MATHEMATICS FORP c c
HYSICAL SCIENCE A c c
ND ENGINEERING
c
Symbolic Computing Applications in Maple and Mathematica
c c c c c c
Frank E. Harris
c c
INSTRUCTOR’SM
ANUAL
c
, Mathematics for Physical Science and Engineering: Symbo
c c c c c c
lic Computing Applications in Maple and Mathematica
c c c c c c
Instructor’s Manual c
Frankc E.c Harris
UniversitycofcUtah,cSaltcLakeccCity,ccUTcan
dc Universityc ofc Florida,c Gainesville,c FL
,Academicc Pressc isc anc imprintc ofc Elsevier
225c Wymanc Street,c Waltham,c MAc 02451,c USA
Thec Boulevard,c Langfordc Lane,c Kidlington,c Oxford,c OX5c 1GB,c UKcCopyrig
htc ©c 2014c Elsevierc Inc.c Allc rightsc reserved
Noc partc ofc thisc publicationc mayc bec reproduced,c storedc inc ac retrievalc systemc orc transmitte
dcincanycformcorcbycanycmeanscelectronic,cmechanical,cphotocopying,crecordingcorcotherwisecwi
thoutc thec priorc writtenc permissionc ofc thec publisher.
Permissionsc mayc bec soughtc directlyc fromc Elsevier’sc Sciencec &c Technologyc Rightsc Departmen
tcincOxford,cUK:cphonec(c44)
+ c(0)c1865c843830;cfaxc(c44) + c(0)c1865c853333;cemail:cpermissionsc@
elsevier.com.cAlternativelycyouccancsubmitc yourc requestc onlinec byc visitingc thec Elseviercwebc
sitecatchttp://elsevier.com/locate/permissions,candcselectingcObtainingcpermissionctocusecElse
vierc material.
Notice
Nocresponsibilityciscassumedcbycthecpublishercforcanycinjurycand/orcdamagectocpersonscorcpro
pertycascacmattercofcproductscliability,cnegligencecorcotherwise,corcfromcanycusecorcopera-
ctionc ofc anyc methods,c products,c instructionsc orc ideasc containedc inc thec materialc herein.
BritishcLibrarycCataloguingcincPublicationcData
Ac cataloguec recordc forc thisc bookc isc availablec fromc thec Britishc Library
LibrarycofcCongresscCataloging-in-PublicationcData
Ac catalogc recordc forc thisc bookc isc availablec fromc thec Libraryc ofc Congress
ISBN:c978-0-12-801000-6
Forc informationc onc allc Academicc Pressc publication
scvisitc ourc webc sitec atc store.elsevier.com
Printedc andc boundc inc USA
14c 15c 16c 17c 18cccc 10c 9c 8c 7c 6c 5c 4c 3c 2c 1
, Contents
0 Introduction 1
1 Computers,cScience,candcEngineering 3
1.1 Computing:c Historicalc Note .................................................................................................3
1.2 Basicsc ofc Symbolicc Computing ..........................................................................................3
1.3 Symbolicc Computationc Programs ....................................................................................8
1.4 Procedures................................................................................................................................. 10
1.5 Graphsc andc Tables ................................................................................................................ 12
1.6 Summary:c Symbolicc Computing..................................................................................... 15
2 InfinitecSeries 16
2.1 Definitionc ofc Series .............................................................................................................. 16
2.2 Testsc forc Convergence ........................................................................................................ 18
2.3 Alternatingc Series.................................................................................................................. 20
2.4 Operationsc onc Series ........................................................................................................... 21
2.5 Seriesc ofc Functions ............................................................................................................... 22
2.6 Binomialc Theorem ................................................................................................................ 26
2.7 Somec Importantc Series ...................................................................................................... 29
2.8 Somec Applicationsc ofc Series............................................................................................ 29
2.9 Bernoullic Numbers ............................................................................................................... 30
2.10 Asymptoticc Series ................................................................................................................. 32
2.11 Euler-Maclaurinc Formula .................................................................................................. 32
3 ComplexcNumberscandcFunctions 35
3.1 Introduction ............................................................................................................................. 35
3.2 Functionsc inc thec Complexc Domain .............................................................................. 36
3.3 Thec Complexc Plane ..................................................................................................... 38
3.4 Circularc andc Hyperbolicc Functions ............................................................................. 40
3.5 Multiple-Valuedc Functions ............................................................................................... 43
4 VectorscandcMatrices 47
4.1 Basicsc ofc Vectorc Algebra ................................................................................................... 47
4.2 Dotc Product............................................................................................................................... 50
4.3 Symbolicc Computing,c Vectors ................................................................................ 51
HYSICAL SCIENCE A c c
ND ENGINEERING
c
Symbolic Computing Applications in Maple and Mathematica
c c c c c c
Frank E. Harris
c c
INSTRUCTOR’SM
ANUAL
c
, Mathematics for Physical Science and Engineering: Symbo
c c c c c c
lic Computing Applications in Maple and Mathematica
c c c c c c
Instructor’s Manual c
Frankc E.c Harris
UniversitycofcUtah,cSaltcLakeccCity,ccUTcan
dc Universityc ofc Florida,c Gainesville,c FL
,Academicc Pressc isc anc imprintc ofc Elsevier
225c Wymanc Street,c Waltham,c MAc 02451,c USA
Thec Boulevard,c Langfordc Lane,c Kidlington,c Oxford,c OX5c 1GB,c UKcCopyrig
htc ©c 2014c Elsevierc Inc.c Allc rightsc reserved
Noc partc ofc thisc publicationc mayc bec reproduced,c storedc inc ac retrievalc systemc orc transmitte
dcincanycformcorcbycanycmeanscelectronic,cmechanical,cphotocopying,crecordingcorcotherwisecwi
thoutc thec priorc writtenc permissionc ofc thec publisher.
