MATHEMATICS FOR m m
PHYSICAL SCIENCE m m
AND ENGINEERING
m
Symbolic Computing Applications in Maple and Mathematica
m m m m m m
Frank E. Harris
m m
INSTRUCTOR’S M
ANUAL
m
, Mathematics for Physical Science and Engineering: Sym
m m m m m m
bolic Computing Applications in Maple and Mathematica
m m m m m m
Instructor’s Manual
m
Frankm E.m Harris
UniversitymofmUtah,mSaltmLakemmCity,mmU
Tmandm Universitym ofm Florida,m Gainesvill
e,m FL
,Academicm Pressm ism anm imprintm ofm Elsevier
225m Wymanm Street,m Waltham,m MAm 02451,m USA
Them Boulevard,m Langfordm Lane,m Kidlington,m Oxford,m OX5m 1GB,m UKmCop
yrightm ©m 2014m Elsevierm Inc.m Allm rightsm reserved
Nom partm ofm thism publicationm maym bem reproduced,m storedm inm am retrievalm systemm orm tran
smittedminmanymformmormbymanymmeansmelectronic,mmechanical,mphotocopying,mrecordingmorm
otherwisemwithoutm them priorm writtenm permissionm ofm them publisher.
Permissionsm maym bem soughtm directlym fromm Elsevier’sm Sciencem &m Technologym Rightsm Depar
tmentminmOxford,mUK:mphone
+ m(m44)m(0)m1865m843830; + mfaxm(m44)m(0)m1865m853333;memail:m
yourm requestm onlinem bym visitin
gm them Elseviermwebmsitematmhttp://elsevier.com/locate/permissions,mandmselectingmObtainin
gmpermissionmtomusemElsevierm material.
Notice
Nomresponsibilitymismassumedmbymthempublishermformanyminjurymand/ormdamagemtompersonsm
ormpropertymasmammattermofmproductsmliability,mnegligencemormotherwise,mormfrommanymusemo
rmopera-
mtionm ofm anym methods,m products,m instructionsm orm ideasm containedm inm them materialm herein.
BritishmLibrarymCataloguingm inmPublicationmData
Am cataloguem recordm form thism bookm ism availablem fromm them Britishm Library
Librarym ofm Congressm Cataloging-in-Publicationm Data
Am catalogm recordm form thism bookm ism availablem fromm them Librarym ofm Congress
ISBN:m 978-0-12-801000-6
Form informationm onm allm Academicm Pressm publicati
onsmvisitm ourm webm sitem atm store.elsevier.com
Printedm andm boundm inm USA
14m 15m 16m 17m 18mmmm 10m 9m 8m 7m 6m 5m 4m 3m 2m 1
, Contents
0 Introduction 1
1 Computers,mScience,mandmEngineering 3
1.1 Computing:m Historicalm Note ..............................................................................................3
1.2 Basicsm ofm Symbolicm Computing .......................................................................................3
1.3 Symbolicm Computationm Programs ..................................................................................8
1.4 Procedures................................................................................................................................. 10
1.5 Graphsm andm Tables .............................................................................................................. 12
1.6 Summary:m Symbolicm Computing .................................................................................. 15
2 InfinitemSeries 16
2.1 Definitionm ofm Series ............................................................................................................ 16
2.2 Testsm form Convergence...................................................................................................... 18
2.3 Alternatingm Series ................................................................................................................ 20
2.4 Operationsm onm Series......................................................................................................... 21
2.5 Seriesm ofm Functions............................................................................................................. 22
2.6 Binomialm Theorem ............................................................................................................... 26
2.7 Somem Importantm Series .................................................................................................... 29
2.8 Somem Applicationsm ofm Series ........................................................................................ 29
2.9 Bernoullim Numbers .............................................................................................................. 30
2.10 Asymptoticm Series ................................................................................................................ 32
2.11 Euler-Maclaurinm Formula ................................................................................................. 32
3 ComplexmNumbersmandmFunctions 35
3.1 Introduction ............................................................................................................................. 35
3.2 Functionsm inm them Complexm Domain ......................................................................... 36
3.3 Them Complexm Plane ................................................................................................... 38
3.4 Circularm andm Hyperbolicm Functions .......................................................................... 40
3.5 Multiple-Valuedm Functions .............................................................................................. 43
4 VectorsmandmMatrices 47
4.1 Basicsm ofm Vectorm Algebra ................................................................................................ 47
4.2 Dotm Product ............................................................................................................................. 50
4.3 Symbolicm Computing,m Vectors .............................................................................. 51
PHYSICAL SCIENCE m m
AND ENGINEERING
m
Symbolic Computing Applications in Maple and Mathematica
m m m m m m
Frank E. Harris
m m
INSTRUCTOR’S M
ANUAL
m
, Mathematics for Physical Science and Engineering: Sym
m m m m m m
bolic Computing Applications in Maple and Mathematica
m m m m m m
Instructor’s Manual
m
Frankm E.m Harris
UniversitymofmUtah,mSaltmLakemmCity,mmU
Tmandm Universitym ofm Florida,m Gainesvill
e,m FL
,Academicm Pressm ism anm imprintm ofm Elsevier
225m Wymanm Street,m Waltham,m MAm 02451,m USA
Them Boulevard,m Langfordm Lane,m Kidlington,m Oxford,m OX5m 1GB,m UKmCop
yrightm ©m 2014m Elsevierm Inc.m Allm rightsm reserved
Nom partm ofm thism publicationm maym bem reproduced,m storedm inm am retrievalm systemm orm tran
smittedminmanymformmormbymanymmeansmelectronic,mmechanical,mphotocopying,mrecordingmorm
otherwisemwithoutm them priorm writtenm permissionm ofm them publisher.
