Cauchy's Cours d'analyse: an annotated translation
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Edition: | 1. Aufl. |
| Series: | Sources and studies in the history of mathematics and physical series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 411 S. 235 mm x 155 mm |
| ISBN: | 9781441905482 |
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Record in the Search Index
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|---|---|
| adam_text | Titel: Cauchy¿s Cours d¿analyse
Autor: Bradley, Robert E
Jahr: 2009
Contents
Translators Preface................................................ vii
Introduction....................................................... 1
Preliminaries...................................................... 5
1 On real functions............................................... 17
1.1 General considerations on functions........................... 17
1.2 On simple functions......................................... 18
1.3 On composite functions...................................... 19
2 On infinitely small and infinitely large quantities, and on the
continuity of functions. Singular values of functions in various
particular cases................................................ 21
2.1 On infinitely small and infinitely large quantities................. 21
2.2 On the continuity of functions................................ 26
2.3 On singular values of functions in various particular cases......... 32
3 On symmetric functions and alternating functions. The use of these
functions for the solution of equations of the first degree in any
number of unknowns. On homogeneous functions.................. 49
3.1 On symmetric functions...................................... 49
3.2 On alternating functions..................................... 51
3.3 On homogeneous functions................................... 56
4 Determination of integer functions, when a certain number of
particular values are known. Applications......................... 59
4.1 Research on integer functions of a single variable for which a
certain number of particular values are known................... 59
4.2 Determination of integer functions of several variables, when a
certain number of particular values are assumed to be known....... 64
4.3 Applications............................................... 67
xviii Contents
5 Determination of continuous functions of a single variable that
satisfy certain conditions........................................ 71
5.1 Research on a continuous function formed so that if two such
functions are added or multiplied together, their sum or product is
the same function of the sum or product of the same variables...... 71
5.2 Research on a continuous function formed so that if we multiply
two such functions together and then doublé the product, the result
equals that function of the sum of the variables added to the same
function of the difference of the variables....................... 77
6 On convergent and divergent series. Rules for the convergence of
series. The summation of several convergent series................. 85
6.1 General considerations on series............................... 85
6.2 On series for which ali the terms are positive.................... 90
6.3 On series which contain positive terms and negative terms......... 96
6.4 On series ordered according to the ascending integer powers of a
single variable..............................................102
7 On imaginary expressions and their moduli........................117
7.1 General considerations on imaginary expressions................117
7.2 On the moduli of imaginary expressions and on reduced expressions. 122
7.3 On the real and imaginary roots of the two quantities +1 and ? 1
and on their fractional powers.................................132
7.4 On the roots of imaginary expressions, and on their fractional and
irrational powers............................................143
7.5 Applications of the principles established in the preceding sections. 152
8 On imaginary functions and variables.............................159
8.1 General considerations on imaginary functions and variables.......159
8.2 On infinitely small imaginary expressions and on the continuity of
imaginary functions.........................................165
8.3 On imaginary functions that are symmetric, alternating or
homogeneous..............................................167
8.4 On imaginary integer functions of one or several variables.........167
8.5 Determination of continuous imaginary functions of a single
variable that satisfy certain conditions..........................172
9 On convergent and divergent imaginary series. Summation of some
convergent imaginary series. Notations used to represent imaginary
functions that we find by evaluating the sum of such series..........181
9.1 General considerations on imaginary series.....................181
9.2 On imaginary series ordered according to the ascending integer
powers of a single variable...................................188
9.3 Notations used to represent various imaginary functions which
arise from the summation of convergent series. Properties of these
same functions.............................................202
Contents xix
10 On real or imaginary roots of algebraic equations for which the
left-hand side is a rational and integer function of one variable. The
