Aa Cmpn III Am3(Div1)

7/23/2019 Aa Cmpn III Am3(Div1)

http://slidepdf.com/reader/full/aa-cmpn-iii-am3div1 1/12

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.

*



!# ,

!%

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



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



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



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

http://www.intel.com/

http://www.intel.com/



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.

http://nptel.iitm.ac.in/



http://www.nxpsemiconductors.com/

http://www.atmel.com/

http://ocw.mit.edu/

http://ocw.mit.edu/

http://ocw.mit.edu/

http://www.ee.iitb.ac.in/

http://www.kiel.com/

http://www.youtube.com/watch?v=liRPtvj7bFU

http://www.youtube.com/watch?v=p4RcMLFIr5o

http://www.youtube.com/watch?v=I78iyzXQrP4


http://www.nxpsemiconductors.com/

http://www.atmel.com/

http://ocw.mit.edu/

http://www.ee.iitb.ac.in/

http://www.kiel.com/

http://www.youtube.com/watch?v=liRPtvj7bFU

http://www.youtube.com/watch?v=p4RcMLFIr5o

http://www.youtube.com/watch?v=I78iyzXQrP4



?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

Studentsstudy the Topics and

write the$nswers.(et practiceto solveuniversity0uestions..

%hapters 9

> andwrittensolution

e&pected.

"ook 9,<,:,C,> ofthe

referencelist.


: Laplacetransform

Studentsstudy the Topics andwrite the

$nswers.(et practiceto solveuniversity0uestions.

%hapters <

E andwrittensolutione&pected.

"ook 9,<,:,C,> ofthereference

list.




C InverseLaplacetransforms.

Studentsstudy the Topics andwrite the$nswers.

(et practiceto solveuniversity0uestions.

%hapters <

H andwrittensolutione&pected.



> omple!varia"le

Studentsstudy the Topics andwrite the$nswers.(et practice

to solveuniversity0uestions.

%hapters :

; andwrittensolutione&pected.



E onformal mapping

Studentsstudy the Topics andwrite the$nswers.(et practiceto solve

university0uestions.

%hapters :

D andwrittensolutione&pected.


Aebsite 9

to E of the)eferencelist

H Vectoralge"ra

Studentsstudy the Topics andwrite the$nswers.(et practiceto solveuniversity

0uestions.

%hapters C

9= andwrittensolutione&pected.


Aebsite 9to E of the

)eferencelist

; Vectorcalculus

Studentsstudy the Topics andwrite the$nswers.(et practice

%hapters C

99 andwrittensolutione&pected.




to solveuniversity0uestions.


D /0transform

Studentsstudy the Topics andwrite the$nswers.(et practiceto solveuniversity0uestions.

%hapters >

9< andwrittensolutione&pected.



9= Inverse 10

transform

Students

study the Topics andwrite the$nswers.(et practiceto solveuniversity0uestions.

%hapter

s >

9: and

writtensolutione&pected.

"ook 9,

<,:,C,> ofthereferencelist.


Tutorial ' Assignment polic&

o ofTutorials23

Time ' da&sgiven forcompletion

Assessmentpolic&

4and+ritten '

Laser print

.rading '#ar%ingpolic&

$ll Tutorials *isplayedAeek 9Submitted onSame hour

Same day(raded

and written 9=

Term $or% ompositionAttendance025 #ar%s

6e7avior in classroom082 #ar%sTutorial082 mar%sTotal095 #ar%s



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 '



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



9C >: to >E

(uest lectureJ0uiz test !4

!#, !% lack '

Academic Administration Document Prepared by …

Prof. 2asir $nsari

Documents

Aa Cmpn III Am3(Div1)