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7/23/2019 Aa Cmpn III Am3(Div1)
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Lesson Plan Applied Mathematics by Prof.Nasir Ansari
1 Scheme (As specified by the University) and Distribution of Work Hours
Theory IA Tests Practical Tutorial Term Work Total
Hours/Week 4 -- 3 -- 7
Marks 80 20 -- 25 00
2 P! and !utcomes
2"1 Pro#ram$ ducationa% !b&ectives (P!'s) of Under#raduate Pro#ram in (Department)
!4 To "re"are stu#e$ts %or success%ul careers that meets the &lo'al I$#ustrial a$# !or"oratere(uireme$ts)
*
!4 To provide students with a sound foundation in Mathematics andprepare them for graduate studies. --
!4 To provide students with mathematics fundamental necessary toformulate, solve and analyze engg. Problems. *
!4 To provide opportunity for students to work as part of teams on
multi disciplinary projects)
*
!4 To i$culcate "ro%essio$al ethics a$# co#es o% "ro%essio$al "ractice) --
!4 To im"art "ro%icie$cy i$ usi$& har#+are a$# so%t+are tools i$ or#er to #e#uce results, a$alye,#esi&$ a$# #e.elo" e$&i$eeri$& solutio$s)
*
2"2 Pro#ram !utcomes
!# ,
!%
ra#uates are e"ecte# to #emo$strate k$o+le#&e o% A""lie# Mathematics, I)T) 1$&i$eeri$&)
*
!# ,
!%
ra#uates are e"ecte# to ha.e the a'ility to i#e$ti%y, %ormulate a$# sol.e I)T) e$&i$eeri$&*
!# ,
!%
Students will demonstrate basic knowledge of aplace Transform.!ourier series, "essel !unctions, #ector $lgebra and %omple&#ariable.
*
7/23/2019 Aa Cmpn III Am3(Div1)
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!# ,
!%
Students will demonstrate an ability to identify formulate and solveelectronics and telecommunication 'ngg. problem using $ppliedMathematics
*
!# ,
!%
Students will show the understanding of impact of 'ngg.Mathematics on Telecom 'ngg.
Students who can participate and succeed in competitive e&amslike ($T', ()'.
*
!# ,
!%
ra#uates are e"ecte# to com"ly +ith co$#uct a$# co#e o% "ro%essio$al ethics)--
!# ,
!%
ra#uates are a'le to #emo$strate e%%ecti.e .er'al a$# +ritte$ commu$icatio$s skills)--
!# ,
!%
ra#uates are e"ecte# to ha.e the ratio$ale to relate the im"act o% e$&i$eeri$& solutio$s o$society, cou$try a$# huma$ity) *
Sy%%abus ei#hta#e* +arks and time re,uired
Unit -o" Detai%s.eachin# Hours
+arks Wei#ht/y 0
Laplace Transform (LT) of StandardFunctions: *e+nition.unilateral and bilateral aplace Transform, Tof sin(at), cos(at),eat ,t n , sinh(at), cosh(at), erf(t), eavi-sideunit step, dirac-deltafunction, T of periodic functionProperties of Laplace Transform:inearity, +rst shifting
theorem, second shifting theorem,multiplication byt n , division by t , aplace Transform ofderivatives and integrals, change ofscale, convolution theorem, initial and +nalvalue theorem,Parsavels identityInverse Laplace Transform: Partial fraction
24
7/23/2019 Aa Cmpn III Am3(Div1)
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method, long divisionmethod, residue methodApplications of Laplace Transform:Solution of ordinarydi/erential e0uations
2Introduction: *e+nition, *irichletsconditions, 'ulers formulaeFourier Series of Functions: '&ponential,trigonometricfunctions, even and odd functions, half rangesine and cosineseries%omple& form of !ourier series, orthogonaland orthonormal setof functions, !ourier integral representation
