Titre :	Courses and exercises maths 1 analysis and algebra
Type de document :	document électronique
Auteurs :	Louiza Derbal
Editeur :	Sétif:UFA1
Année de publication :	2025
Importance :	1 vol (112 p.)
Langues :	Anglais (eng)
Catégories :	Publications pédagogiques:Mathématiaue P/P
Mots-clés :	Analysis and algebra
Note de contenu :	Contents Introduction1 1 Sets,relationsandapplications2 1.1 Sets.......................................3 1.1.1 DeÂ…nitionofsets............................3 1.1.2 CardinalityofaÂ…niteset.......................3 1.1.3 Operationsonsets...........................3 1.1.4 Lawsforoperationsonsets......................7 1.1.5 Setofparts................................8 1.1.6 Cartesianproduct...........................8 1.2 Relations....................................10 1.2.1 Equivalencerelation..........................12 1.2.2 Orderrelation.............................14 1.3 Applications...................................15 1.3.1 DeÂ…nitionofanapplication......................15 1.3.2 Restrictingandextendinganapplication...............17 1.3.3 Directimageandinverseimage....................17 1.3.4 Injective,surjectiveandbijectiveapplication............19 1.4 Somemethodsofproof.............................20 2 StructureofrealnumbersÂ…eld R 22 2.1 Setofrationalnumbers Q. ...........................22 2.1.1 Integersnumbers............................22 2.1.2 Rationalnumbers............................22 2.2 Irrationalnumbers...............................23 2.3 Realnumbers..................................24 2.3.1 AxiomaticdeÂ…nition..........................24 2.3.2 Absolutevalue.............................26 2.3.3 Boundedsetsof R . ..........................28 2.3.4 Densegroupsin R . ..........................32 2.3.5 Intervalsin R . .............................33 3 Realfunctionsofarealvariable35 3.1 Introduction..................................35 3.1.1 Boundedfunctions,monotonicfunctions...............35 3.1.2 Odd,even,periodicfunction.....................36 3.1.3 Algebraicoperationsonfunctions...................37 3.1.4 Limitofafunction...........................38 3.1.5 Limittheorems.............................41 3.1.6 Operationsoflimits..........................41 3.2 Continuityofafunction............................43 3.2.1 GeneraldeÂ…nitions...........................43 3.2.2 Operationsoncontinuousfunctions..................46 3.2.3 Continuityofcompositionfunctions.................47 3.2.4 TheIntermediateValueTheorem...................47 3.2.5 Uniformcontinuity...........................48 3.3 Derivablefunction...............................51 3.3.1 DeÂ…nitionandproperties.......................51 3.3.2 One-sidedderivatives..........................52 3.3.3 Operationsonderivativefunctions..................53 3.3.4 Derivativeofusualfunctions.....................55 3.3.5 The nth derivative...........................56 3.3.6 HôpitalÂ’srule:.............................66 3.4 Elementaryfunctions..............................68 3.4.1 Trigonometricfunctions........................69 3.4.2 Exponentialfunction..........................75 3.4.3 Logarithmfunction...........................76 3.4.4 Logarithmfunctionofanybase....................77 3.4.5 Power(Exponential)function.....................78 3.4.6 Hyperbolicfunctionsandtheirinverses...............78 4 Internalcompositionlaws88 4.1 Group,Subgroups...............................90 4.2 RingStructure.................................94 4.3 StructureofaÂ…eld(body)...........................94 5 Vectorspaces96 5.1 Vectorspace...................................96 5.1.1 Vectorsubspace............................97 5.1.2 Intersectionandunionofvectorsubspaces..............98 5.1.3 Sumoftwovectorsubspaces.....................99 5.1.4 Directsumoftwovectorsubspaces..................99 5.1.5 Generating,free,andbasisfamilies..................100 5.1.6 Dimensionofvectorspaces......................104 5.2 Linearapplications...............................108 5.2.1 DeÂ…nitionsandexamples.......................108 5.2.2 Linearmapsanddimension......................109
Côte titre :	PM/0047
En ligne :	http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/6584/1/DERBAL%20Louiz [...]

