Academic Year 2013-14

Department of Science and Humanities

Certificate program:

BAISC MATHEMATICS

)

(

EXCEL ENGINEERING COLLEGEKOMARAPALAYAM_ 637 303

DEPARTMENT OF SCIENCE AND HUMANITIES

ACADEMIC YEAR: 2013-14 (ODD SEMESTER)

REOUISITION LETTER & BUDGET PROPOSALFrom

Mrs.O.R.LalithaAssistant Professor,Department of Mathematics,Excel Engineering College.Komarapalayam

To

The Principal,

Excel Engineering College,

Komar apal ayam.

Respected Sir,

Sub: Approval to Conduct Certificate Program Course and Budget Expenditure reg.

Depanment of Mathematics is planned to conduct Certificate program Course for theacademic year 2013-14. About 52 Students are willing to enroll their Dames for the course.Kindly accord permission for conducting the Cedificate Course titled..Basic Mathematics', alldalso approve the budget for conducting the course. Budget Expenses:

Thanking YoLr YottrsTrry+d'-Mrs.O.R.Lalitha

(Program Coordinator)

Itc1etacdofS&IEnl Faghrcrtng 6o1.t"

Konarapalryrn - 637 303.

Program Title Scheduled from No. ofStudentsAmount (Per StudentRs. l0 for C_ertificate)

Cedificate

Course

Basic

Mathematics

03-02-20r4

To

t4-03.201452 52.t0=520l

(

ffi fXf.el Engineering College

Komarapalny am - 637 303.

Management, Principal, Head of the Department and Staff MembersCordially inuite you to the lnaugural function for the

"Value Added Course on -BASIC MATHEMATICS"On 03rd February 2014 at 09.15 A.M.

Venue: API Abdulkalam Hall @EEC campus

n r of , D r. A.K.N at e S an,, m.c o m.,MB A.,M. p hi t.,Fr A,p HF

Chairman - Excel Group hstitution\,has kindly consented to preside over the function

Dr,N.M athan Karthick., mnns.,m.a.s".(Diqbetotosy )

Vice Chairman - Excel Group Institutions,Will honor the Speaker

Dr.M.MarudaiProfessor, Department of Mathemtics

Bharathidasan Universi $Trichy

In the presence of

Dr.V.K. Shunmughanaathan.,v.E.,nn.oPrincipal, Excel Engineering College

All are invited l,?

'l/run e*ezmed. putenrp i.6 frigfrfuy oolirilzd.

10.10 A.M

10.20 A.M

10.30 A.M

10.30 A.M

1.00 P.M

Session I

AGENDA

- Prayer

- Lightning of Kqthuvizhaku by Dignitaries

- Honouring of Speaker by Dr.L.Vinayagamoorthi, HoD/S&H

- Presidential Address by Mrs.O.R.Lalitha Programme Coordinatol

Presentation by Speaket

Lunch Break

()

(

Session II

2.00 P,M - Presentation by SPeakel

4.30 P.M - Valedictory

4.35 P.M - Vote of Thanks by Mr.V.Manimekalai

National Anthem

i-ji.- EXCEL ENGINEERING COLLEGE\, 1,1''l KOMARAPALYAM

-l '-' ..-'- DEPARTMENT oF SCIENCE AND HUMANITIESCerfificate Course on Basic Mathcmatics