24
3 Scalar and Vector Product1 Scalar andvector product of three
and four vectors and their propertiesVector Dierentiation: (radient of scalarpoint function,divergence and curl of vector point functionProperties: Solenoidal and irrotationalvector +elds, conservativevector +eldVector Integral: ine integral, (reenstheorem in a plane,(auss divergence theorem, Stokes theorem
8
4 omple! Varia"le $nalytic !unction1
2ecessary and su3cient conditions, %auchy)eiman e0uation in polar formarmonic function, orthogonal trajectories#apping: %onformal mapping, bilineartransformations, crossratio, +&ed points, bilinear transformation ofstraight lines and circles 'ase# o$ these lo&ics)
24
5 4-transform of standard functions such as 45an6,45np6.Properties of 4-transform 1inearity, %hange of
scale, Shifting property,
Multiplication of 7, 8nitial and +nal value,%onvolution theorem 5all without proof6
08 0
.ota% 2 1 0
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3 Prere,uisite Sub&ect$s
o) ra$ch emester ame o% the u'6ect
i) !MP 2th st# imit, eri.ati.e, I$te&ratio$ Tri&o$ometric
ii) !MP Partial #eri.ati.e e"a$sio$ com"le $um'er
iii) !MP 2ou'le tri"le i$te&ratio$ eta 9 amma %u$ctio$ solutio$ o%#i%%ere$tial e(uatio$
" a 4e%evance to future sub&ects
o) ra$ch emester ame o% the u'6ect
!MP I: Maths4
2 !MP III T
3 !MP I: !om"uter &ra"hics
4 !MP I: T!
" b 4e%evance to %ife
o) ;eal i%e Ma""i$&
I$#ustrial !o$trollers a$# Automatio$
2 <%%ice Automatio$, !om"uters, Peri"herals, I/< e.ices
5 6ap Ana%ysis and +iti#ation
r) o A etailsa) =uit M)!)=)o$ a"lace tra$s%orm') uest ecture Week 7> ?A""licatio$ o% mathematics i$ e$&i$eeri$& su'6ects
8 Past 4esu%ts
9ear Sub&ect* +athematicsec -200ec -20ec -202ec-203
: .opics hich brin# the resu%t don
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Sr" -o .opics
) :ector al&e'ra 9.ector calculus2) a"lace tra$s%orm
7 ;ourse Administration
@)a ;e(uire# A.aila'le
o) o% ectures40
40 as "rescri'e# 'y the $i.ersity B 0 to co.erthe A / !lass Test / =ui acti.ities
400 1tra ectures +oul# 'e
sche#ule# to com"lete aca#emics
7"b"i /ooks Used and 4ecommended to Students
.e<t and 4eference /ooksRecommended Books:
9. igher 'ngineering Mathematics by (rewal ". S. :; th edition, 7hanna Publication<==>.<. ?peration )esearch by ira @ (upta,S %hand.:. $ Te&t "ook of $pplied Mathematics #ol. 8 @ 88 by P.2.Aartilar @
B.2.Aartikar, Pune, #idyarthi (riha Prakashan., Pune.C. Probability and Statistics for 'ngineering, *r. B )avichandran, Ailey-8ndia.>. Mathematical Statistics by . % Sa&ena, S %hand @ %o.Reference Books:
9. $dvanced 'ngg. Mathematics by %. )ay Aylie @ ouis "arrett.TM 8nternational'dition.<. Mathematical Methods of Science and 'ngineering by 7anti ". *atta, %engageearning.:. $dvanced 'ngineering Mathematics by 7reyszig '. Dth edition, Bohn Ailey.C. . ?peration )esearch by ira @ (upta,S %hand.>. 'ngineering optimization 5Theory and Practice6 by Singiresu S.)ao, 2ew $ge8nternational publication.E. Probability by Seymour ipschutz, Mc(raw-ill publication.