Courses and exercises maths 1 analysis and algebra [document électronique] / Louiza Derbal . - [S.l.] : Sétif:UFA1, 2025 . - 1 vol (112 p.).
Langues : Anglais (eng)

Catégories :	Publications pédagogiques:Mathématiaue P/P
Mots-clés :	Analysis and algebra
Note de contenu :	Contents Introduction1 1 Sets,relationsandapplications2 1.1 Sets.......................................3 1.1.1 DeÂ…nitionofsets............................3 1.1.2 CardinalityofaÂ…niteset.......................3 1.1.3 Operationsonsets...........................3 1.1.4 Lawsforoperationsonsets......................7 1.1.5 Setofparts................................8 1.1.6 Cartesianproduct...........................8 1.2 Relations....................................10 1.2.1 Equivalencerelation..........................12 1.2.2 Orderrelation.............................14 1.3 Applications...................................15 1.3.1 DeÂ…nitionofanapplication......................15 1.3.2 Restrictingandextendinganapplication...............17 1.3.3 Directimageandinverseimage....................17 1.3.4 Injective,surjectiveandbijectiveapplication............19 1.4 Somemethodsofproof.............................20 2 StructureofrealnumbersÂ…eld R 22 2.1 Setofrationalnumbers Q. ...........................22 2.1.1 Integersnumbers............................22 2.1.2 Rationalnumbers............................22 2.2 Irrationalnumbers...............................23 2.3 Realnumbers..................................24 2.3.1 AxiomaticdeÂ…nition..........................24 2.3.2 Absolutevalue.............................26 2.3.3 Boundedsetsof R . ..........................28 2.3.4 Densegroupsin R . ..........................32 2.3.5 Intervalsin R . .............................33 3 Realfunctionsofarealvariable35 3.1 Introduction..................................35 3.1.1 Boundedfunctions,monotonicfunctions...............35 3.1.2 Odd,even,periodicfunction.....................36 3.1.3 Algebraicoperationsonfunctions...................37 3.1.4 Limitofafunction...........................38 3.1.5 Limittheorems.............................41 3.1.6 Operationsoflimits..........................41 3.2 Continuityofafunction............................43 3.2.1 GeneraldeÂ…nitions...........................43 3.2.2 Operationsoncontinuousfunctions..................46 3.2.3 Continuityofcompositionfunctions.................47 3.2.4 TheIntermediateValueTheorem...................47 3.2.5 Uniformcontinuity...........................48 3.3 Derivablefunction...............................51 3.3.1 DeÂ…nitionandproperties.......................51 3.3.2 One-sidedderivatives..........................52 3.3.3 Operationsonderivativefunctions..................53 3.3.4 Derivativeofusualfunctions.....................55 3.3.5 The nth derivative...........................56 3.3.6 HôpitalÂ’srule:.............................66 3.4 Elementaryfunctions..............................68 3.4.1 Trigonometricfunctions........................69 3.4.2 Exponentialfunction..........................75 3.4.3 Logarithmfunction...........................76 3.4.4 Logarithmfunctionofanybase....................77 3.4.5 Power(Exponential)function.....................78 3.4.6 Hyperbolicfunctionsandtheirinverses...............78 4 Internalcompositionlaws88 4.1 Group,Subgroups...............................90 4.2 RingStructure.................................94 4.3 StructureofaÂ…eld(body)...........................94 5 Vectorspaces96 5.1 Vectorspace...................................96 5.1.1 Vectorsubspace............................97 5.1.2 Intersectionandunionofvectorsubspaces..............98 5.1.3 Sumoftwovectorsubspaces.....................99 5.1.4 Directsumoftwovectorsubspaces..................99 5.1.5 Generating,free,andbasisfamilies..................100 5.1.6 Dimensionofvectorspaces......................104 5.2 Linearapplications...............................108 5.2.1 DeÂ…nitionsandexamples.......................108 5.2.2 Linearmapsanddimension......................109
Côte titre :	PM/0047
En ligne :	http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/6584/1/DERBAL%20Louiz [...]