# Engr 213 Outline 2014 Judy-2

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OUTLINE DIFFERENTIAL EQUATION
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CONCORDIA UNIVERSITYFACULTY OF ENGINEERING AND COMPUTER SCIENCEAPPLIED ORDINARY DIFFERENTIAL EQUATIONS - ENGR 213/2 sect. ---, FALL 21! Instructor: Alexey KokotovOffice:LB 921-5Email: alexeykokotov!concor iacaLectures:#-\$% &9'(% 11-)5---1'-**Office +ours: ,ues ay% 1)-)51.-** /ourse coor inator: 0r eorios & 3atistasEmail: vatistas!encsconcor iaca C #\$se Desc\$%&t% '(  ,+is course intro uces first year enineerin stu ents to t+e t+eory an a44lication of or inary ifferential euations 0efinition an ,erminoloy% Initial-3alue6ro7lems% 8e4ara7le 0ifferential Euations% Linear Euations% Exact Euations% 8olutions 7y8u7stitution% Linear o els Ort+oonal ,raectories% /om4lex ;um7ers% \$orm of /om4lex ;um7ers: 6o<ers an =oots% 6reliminary ,+eory: Linear Euations% &omoeneous Linear Euations <it+ /onstant /oefficients% >n etermine /oefficients% 3ariation of 6arameters%/auc+y-Euler Euation% =e uction of Or er% Linear o els: Initial 3alue% =evie< of 6o<er 8eries% 6o<er 8eries 8olutions% 6reliminary ,+eory% &omoeneous Linear 8ystems% 8olution 7y0iaonalisation% ;on-&omoeneous Linear 8ystemsLectures: t+ree +ours 4er <eek ,utorial: t<o +ours 4er <eek ;O,E: 8tu ents <+o +ave receive cre it for EA, 212 an 2'2 may not take t+is course for cre it ?6rereuisite: A,& 2*)?c@e4 at+ematics 1*5 4reviously or concurrently A,& 2*5 ?c@e4 at+ematics 2*' Te)t* +(  A vance Enineerin at+ematics% 7y 0ennis  Cill an #arren 8 #ri+t% 5t+ E ition% 6u7lis+e 7y Dones an Bartlett% 2*1) G\$%' Sce0e( i term exams2*% 1* eac+ ? urin t+e tutorial Assinments1* ?+an e in an returne urin t+e tutorial\$inal exam(*If t+e ra e of t+e final exam is 7etter t+an t+e com7ine mark of t+e t<o mi -term examinations%t+en it <ill carry 9* of t+e final ra e If t+e stu ent misses a mi -term test for any reason%inclu in illness% t+en t+e final examination <ill count for 9* of t+e final ra e 8tu ents areres4onsi7le for fin in out t+e ate of t+e final exam ,+e Examination Office 4osts t+e time an  4lace of t+e final exam once t+e sc+e ule 7ecomes availa7le Any conflicts or 4ro7lems <it+ t+esc+e ulin of t+e final exam must 7e re4orte irectly to t+e Examination Office 8tu ents areex4ecte to 7e availa7le until t+e en of t+e final examination 4erio  /onflicts ue to travel 4lans <ill not 7e accommo ate  YOU MUST PASS TE FINAL EAM TO PASS TE COURSE PLEASE NOTE(  Electronic communication evices ?inclu in cell4+ones <ill not 7e allo<e in examination rooms Only F\$aculty A44rove /alculatorsG <ill 7e allo<e in examination rooms H8&A=6 EL-5'1 or /A8IO \$-'**8J  Sect% 's T &%cs 110efinition an ,erminoloy12Initial 3alue 6ro7lems228e4ara7le Euations2'Linear Euations2)Exact Euations258olutions 7y 8u7stitution2(Linear o els ?ro<t+ an 0ecay% ;e<tons La< of /oolin1(1/om4lex ;um7ers1(26o<ers an =oots'1,+eory of Linear Euations''&omoeneous Linear Euations <it+ /onstant /oefficients')>n etermine /oefficients'53ariation of 6arameters'./auc+y Euler Euations '(;onlinear Euations% =e uction of Or er ?Exam4les1% 2'Linear o els Initial 3alue 6ro7lems ?Exam4les 1% '% )% 5% .