7"b"ii4e%evant Websites(4eputed Universities and !thers) for -otes$Animation$=ideos 4ecommended
to Students
Web Site and >nternet ;ontents 4eferences
1) +++)i$tel)com
7/23/2019 Aa Cmpn III Am3(Div1)
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2) htt">// $"tel )iitm)ac)i$
3) htt">//+++)$"semico$#uctors)com
4) htt">//+++)atmel)com
5) htt">// oc+ )mit )e#u
6) +++)ee)iit')ac)i$
7) +++)kiel)com8) htt">//+++)youtu'e)com/+atchC.Dli;Pt.67'E
9) htt">//+++)youtu'e)com/+atchC.D"4;cMEIr5o
10) htt">//+++)youtu'e)com/+atchC.DI78iyF=rP4
7"b"iii +a#a?ines$@ourna%s Used and 4ecommended to Students
Ma&ai$es Gour$als
Mathematic to#ay I$#ia$ society %or "ure a$# a""lie# mathematics
Mathematical scie$ce
7"c Study +ateria%
otes = 1= i&ital !o$te$ts
es es es e$eratio$ i$ Pro&ress
7"d"ii Week%y .est
$ee%l& ' Internal Assessment Test
o of tests First testli%el& in *+ee%
S&lla"us Details a"outpattern
,emedialpolic&
First IA Test $s per 8nstitute
Schedule
!ourier series @
aplacetransform
!ill in the "lanks 5M%F6
9= Marks?ne Short Fuestion
> Marks.?ne Short Fuestion
> Marks
2o )e-test.
8$ ead of passing Gtest 8n the
2e&tSemester
if8$ head 7T
applies.
Second IA Test $s per 8nstituteSchedule
%omple&variable
#ector calculus
!ill in the "lanks 5M%F69= Marks
?ne Short Fuestion> Marks.
7/23/2019 Aa Cmpn III Am3(Div1)
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?ne Short Fuestion> Marks
7"d"iii .utoria%s Pop Bui?
Tutorial
o
Title -utcomee!pected
Alliedstud&
$ee% o
Individual ' .roupactivit&
,eference:
"oo%'+e"site
'Paper9 Fourier
seriesStudentsstudy the Topics andwrite the$nswers.(et practiceto solveuniversity0uestions.
%hapters 9
C andwrittensolutione&pected.
"ook 9,<,:,C,> ofthereferencelist.
Aebsite 9to E of the)eferencelist
< Fourierseries
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> andwrittensolution
e&pected.
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: Laplacetransform
Studentsstudy the Topics andwrite the
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7/23/2019 Aa Cmpn III Am3(Div1)
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C InverseLaplacetransforms.
Studentsstudy the Topics andwrite the$nswers.
(et practiceto solveuniversity0uestions.
%hapters <
H andwrittensolutione&pected.
"ook 9,<,:,C,> ofthereferencelist.
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> omple!varia"le
Studentsstudy the Topics andwrite the$nswers.(et practice
to solveuniversity0uestions.
%hapters :
; andwrittensolutione&pected.
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E onformal mapping
Studentsstudy the Topics andwrite the$nswers.(et practiceto solve
university0uestions.
%hapters :
D andwrittensolutione&pected.
"ook 9,<,:,C,> ofthereferencelist.
Aebsite 9
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H Vectoralge"ra
Studentsstudy the Topics andwrite the$nswers.(et practiceto solveuniversity
0uestions.
%hapters C
9= andwrittensolutione&pected.
"ook 9,<,:,C,> ofthereferencelist.
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; Vectorcalculus
Studentsstudy the Topics andwrite the$nswers.(et practice
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"ook 9,<,:,C,> ofthereferencelist.
7/23/2019 Aa Cmpn III Am3(Div1)
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to solveuniversity0uestions.
Aebsite 9to E of the)eferencelist
D /0transform
Studentsstudy the Topics andwrite the$nswers.(et practiceto solveuniversity0uestions.