solution of equations of this kind by algebra or trigonometry........217
10.1 We can satisfy any equation for which the left-hand side is a
rational and integer function of the variable x by real or imaginary
values of that variable. Decomposition of polynomials into factors
of the first and second degree. Geometrie representation of real
factors of the second degree..................................217
10.2 Algebraic or trigonometrie solution of binomial equations and of
some trinomial equations. The theorems of de Moivre and of Cotes. 229
10.3 Algebraic or trigonometrie solution of equations of the third and
fourth degree...............................................233
11 Decomposition of rational fractions...............................241
11.1 Decomposition of a rational fraction into two other fractions of
the same kind..............................................241
11.2 Decomposition of a rational fraction for which the denominator is
the product of several unequal factors into simple fractions which
have for their respective denominators these same linear factors
and have Constant numerators.................................245
11.3 Decomposition of a given rational fraction into other simpler ones
which have for their respective denominators the linear factors of
the first rational fraction, or of the powers of these same factors,
and constants as their numerators..............................251
12 On recurrent series.............................................257
12.1 General considerations on recurrent series......................257
12.2 Expansion of rational fractions into recurrent series..............258
12.3 Summation of recurrent series and the determination of their
general terms...............................................264
Note I - On the theory of positive and negative quantities................267
Note II - On formulas that resnlt from the use of the signs or , and
on the averages among several quantities..........................291
Note III - On the numerical solution of equations......................309
Note IV - On the expansion of the alternating function
(y-x)x(z-jc)(z-y)x...x(v-*)(v-y)(v-z)...(v-ii)..........351
Note V - On Lagrange s interpolation formula.........................355
Note VI - On figurate numbers.......................................359
Note VII - On doublé series..........................................367
xx Contents
Note VIII - On formulas that are used to convert the sines or cosines of
multiples of an are into polynomials, the different terms of which
have the ascending powers of the sines or the cosines of the same
are as factors...................................................375
Note IX - On produets composed of an infinite number of factors........385
Page Concordance of the 1821 and 1897 Editions ......................397
References.........................................................403
Index.............................................................407
|
| any_adam_object | 1 |
| author | Bradley, Robert E. Sandifer, Charles Edward 1951- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| era | Geschichte 1821 gnd |
| era_facet | Geschichte 1821 |
| format | Book |
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| spelling | Bradley, Robert E. Verfasser (DE-588)142319309 aut Cours d'analyse Cauchy's Cours d'analyse an annotated translation Robert E. Bradley ; C. Edward Sandifer 1. Aufl. New York, NY Springer 2009 XX, 411 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Sources and studies in the history of mathematics and physical series Cauchy, Augustin Louis 1789-1857 (DE-588)118519735 gnd rswk-swf Geschichte 1821 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf (DE-588)4135952-5 Quelle gnd-content Analysis (DE-588)4001865-9 s Geschichte 1821 z DE-604 Cauchy, Augustin Louis 1789-1857 (DE-588)118519735 p Sandifer, Charles Edward 1951- Verfasser (DE-588)138206724 aut Cauchy, Augustin Louis 1789-1857 Begründer eines Werks (DE-588)118519735 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022653345&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bradley, Robert E. Sandifer, Charles Edward 1951- Cauchy's Cours d'analyse an annotated translation Cauchy, Augustin Louis 1789-1857 (DE-588)118519735 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)118519735 (DE-588)4001865-9 (DE-588)4135952-5 |
| title | Cauchy's Cours d'analyse an annotated translation |
| title_alt | Cours d'analyse |
| title_auth | Cauchy's Cours d'analyse an annotated translation |
| title_exact_search | Cauchy's Cours d'analyse an annotated translation |
| title_full | Cauchy's Cours d'analyse an annotated translation Robert E. Bradley ; C. Edward Sandifer |
| title_fullStr | Cauchy's Cours d'analyse an annotated translation Robert E. Bradley ; C. Edward Sandifer |
| title_full_unstemmed | Cauchy's Cours d'analyse an annotated translation Robert E. Bradley ; C. Edward Sandifer |
| title_short | Cauchy's Cours d'analyse |
| title_sort | cauchy s cours d analyse an annotated translation |
| title_sub | an annotated translation |
| topic | Cauchy, Augustin Louis 1789-1857 (DE-588)118519735 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Cauchy, Augustin Louis 1789-1857 Analysis Quelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022653345&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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