Permissionsc mayc bec soughtc directlyc fromc Elsevier’sc Sciencec &c Technologyc Rightsc Departmen
tcincOxford,cUK:cphonec(c44)
+ c(0)c1865c843830;cfaxc(c44) + c(0)c1865c853333;cemail:cpermissionsc@
elsevier.com.cAlternativelycyouccancsubmitc yourc requestc onlinec byc visitingc thec Elseviercwebc
sitecatchttp://elsevier.com/locate/permissions,candcselectingcObtainingcpermissionctocusecElse
vierc material.
Notice
Nocresponsibilityciscassumedcbycthecpublishercforcanycinjurycand/orcdamagectocpersonscorcpro
pertycascacmattercofcproductscliability,cnegligencecorcotherwise,corcfromcanycusecorcopera-
ctionc ofc anyc methods,c products,c instructionsc orc ideasc containedc inc thec materialc herein.
BritishcLibrarycCataloguingcincPublicationcData
Ac cataloguec recordc forc thisc bookc isc availablec fromc thec Britishc Library
LibrarycofcCongresscCataloging-in-PublicationcData
Ac catalogc recordc forc thisc bookc isc availablec fromc thec Libraryc ofc Congress
ISBN:c978-0-12-801000-6
Forc informationc onc allc Academicc Pressc publication
scvisitc ourc webc sitec atc store.elsevier.com
Printedc andc boundc inc USA
14c 15c 16c 17c 18cccc 10c 9c 8c 7c 6c 5c 4c 3c 2c 1
, Contents
0 Introduction 1
1 Computers,cScience,candcEngineering 3
1.1 Computing:c Historicalc Note .................................................................................................3
1.2 Basicsc ofc Symbolicc Computing ..........................................................................................3
1.3 Symbolicc Computationc Programs ....................................................................................8
1.4 Procedures................................................................................................................................. 10
1.5 Graphsc andc Tables ................................................................................................................ 12
1.6 Summary:c Symbolicc Computing..................................................................................... 15
2 InfinitecSeries 16
2.1 Definitionc ofc Series .............................................................................................................. 16
2.2 Testsc forc Convergence ........................................................................................................ 18
2.3 Alternatingc Series.................................................................................................................. 20
2.4 Operationsc onc Series ........................................................................................................... 21
2.5 Seriesc ofc Functions ............................................................................................................... 22
2.6 Binomialc Theorem ................................................................................................................ 26
2.7 Somec Importantc Series ...................................................................................................... 29
2.8 Somec Applicationsc ofc Series............................................................................................ 29
2.9 Bernoullic Numbers ............................................................................................................... 30
2.10 Asymptoticc Series ................................................................................................................. 32
2.11 Euler-Maclaurinc Formula .................................................................................................. 32
3 ComplexcNumberscandcFunctions 35
3.1 Introduction ............................................................................................................................. 35
3.2 Functionsc inc thec Complexc Domain .............................................................................. 36
3.3 Thec Complexc Plane ..................................................................................................... 38
3.4 Circularc andc Hyperbolicc Functions ............................................................................. 40
3.5 Multiple-Valuedc Functions ............................................................................................... 43
4 VectorscandcMatrices 47
4.1 Basicsc ofc Vectorc Algebra ................................................................................................... 47
4.2 Dotc Product............................................................................................................................... 50
4.3 Symbolicc Computing,c Vectors ................................................................................ 51