%hapters >
9< andwrittensolutione&pected.
"ook 9,<,:,C,> ofthereferencelist.
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9= Inverse 10
transform
Students
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%hapter
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9: and
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Tutorial ' Assignment polic&
o ofTutorials23
Time ' da&sgiven forcompletion
Assessmentpolic&
4and+ritten '
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.rading '#ar%ingpolic&
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and written 9=
Term $or% ompositionAttendance025 #ar%s
6e7avior in classroom082 #ar%sTutorial082 mar%sTotal095 #ar%s
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1 Cesson P%an
ompre7ensive Lesson Plan
$ee
%
Lecture
o
Date Topic planned ' IV '.uest
lecture ' Video ' an&ot7er activit&
P- -utcome
me
9 9 to C 8;'2<'928;
Laplace transform *e+nition,, aplace transform ofstandardfunctions- Sinat, %osat I!irst Shifting theorem%hange of scale property
!4
!# , !% lack '
8='2<'928;
< > to ; <9J=HJ<=9C
Second Shifting theorem%onvolution theorem5without proof6 8nverseaplace transformsSolution of ?rdinarydi/erential
!4
!#, !% lack '
<>J=HJ<=9C
: D to 9< <;J=HJ<=9C
e0uations using theaplace aplace transformof Periodic functionseaviside Knit Stepfunction *irac-deltafunction
!4
!# ,!% lack '
=9J=;J<=9C
C 9: to 9E =CJ=;J<=9C
Fourier Series *iricheltLsconditions 5statementonly 'ulerLs formulae5with Proof6 !ourier Seriesof function with period
!4
!#, !% lack '
=;J=;J<=9C
> 9H to <= 99J=;J<=9C
!ourier series of functionshaving !ourier series ofodd and even alf range!ourier series ParsevalLsidentity 5without proof6,
!4
!#, !% lack '
9CJ=;J<=9C
E <9 to <C 9DJ=;J<=9C %omple& form of !ourier
Series $rbitrary period <$rbitrary period <
!4
!#, !% lack '
<<J=;J<=9C
H <> to <; <EJ=;J<=9C
?rthogonal @?rthonormal set
!4 !#, !% lack '
7/23/2019 Aa Cmpn III Am3(Div1)
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o/unction 8dea of !ourier8ntegral !ourier Sine and%osine 8ntegral !ourierSine and %osine
Transforms
<;J=;J<=9C
; <D to :< =9J=DJ<=9
C
omple! varia"les
$nalytic function Polarform$nalytic function bymilnethompson Methodharmonic function
!4
!#, !% lack '
=>J=DJ<=9C
D :: to :E =;J=DJ<=9C
%onformal mappingbilinear mapping%artesian and polar form 1am"les
!4
!#, !% lack '
9<J=DJ<=9C
9= :H to C= 9>J=DJ<=9
C
/ transform 4-transform
of standard functions suchas 45an6, 45np6. Propertiesof 4-transform 1inearity,%hange of scale, Shiftingproperty,Multiplication of 7, 8nitialand +nal value,%onvolution theorem 5allwithout proof6
!4
!#, !% lack '
9DJ=DJ<=9C
99 C9 to CC <<J=DJ<=9C
8nverse 4 transform1
"inomial '&pansion andMethod of Partial fraction.=ector ;a%cu%uscalar 9 .ector "ro#uct o% three,%our .ectors
!4
!#, !% lack '
<EJ=DJ<=9C
9< C> to C; ------------ ole$oi#al,irratio$al,co$ser.ati.e.ector %iel#,ole$oi#al,irratio$al,co$ser.ati.e.ector %iel#Vector integration
!4
!#, !% lack '
-------------
9: CD to >< =HJ9=J<=9C
scalar potential @ lineintegralwork done, greenstheoremstrokes theorem 5 withoutproof6 (auss *ivergencetheorem,
!4
!#, !% lack '
9=J9=J<=9C