Maths in Chemistry: Numerical Methods for Physical and Analytical Chemistry PDF
Preview Maths in Chemistry: Numerical Methods for Physical and Analytical Chemistry
PrernaBansal MathsinChemistry Also of Interest MolecularSymmetryandGroupTheory. ApproachesinSpectroscopyandChemicalReactions R.C.Maurya,J.M.Mir, ISBN----,e-ISBN---- ElementalAnalysis. AnIntroductiontoModernSpectrometricTechniques GerhardSchlemmer,LieveBalcaen,JoséLuisTodolí,Michael W.Hinds, ISBN----,e-ISBN---- PhysicalChemistryofPolymers. AConceptualIntroduction SebastianSeiffert, ISBN----,e-ISBN---- AppliedElectrochemistry KrystynaJackowska,PawełKrysiński, ISBN----,e-ISBN---- OrganicChemistry. FundamentalsandConcepts JohnM.McIntosh, ISBN----,e-ISBN---- Prerna Bansal Maths in Chemistry Numerical Methods for Physical and Analytical Chemistry Author Dr.PrernaBansal UniversityofDelhi RajdhaniCollege MahatmaGandhiMarg 110015Delhi [email protected] ISBN978-3-11-069531-1 e-ISBN(PDF)978-3-11-069532-8 e-ISBN(EPUB)978-3-11-069548-9 LibraryofCongressControlNumber:2020938296 BibliographicinformationpublishedbytheDeutscheNationalbibliothek TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie; detailedbibliographicdataareavailableontheInternetathttp://dnb.dnb.de. ©2020WalterdeGruyterGmbH,Berlin/Boston Coverimage:berya113/iStock/GettyImagesPlus Typesetting:IntegraSoftwareServicesPvt.Ltd. Printingandbinding:CPIbooksGmbH,Leck www.degruyter.com Dedicated To MyParents Acknowledgement I owe this book to all those who encouraged me in some way or another to write thisbook.Thesourceofinspirationforwritingthisbookcamefrommystudents. IentirelydedicatethisbooktomybelovedParentswholovemeimmenselyand unconditionally and without whom I would have not been able to start writing a book in the first place. They have been a source of constant strength, support and love in difficult times. Iam highly indebted for their constant patience for bearing withmewhileIwaswritingthisbook. I would also like to express my heartfelt gratitude to my brother Mayank for putting up with me when I used to make odd asks. I also owe a special thanks to my two lovelies Divit and Ishaani for their beautiful smiles and laughters which used to meltmy stress in a blink. Thisacknowledgement would have been incom- plete without mentioning my beautiful sister Sonia for her excellent advice at all timeswhenwhenshewasbusywithherPh.Dwork. I express my gratitude to all my students who believed in me and kept asking metowriteabookwhichcanprovideallthementionedtopicsunderasinglewing. Iwouldalsoliketoexpressmysinceregratitudetoallmyteacherswhotaughtme andinspiredmetobetheone. I also express a sincere word of thanks to my Husband Anup Goel who kept boostingmymoraleduringthefinalstagesofthismanuscriptcompletionforwhen Imethimfirst.Ireallyowehimforhisconstantsupportandencouragementduring theentireprocessofitsproofreading. I also owe a word of thanks to my new family including my Father-in-law, Mother-in-law and my Brother-in-law for their support during the proof reading of thisbook. IexpressmysincerethankstothepublisherDeGruyter’sfortheircooperation and processingof this manuscript.I alsowant to expressa special word of thanks to Emma Svensson, Ute Skambraks and Dipti Dange for their constant help and support. Aboveall,IwouldliketosaythankstoThakurjiforprovidingmecourage,mo- tivation,strengthandaboveall,hisgraceforgivingmeenoughcourageforwriting thisbook. July2020 https://doi.org/10.1515/9783110695328-202 Contents Acknowledgement VII Chapter1 Unitsandmeasurements 1 1.1 Introduction 1 1.2 Basicarithmeticoperations 1 1.3 Hierarchyofoperations 2 1.4 Classificationofunitsystem 3 1.4.1 Metricsystemofunits 3 1.4.2 Classificationofmetricsystemofunits 4 1.5 Definitionofbaseunits 5 1.6 Interconversionofunits 8 1.7 Significantfigures 9 1.8 Rulesforperformingarithmeticoperations 10 1.8.1 Additionandsubtraction 10 1.8.2 Multiplicationanddivision 11 1.8.3 Mixedmathematicaloperations 12 1.9 Roundingoffsignificantfigures 13 1.10 Problemsforpractice 14 Chapter2 Uncertaintiesanderrors 17 2.1 Introduction 17 2.2 Absoluteandrelativeuncertainty 20 2.3 Propagationofuncertainty 21 2.4 Roundingoffuncertainties 28 2.5 Classificationoferrors 28 2.6 Problemsforpractice 29 Chapter3 Somemathematicalfunctions 31 3.1 Introduction 31 3.2 Classificationoffunctions 31 3.2.1 Linearfunction 31 3.2.2 Exponential 32 3.2.3 Logarithmicfunction 34 3.2.4 Polynomials 36 3.2.5 Powerfunction 37 3.2.6 Circle 37 3.2.7 Rationalnumber 38 X Contents 3.2.8 Partialfractions 39 3.2.9 Trigonometricfunctions 39 3.2.9.1 Inversetrigonometricfunctions 42 3.2.9.2 Hyperbolictrigonometricfunctions 42 3.2.10 Taylor’sseries 42 3.2.10.1 Maclaurinseries 43 3.2.11 Coordinatesystems 43 3.2.12 Numbersystem 45 3.3 Problemsforpractice 48 Chapter4 Descriptivestatistics 49 4.1 Introduction 50 4.2 Mean 50 4.2.1 Arithmeticmean 51 4.2.2 Weightedmean 51 4.2.3 Geometricmean 51 4.2.4 Harmonicmean 52 4.3 Median 52 4.4 Mode 53 4.5 Standarddeviation 53 4.6 Variance 54 4.7 Coefficientofvariation 54 4.8 Dataanalysis 57 4.8.1 Q-test 57 4.8.2 Confidencelimit 59 4.8.3 t-Test 59 4.8.4 F-test 62 4.9 Distributionoferrors 65 4.9.1 Gaussiandistribution 65 4.9.2 Binomialdistribution 66 4.9.3 Poisson’sdistribution 67 4.10 Statisticaltoolsusingspreadsheets 67 4.11 Problemsforpractice 70 Chapter5 Numericalcurvefitting 71 5.1 Introduction 71 5.2 Correlation 71 5.2.1 Pearsoncorrelationcoefficient 72 5.2.2 Spearman’srankcorrelationcoefficient 72 5.3 Regression 73
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