Numerical Methods with Python: for the Sciences

326 Pages·2023·17.008 MB·English

by  William Miles

WilliamMiles
NumericalMethodswithPython
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William Miles
Numerical
Methods with
Python
�
for the Sciences
MathematicsSubjectClassification2010
Primary:34-04,35-04;Secondary:92C45,92D25,34C28,37D45
Author
WilliamMiles,PhD
StetsonUniversity
DepartmentofMathematicsandComputerScience
421N.WoodlandBlvd.
Deland32723
FLUSA
[email protected]
ISBN978-3-11-077645-4
e-ISBN(PDF)978-3-11-077664-5
e-ISBN(EPUB)978-3-11-077693-5
LibraryofCongressControlNumber:2022950763
BibliographicinformationpublishedbytheDeutscheNationalbibliothek
TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie;
detailedbibliographicdataareavailableontheInternetathttp://dnb.dnb.de.
©2023WalterdeGruyterGmbH,Berlin/Boston
Coverimage:E.K.Miles
Typesetting:VTeXUAB,Lithuania
Printingandbinding:CPIbooksGmbH,Leck
www.degruyter.com
�
ThisbookisdedicatedtoAndiandEmmy.Tohavetheminmylifeisablessingbeyond
measure.

Acknowledgment
IthankWilliamWoodandSammiSmithfortakingthetimetoreadandeditlargesec-
tionsofthetext.Ialsothankmystudents,HalleBlock,EmilyMehigan,andCaseyRamey,
foralertingmeoferrorsastheytookthecourse.
https://doi.org/10.1515/9783110776645-201

Contents
Acknowledgment�VII
1 Introduction�1
2 ThebasicoperationsinPython�3
2.1 ObtainingPython�3
2.2 Addition,subtraction,multiplication,anddivision�3
2.3 Powers�8
2.4 Displayingoutput�8
2.5 Exercises�10
3 Functions�11
3.1 Exponentials,logs,andtrigfunctions�11
3.2 Variables�13
3.3 Definingandusingmathematicalfunctions�17
3.4 Gettinginputfromthekeyboard�19
3.5 Graphingfunctions�20
3.6 Exercises�38
4 Matrices,vectors,andlinearsystems�41
4.1 Matriceswithnumpy�41
4.1.1 Additionandsubtraction:A±B�44
4.1.2 Component-wisemultiplication:A∗B�46
4.1.3 Component-wisedivision:A/B�47
4.1.4 Scalarmultiplication:cA�48
4.1.5 Standardmatrixmultiplication�49
4.2 Matrixinversion�51
4.2.1 Theidentitymatrix�52
4.2.2 Theinverseofamatrix�53
4.3 Linearsystems�57
4.4 Exercises�68
5 Iteration�71
5.1 Findingroots:thebisectionmethod�71
5.2 Euler’smethodfordifferentialequations�80
5.2.1 Systemsofdifferentialequationsandhigher-orderdifferential
equations�91
5.2.2 Interpolation—usingtheapproximations�99
5.3 Exercises�101
X � Contents
6 Statistics�103
6.1 Filehandling�103
6.2 Descriptivestatistics�118
6.3 Probability�123
6.3.1 Numericalintegration�125
6.4 Confidenceintervalforthemeanofapopulation�132
6.5 Hypothesistesting�140
6.6 Comparinggroups�147
6.6.1 Comparingmeansoftwogroups�147
6.6.2 Comparingmeansofmorethantwogroups�152
6.7 Exercises�157
7 Regression�161
7.1 Linearregression�161
7.1.1 Correlation�170
7.1.2 Multiplelinearregression�171
7.2 Logisticregression�178
7.2.1 Digitrecognitionmodel�186
7.3 Neuralnetworks�193
7.4 Exercises�206
A Pythoncode�209
A.1 Chapter2code�209
A.2 Chapter3code�209
A.3 Chapter4code�216
A.4 Chapter5code�221
A.5 Chapter6code�228
A.6 Chapter7code�240
B Solutions�249
Index�313
IndexofPythonCommands�315