Academic Yeir 2013-l,l

SNo DEPARTMENl Nanre of the Sludent

1 AERO ABINAYA L

2 AERO ADEL MOHAMMED ABDU ABBAS A

3 AERO AJITH KUMAR R

4 AERO DINESHKUMAR M

5 AERO DIVAKAR A

6 AERO HARI SHANKAR V

I AERO JEEVA P

8 AERO I UBIN CHACKO

9 AERO KAMALRAJ D

10 AERO KANIMOZHI M

11 AERO KASM IR ANTHIREYAN A

12 CIVIL DHANAVEL T

13 CIVIL DINESH T

14 CIVIL DURAIRA] M

15 CIVIL ELANGO P

16 C VIL ELANGO R

1/ CIVIL GEBA INGO

18 CIVIL GOMATHI M

CIVIL GOPINATH N

20 ctvtt GOWTHAMI R

21 CIVIL GUHAN S

22 CIV L GU NASHELAN B 5

23 CIVIL HARI HARA AARTHI S

24 C'VIL JANARDHANAN M

25 CIVIL JANARTHANAN P

26 csE DHARSHINI PRIYA L

27 csE DHEIESH S M NAN DHA

28 CSE ELAKIYA K

29 c5E GNANA SEKARAN K

30 csE JEMIYA RECHAL JOHN

c5E JENIFER M

32 csE JOSIT MATHEW

33 csE KANNAN K

34 csE NIRMAL A

csE NONGTHOI\4 BAM SOPHIA DEVI

36 RNAPRIYA MK

37 RAMYA KRISHNA D

38 csE SAMINATHAN K

39 csE SANGEETHA A

40 SANTHIYA M

41 SASIREKA N

42 SETHUBATHIS

43 csE SREEPRIYA ANAND

44 c5E SRIVIDHYA M

4S csE SUGANYA J @

46 csE SUKI VIKNESH S

47 CSE SUN DARESAN P

48 c5E THOMAS 5UN NY

49 ECE ABILASH KRISHNAN T

50 ECE AKILAN R

ECE ANITHA R

ECE ARAVIND P

(

( Academic coordinator

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EXCEL ENGINEERING COLLEGEKOMARAPALAYAM - 637303

DEPARTMENT OF SCIENCE AND HUMANITIESCERTIFICATE PROGRAM COURSE CONTENT

BASIC MATHEMATICS

ACADEMIC YEAR 2OI3-14 DURATION: 30HOURS

a

('

S.No Topicst Convergency and divergency ofseries - defiDitions - elementaryresults Comparison

tests -De Alembens and Culgll11$ls.2 Absolute convergence - series ofpositive terms -bauchy\ condensation T

Cauchy's root test -Raabe's test.Theory of equations: Roots of anfficoefficients . Transformations ofequations. CharacLer and position ofroots-Descanes'rule of signs Symmetric function of roots

3

4 Sphere : Standard equation ofa sphere- results based on the p-operties ofi spheretangent plane to a sphere Equations ofacircl€. Cone whose vertex is at the origrnenveloping cone ofa sphere Right circular cone Equation ofa cylinder- right

5 Logarithm ofcomplex munbers - Summation oftrigonometric series _ Sum of Sines ofn angles in A.P - Sum ofCosines ofn angles in A.P- Summation using ComplexQuantities (Series in G.P, Binomial and Exponential seri€s onlv).

64Pd-Course Coordinator

$Afl

Academic Year 2013-14

EXCEL ENGINEERING COLLEGEKOMARAPALAYAM _ 637 303

DEPARTMENT OF SCIENCE AND HUMANITIESCERTIFICATE PROGRAM COURSE PLAN

COURSE NAME: BASIC MATHEMATICS

(

(

Etad of tlc llcPrtncntDcosrt nof S&E

nxccl fn;hertag CoUege

Kornarapalslrm ' 637 i03'

S.No. Date Topics to be Covered Handling by

I 0l 02 14 Convergency of series Mrs.O.R.Lalitha2 04.02.14 divergency of series Mrs,O.R.Lalitha3 05.02.14 Definitions of Convergency and Divergency of series Mrs.O,R,Lalitha4 06.02.14 ComDarison tests Mrs.O,R.Lalitha5 0'7.02.14 De Alemberts ratio Test Mrs.O.R.Lalitha6 10.02.14 CauchY's tests Mrs.O.RLalitha7 I1.02.14 Absolute convergence Mrs.O.R.Lalitha8 12.02.t4 Series of positive terms Mrs.O,R.Lalitha9 13.02.t4 Cauchy's condensation Test Mrs.O.R.Lalitha10 l4.02.14 Cauchy's root rest Mrs.O.R.Lalithall r7.02.14 Raabe's test. Mrs.O.R.Lalithat2 18.02.14 'Iheory of equatiolls -Introduction Mrs.O.R.Lalithal3 19.02.t4 Roots of an equation Mrs,O.R.Lalithat4 20.02.14 Relations connectins the roots and coefficients . Mrs.O.R.Lalitha

l5 2t.02.14 Transformations of equations Mrs.O.R.Lalitha

16 24.02.14 Character and Dosition ofroots- Descartes'rule ofsigns Mrs.O.R.Lalithal7 25.02 14 Svmmetric iirnction of roots Mrs.O.R.Lalitha18 26 U.t4 Sphere I Standard equation ofa sphere Mrs.O.R.Lalitha19 27.02.14 Results based on the properties ofa sphere Mrs.O.R.Lalitha20 28.02.t4 Tangent plane to a sphere Mrs.O,R.Lalitha2l 0t.03.14 Equations ofacircle Mrs.O,R.Lalitha22 04 03.14 Cone whose \'ertex is at the origin Mrs.O.R.Lalitha23 05 03 14 Enveloping cone- ofa sphere Mrs.O.R.Lalitha

