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to Applied Data Analysis and Machine Learning","9. Recurrent Neural Networks","11. Data Analysis and Machine Learning:","1. Elements of Probability Theory and Statistical Data Analysis","2. Getting started, our first data and Machine Learning encounters","3. Linear Regression and more Advanced Regression Analysis","4. Logistic Regression","5. Neural networks, from the simple perceptron to deep learning","6. Support Vector Machines, overarching aims","7. Dimensionality Reduction","8. Convolutional Neural Networks","Introduction","Space, Time, Motion, Reference Frames and Reminder on vectors and other mathematical quantities","Basic Steps of Scientific Investigations","Work, Energy, Momentum and Conservation laws","Harmonic Oscillator","Two-body Problems","Non-inertial Frames, Translation and Rotating Coordinate Systems","Content with notebooks","Content with notebooks","Introduction","Space, Time, Motion, Reference Frames and Reminder on vectors and other mathematical quantities","Basic Steps of Scientific Investigations","Work, Energy, Momentum and Conservation laws","Harmonic Oscillator","Two-body Problems","Non-inertial Frames, Translation and Rotating Coordinate Systems","Content in Jupyter Book","PHY321, Classical Mechanics I, Michigan State University, Spring 2021","Code of Conduct","Contributing","LectureNotes","Content in Jupyter Book","Welcome to your Jupyter Book","Markdown Files","Content with notebooks","Markdown Files"],titleterms:{"break":28,"case":[3,8,12,21],"class":6,"final":[1,7,9,10,12,13,14,21,22,23,28],"function":[1,3,5,6,7,8,9],"import":[3,4,10,12,21],"new":[1,10],"transient":[15,24],"try":[1,10],Adding:[5,8,14,23,34,36],And:[4,13,22],Going:[13,22],Ising:5,NNs:10,ODE:1,ODEs:1,OLS:5,One:[13,22],The:[1,2,3,5,6,7,8,9,10,13,14,15,17,22,23,24,26],Then:[13,22],Useful:[4,12,21],Using:[1,7,34,36],With:[1,2,10],about:[2,4],abov:[11,20],acceler:[12,13,17,21,22,26],act:[13,22],activ:7,actual:3,add:10,adjust:7,advanc:5,again:10,aim:[5,8],air:[12,13,21,22],aka:5,algebra:[5,12,17,21,26],algorithm:[5,7,9,14,23],all:8,altern:[15,24],analysi:[0,2,3,5,9],analyt:[1,12,21],angular:[14,23],anoth:5,appli:0,approach:[0,2,5,8,13,22],approxim:7,april:28,architectur:7,arrai:[4,12,21],artifici:7,asap:28,aspect:0,assumpt:5,attempt:[8,12,21],attribut:29,autocorrel:3,autograd:1,automat:1,averag:[12,21],back:[1,7,8,9],backend:7,background:5,ballist:[13,22],basebal:[12,21],basic:[4,5,6,9,12,13,14,21,22,23],bay:2,bayesian:2,befor:9,best:2,beta:[5,15,24],better:[3,5,8],bia:5,bias:[0,7],binari:7,bind:[4,5],binomi:3,block:[3,13,15,18,19,22,24,35],bodi:[16,25],boldsymbol:5,book:[27,31,32,33],bootstrap:[3,5],boston:5,breast:9,brief:[4,5,10],bring:7,bug:30,build:[7,10,14,23,31],buld:[14,23],calcul:3,can:5,cancer:9,center:[9,16,25],central:3,centrifug:[16,17,25,26],chain:7,chi:5,choic:[0,7],choos:7,cifar01:10,citat:[34,36],classic:[9,13,15,22,24,28],classif:[7,9],classifi:8,cnn:10,code:[1,2,3,5,7,8,9,12,14,15,16,18,19,21,23,24,25,29,30,34,35,36],coin:2,collect:[7,10],compact:[12,21],compar:1,compil:10,compon:9,comput:[3,9,12,21],computation:5,concept:[3,11,20],conduct:[29,30],confid:2,conserv:[14,23],constant:[12,21],content:[18,19,27,32,35],continu:[3,9],contn:[13,22],contribut:30,contributor:31,convex:8,convolut:[7,10],coordin:[17,26],corioli:[17,26],correl:[3,5,9,10],cost:[1,7],cote:[14,23],count:2,coupl:[14,23],covari:[2,3,5,9],credit:31,critic:[15,24],cromer:[12,14,21,23],cross:[5,16,25],cumul:3,cython:4,damp:[15,24],dampl:[15,24],data:[0,1,2,3,4,5,7,9,10],dataset:[7,10],date:28,decai:1,decompos:5,decomposit:[5,9],deep:[1,7],defin:[1,7,13,22],definit:[3,7],degre:[5,9],demonstr:3,dens:[5,10],deriv:[7,14,15,16,23,24,25],descent:[1,7],design:[5,9],detail:[1,5,8,10,13,22],develop:7,deviat:3,diagon:9,dice:3,differ:[2,8],differenti:[1,12,13,15,21,22,24],diffus:1,dimens:[12,13,16,21,22,25],dimension:[1,5,8,9],direct:[34,36],discret:[3,12,14,21,23],disguis:3,distribut:3,document:30,doing:7,domain:3,don:10,down:7,driven:[15,24],earth:[14,23],economi:5,effect:[16,17,25,26],element:[2,3,12,21],ellipt:[16,25],encount:[4,12,21],energi:[4,5,14,23],enforc:29,equal:[14,23],equat:[1,5,7,8,12,13,14,15,21,22,23,24],error:[5,14,23],essenti:[],estim:2,etc:[4,10],ethic:0,euler:[1,12,14,17,21,23,26],evalu:[7,10],event:3,exampl:[1,2,3,4,5,7,8,9,10,11,12,14,16,20,21,23,25],execut:[34,36],expect:[3,5],expens:5,experi:3,exponenti:[1,3],express:[5,14,23],extens:[12,21],extrapol:[1,10],extrem:[],factor:[15,24],fair:2,fall:[12,13,17,21,22,26],famili:[5,7],famou:[3,4,12,21],fantast:5,featur:[4,5,8,9,12,21,30],februari:28,feed:7,feedback:30,few:2,field:[13,22],file:[10,34,36],find:[5,12,21],first:[4,7,8,12,13,21,22],fit:[4,5],fix:[5,30],flux:2,fold:5,forc:[13,15,16,17,22,24,25,26],format:[1,10],forward:[1,7],foucault:[17,26],fouri:[15,24],fourier:[15,24],frame:[12,17,21,26],frank:[5,9],freedom:[5,9],frequentist:[0,2],friend:2,from:[2,5,7,10,17,26],full:[1,7,10],funtion:7,galilean:[17,26],gaussian:3,gener:[3,5],geometr:9,get:[4,8,30],going:5,good:0,grade:28,gradient:[1,7],gravit:[16,25],growth:1,handl:[0,4,12,21],happen:5,harmon:[15,16,24,25],height:[12,21],hidden:1,histori:2,host:31,hous:5,how:[3,5,8],hyperbol:7,hyperparamet:7,hyperplan:8,idea:9,identifi:[13,22],iii:1,illustr:[2,11,20],imag:10,implement:[1,3,7,12,21,30],improv:7,includ:[6,12,21],increment:9,inerti:[17,26],infer:2,input:1,instal:[4,12,21],integr:[12,14,21,23],interpret:[5,9],interv:2,introduc:[5,9],introduct:[0,4,6,11,20],investig:[13,22],its:3,jackknif:[3,5],jacobian:1,januari:28,julia:4,jupyt:[27,32,33],kera:[7,10],kernel:[8,9],known:[11,20],kutta:[15,24],label:[12,21],lagrangian:8,lambda:5,languag:0,lasso:5,last:8,law:[13,14,22,23],layer:[1,7,10],learn:[0,1,2,4,5,7,9,28],least:5,lectur:28,lecturenot:31,librari:[4,12,21],likelihood:6,limit:[3,7],linear:[4,5,8,17,26],link:[5,9,28],list:7,lle:9,logist:[6,7,9],machin:[0,2,4,8,9],made:5,magnet:[13,22],mai:28,main:3,mani:[7,11,20],march:28,markdown:[18,19,34,35,36],mass:[4,16,25],materi:28,math:5,mathemat:[5,7,8,12,14,21,23],matric:[4,12,21],matrix:[3,4,5,7,9,12,21],matter:5,maximum:6,mean:[3,9],measur:2,mechan:28,medic:10,meet:[3,4,12,21],mercer:8,mersenn:3,method:[3,5,12,14,15,21,23,24],michigan:28,minim:[1,8],mlp:7,mnist:10,model:[0,2,4,5,7,10,12,13,21,22],moment:3,momentum:[14,23],moon:8,more:[1,4,5,6,8,9,10,12,13,15,21,22,24],motion:[12,13,16,21,22,25],multi:7,multidisciplinari:[],multilay:7,multipl:[2,7],multipli:8,myst:[18,19,34,35,36],name:3,need:[4,1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