% (% '9Linear o els Boun ary 3alue 6ro7lems511 =evie< of 6o<er 8eries ?7ein511=evie< of 6o<er 8eries ?only ra ius of converence512 6o<er 8eries 8olutions1*1 ,+eory of Linear 8ystems1*2 &omoeneous Linear 8ystems1*' 8olution 7y 0iitaliMation1*) ;on-&omoeneous Linear 8ystems1*5 atrix Ex4onential Ass%'0e'ts Ass%'0e't 1 8ection 11: exercises: 1%2%'%5%.%%1*%11%1'%1)%21%2'%2) 8ection 12: exercises: (%9%11%12%1(%1 8ection 1' exercises: 1*% 1' Ass%'0e't 2 8ection 21: exercises: '% )% 2.% 2( 8ection 22: exercises: 2'% 25% 2. 8ection 2': exercises: 19% 22% 2' Ass%'0e't 3 8ection 2): exercises: 1% % 1.% 1(% 19% 22% 2' 8ection 25: exercices: 1% % 1.% 1(% 19% 22% 2' Ass%'0e't ! 8ection 2(: exercises 1'% 1( 8ection 2: exercises 15% 1.% 22 Ass%'0e't  8ection '1 exercises: 1%2'%'1%') 8ection '2 exercises: 1% 2%)%1( Ass%'0e't 4 8ection '' exercises: 1%2%)%29%'1%')%'%)1 Ass%'0e't 5 8ection ') exercises: 1% 2% 29%'18ection '5 exercises: 1%)%22 8ection '. exercises: 1%2%)%5 Ass%'0e't 6 8ection ' exercises: 1%.% 11% 12% 1'   Ass%'0e't 7 8ection 51 exercises: 1(%1% 2*%2( 8ection .1 exercices: 1% 2 Ass%'0e't 1 8ection 1*1: exercises: 5%1.%25 8ection 1*2: exercises: 2%1'%2'%'( Ass%'0e't 11 8ection 1*': exercises: 2%) 8ection 1*): exercise: 5In a ition t+ere <ill 7e one team assinment ?to 7e su7mitte at an a44ro4riate time ,+is <ill  7e an interal 4art of t+e reular assinments T#t \$ 1( E-0%8( siNsi i!encsconcor iaca T#t \$ 2(   E-0%8(  s+atna<imufle+!mailcom  Ass%'0e't M\$+e\$( ----% E-0%8(  ---- CEA9 G\$#te Att\$%*#tes %' ENGR 213( ,+is course em4+asiMes an evelo4s t+e follo<in /EAB ra uate attri7utes: 1 P\$ *8e0 '8:s%s( A' *%8%t: t #se &&\$ &\$%te +' ;8ee ' s+%88s t %e't%<:, < \$0#8te, '8:=e, ' s 8>e c 0&8e) e'%'ee\$%' &\$ *8e0s %' \$e\$ t \$ec s#*st't%te c 'c8#s% 's  8tu ents s+oul 7e a7le to take an enineerin 4ro7lem an t+en formulate from it t+e un erlyin mat+ematical% scientific or enineerin science 4ro7lem \$or exam4le% a stu ent learnin or inary ifferential euations% may +ave t+e calculus material riven an illustrate 7y enineerin 4ro7lems in circuits or mec+anics2 L%<e-8 ' 8e\$'%'( A' *%8%t: t %e't%<: ' t \$ess te%\$ ;' e#ct% '8 'ees %'  c'%' ; \$8, s#<<%c%e't8: t 0%'t%' te%\$ c 0&ete'ce ' c 't\$%*#te t te >'ce0e't < +' ;8ee. Every tec+nical 4rofessional must 7e a7le to learn in e4en ently Almost any course in t+e curriculum coul teac+% exercise an evaluate t+is soft skill \$or exam4le some instruction coul 7e iven on +o< one can 4ick out an summariMe t+e im4ortant  4oints in a c+a4ter in a text7ook ,+en stu ents coul 7e tol t+at t+ey are res4onsi7le for certain material on an exam% <it+out t+at material 7ein lecture on' I'%>%#8 ' te0; \$+( A' *%8%t: t ; \$+ e<<ect%>e8: s  0e0*e\$ ' 8ee\$ %' te0s, &\$e<e\$*8: %'  0#8t%-%sc%&8%'\$: sett%'. Item no 1 is met 4artially t+rou+ t+e a44lication 4ro7lems of A44lie O0Es to 7e foun in t+e text7ook an course notes for E;= 21' to 7e 4rovi e 7y t+e instructor Item no 2' <ill 7e one t+rou+ t<o ,eam Assinments ?over an a7ove to t+e reular ones St#e'ts \$e 8s \$es& 's%*8e < \$ t &%cs c >e\$e %' ss%'0e'ts tt >e ' t *e &\$ese'te %' e%te\$ te \$e#8\$ 8ect#\$es \$ #\$%' t#t \$%8s.I' te e>e't < e)t\$ \$%'\$: c%\$c#0st'ces *e: ' te U'%>e\$s%t:?s c 't\$ 8, tec 'te't '/ \$ e>8#t% ' sce0e %' t%s c #\$se %s s#*@ect t c'e.

Jul 23, 2017

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