution	BVB
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-009979866
oclc_num	1473538
open_access_boolean
owner	DE-91 DE-BY-TUM DE-29T DE-188
owner_facet	DE-91 DE-BY-TUM DE-29T DE-188
physical	XIX, 442 S.
publishDate	1965
publishDateSearch	1965
publishDateSort	1965
publisher	Pergamon Press
record_format	marc
series	International series of monographs on pure and applied mathematics
series2	International series of monographs on pure and applied mathematics
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
url	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
volume_link	(DE-604)BV001888024
work_keys_str_mv	AT faddeevdmitrijk algebradljasamoobrazovanija AT sominskijilʹjasamuilovic algebradljasamoobrazovanija AT faddeevdmitrijk elementaryalgebra AT sominskijilʹjasamuilovic elementaryalgebra

Verfügbarkeit

Bestellen (Login erforderlich)

Inhaltsverzeichnis
Paper/Kapitel scannen lassen

Bibliotheksmagazin

Bestandsangaben von Bibliotheksmagazin
Signatur:	0024 58 A 287-75 Lageplan
Exemplar 1	Ausleihbar Am Standort