Permissionsm maym bem soughtm directlym fromm Elsevier’sm Sciencem &m Technologym Rightsm Depar
tmentminmOxford,mUK:mphone
+ m(m44)m(0)m1865m843830; + mfaxm(m44)m(0)m1865m853333;memail:m
yourm requestm onlinem bym visitin
gm them Elseviermwebmsitematmhttp://elsevier.com/locate/permissions,mandmselectingmObtainin
gmpermissionmtomusemElsevierm material.
Notice
Nomresponsibilitymismassumedmbymthempublishermformanyminjurymand/ormdamagemtompersonsm
ormpropertymasmammattermofmproductsmliability,mnegligencemormotherwise,mormfrommanymusemo
rmopera-
mtionm ofm anym methods,m products,m instructionsm orm ideasm containedm inm them materialm herein.
BritishmLibrarymCataloguingm inmPublicationmData
Am cataloguem recordm form thism bookm ism availablem fromm them Britishm Library
Librarym ofm Congressm Cataloging-in-Publicationm Data
Am catalogm recordm form thism bookm ism availablem fromm them Librarym ofm Congress
ISBN:m 978-0-12-801000-6
Form informationm onm allm Academicm Pressm publicati
onsmvisitm ourm webm sitem atm store.elsevier.com
Printedm andm boundm inm USA
14m 15m 16m 17m 18mmmm 10m 9m 8m 7m 6m 5m 4m 3m 2m 1
, Contents
0 Introduction 1
1 Computers,mScience,mandmEngineering 3
1.1 Computing:m Historicalm Note ..............................................................................................3
1.2 Basicsm ofm Symbolicm Computing .......................................................................................3
1.3 Symbolicm Computationm Programs ..................................................................................8
1.4 Procedures................................................................................................................................. 10
1.5 Graphsm andm Tables .............................................................................................................. 12
1.6 Summary:m Symbolicm Computing .................................................................................. 15
2 InfinitemSeries 16
2.1 Definitionm ofm Series ............................................................................................................ 16
2.2 Testsm form Convergence...................................................................................................... 18
2.3 Alternatingm Series ................................................................................................................ 20
2.4 Operationsm onm Series......................................................................................................... 21
2.5 Seriesm ofm Functions............................................................................................................. 22
2.6 Binomialm Theorem ............................................................................................................... 26
2.7 Somem Importantm Series .................................................................................................... 29
2.8 Somem Applicationsm ofm Series ........................................................................................ 29
2.9 Bernoullim Numbers .............................................................................................................. 30
2.10 Asymptoticm Series ................................................................................................................ 32
2.11 Euler-Maclaurinm Formula ................................................................................................. 32
3 ComplexmNumbersmandmFunctions 35
3.1 Introduction ............................................................................................................................. 35
3.2 Functionsm inm them Complexm Domain ......................................................................... 36
3.3 Them Complexm Plane ................................................................................................... 38
3.4 Circularm andm Hyperbolicm Functions .......................................................................... 40
3.5 Multiple-Valuedm Functions .............................................................................................. 43
4 VectorsmandmMatrices 47
4.1 Basicsm ofm Vectorm Algebra ................................................................................................ 47
4.2 Dotm Product ............................................................................................................................. 50
4.3 Symbolicm Computing,m Vectors .............................................................................. 51