06.03.14 Right circular cone Mrs.O.R,Lalitha25 07 .8.14 Equation ofa cylinder Mrs,O.R.Lalitha26 10.03.14 Right circular cylinder Mrs.O,R.Lalitha

2',7 I 1.03. r 4 Logarithm ofcomplex numbers - Summation oflrigonometric series Mrs.O.R.Lalitha

28 t2.03.t4 Sum ofSines ofn angles rn A P - Sum ofCosines of n angles in A P Mrs.O.R.Lalitha

2913.03.14 Summation using Complex Quantit;es (Series in C.P, Binomial

serres only)Mrs.O.R.Lalitha

3014.03 14 Summation using Complex Quantities (Series in Exponential sefies

onry,Mrs.O.R.Lalitha

31 14.03.14 Evaluation test Mrs.O.R.Lalitha

I\ c^"\4/L.^.--rc cooiDrNAToR

EXCEL ENGINEERING COLLEGEKOMARAPALYAM

DEPARTMENT OFSCIENCE AND HUMANITIES

Certificate Course on Basic Mathematics

Students Feedback ADalYsis

Academic Yean20l3-14 Tot l Strength: 52

C,,

(

I

9'-

z.0

0

Excellent Good Satisfactory

Course Coordinator

IoorqpdrYn - 637 303,

Contents Excelletrt Good Satisfactory Poor

Course Content 28 20 4 0

Technical Skill 25 27 0 0

Itrteraction 30 t2 10 0

Communication skill 40 l0 2 0

Ayerage 31 t7 4 0

No of Studerts Successfully completed:125

lil

ExcEL ENGTNEERING cor.LEGEi<5irar'nApn',.rvntu - rsTJ,oj

o rr*'fi iliit6iq?i;X1*P- #MAN rr I Es

"'"'slmtggprplsspI-*u *n*u,

"AsIc MATHEMATI.S

(.

Academic Year 2013-14

BASIC MATHEMATTCS MCQ

l,Express the ten thousandths place in 1'7389

a)r8

9

o)J

llm2. Find n for which '-c

raortxl-1)(coei.x:' -t l, has non zero value

a) >=1

cl <=2

d) "2

.. tumlS.Evaluate

dl,c\1/,

d)1

4.Rank of the matrix A =

Io o o ollq z 3 o llr o o olL, o 3 o-ld0ul

e)2

5.A set of linear equations is-represented-by 1n: TIt:::uu'ion Ox = b The necessarv

iiliili- i"tlL.iittence ofa solution for this svstem ts

g!1 None of these

6 The system of linear equatLons

(4d-l)x+Y+z=01 -y +z-O\ ,,1 l\-:n\+u- rr4 "

i"i u rion-oluiut 'otution'

ifd equals

l12

u 1/4

ol

f a) Both the statements are false

' b) Both the statements arc rue

9) I is true but lI is false'

is false but ll is true

if""l'in*';*;ii Jff"*11il:li*""1corumn vectors ora matrix A is caled the rank or

t'n**ll; ;:x*1i11;J"xlll lj,,liil'"'i';j?i,""T**1,.i' ""

S.Therankofa3x3matdxC(--Arl)'.tbundbymultiplyinganon-zerocolumnmatrixAofsize; ;';;;;;;-;,. 'ow

matrix B orsize I x 3 is

9.The matlix B = AT, wherc A is any matrix is

skew symmetnc

symmetric about the secondary diagooal

g) always syrnmetrLc

d) another general matdx

10.Eigen values of a real symmetric matrix arg always

a Positive\ " real and imaginary

O negatrve

d) real

11.1f, A, B. C are square matrices ofthe same order' then (ABC)-I is equal to

d C-rA-'B''

bl C-r B-r A-r

91 A' 8-16-r

' c-r B-'

he numberofpoints inthe complex plane' satisfyingthe conditions lz- 2l= 2 '

2 (1- i)+ z (1+ i)=

4is

d)more than 2

13.The argument of the complex number '-1+i' is: +

b)-13s

a)0

c)2

35

c)45

d)-4s

l4.lfxisacomplexcuberootofunityand(1+x)7=A+Bx'thenAandBarerespectivelvequalto:

,t

b)1,1

c)1,0 v'

tt, ,t: - !

15.Two men on a 3-D surface want to meet each other' The surface is given by ' - 'i

They make their move horizontally or vertically with the X_Y plane as their reference lt was observed

that one man was initially at (200, 4OO) and the other at (1OO' 100) Their meet point is decided as (0' 0)

a Given that they travel in straight lines' will they meet?

a)They will meet

b)They Will not meet

with Probability %t information

16, Ifl and B are matrices, then which from the following is tlue ?

d)A+ B+B + A

'l+A

c)AB + BA

d)all are true

( t7.th" outber ofnon-zero rows in an echlon form is called ?

duced echlon folm

b)rank of a matnx

c)coniugate ofthe mat x

d)cofactor of the matrix

l8.The rank of a 3 x 3 matrix C (= AB), found by multiplying a non-zerc column matrix A of

size 3 x I and a non-zero row matrix B of size I x 3, is

a)0I

d2o3

19, ents

51: matrices may be non-singular

52 nx n matrices may be singular

Which ofthe following statements is conect?

4 Sl and 32 are both true

C sr is tue, s2 is false

c). Sl is false, 52 is true

d). Sl and 52 are both false

20 In the matrix equation Px = q which ofthe following is a necessary condition for the

existence of at least one solution for the unknown vector x 1

(

e)

De)

orthogonal

non-smgurar

have A-l exists

both (b) & (c)

Augmented matrix [Pq] must bave the sarne rark as matrix P

Vector q must have only non-zero elements .r-g) Matrix P must be singular

d) None ofthese

2l.Matrix, A =

coso sin@ 0

sin@ cos@ 0

001

22.The matrix B = AT, where A is any matrix is

e) skew syrunetricqmmetric about the secondary diagonat

always symmetric

d) another genqral matrix

Consider the following two statementsl

I. The maximum number of linearly independent colum! vectors ofa matrix A is called rhe lank

ofA.23. lfA is an n x n square matrix, it will be nonsingular is rank A = n'

With reference to thJabove statements, which of the following applies?

C)

a) Both the statements are false

D Both the statements are true

is true but II is false

d) I is false but II is ftue.

24,The system oflinear equations

(4d- l)x+y+z=0-y +z=0(4d-r)z=0has a non-t vial solution, ifd equals

l12

u r/4c) 314

d)t

25.The rank of a 3 x 3 matnxsize 3 x I and anon-zero row

40b)l

2

d). 3

/'

C (= AB), found by multiplying a non-zero column matrix A ofmatrix B of size 1 x 3, is

(r

&Hl'nllclc

J--.]=i. EXCEL ENGINEERING COLLEGE'',-:-t DEPARTMENT OF SCIENCE AND HUMANITIES

Certificate Course on Basic MathematicsAcademic Year 20lJ-1fr

SNO DEPARTMENT Name olthe Student NlAR KS

1 AERO ABINAYA L 24

2 AERO ADEL MOHAMMED ABDU ABBAS A 23

3 AERO AJITH KUMAR R 21

AERO DIN ESHKU MAR M 18

5 AERO DIVAKAR A 19

6 AERO HARI SHANKAR V 22

7 AERO JEEVA P 24

8 AERO JUBIN CHACKO

9 AERO KAMALRAJ D 18

10 AERO KANIMOZHI M 23

11 AERO KASMIR ANTHIREYAN A 24

72 CIVIL DHANAVEL T 21

13 CIVIL DINEsH T 20

14 CIVIL DURAIRAJ M 19

15 CIVIL ELANGO P 24

CIVIL ELANGO R

11 CIVIL GEBA INGO 22

18 CIVIL GOMATHI M 2

t9 CIVIL GOPINATH N I

20 CIVIL GOWTHAMI R 24

21 CIVIL GUHAN S 23

22 CIVIL GUNASHELAN B S 19

23 clvtI HARI HARA AARTHI S 18

24 CIVIL JANARDHANAN M

25 CIVIL JANARTHANAN P 23

26 c5E DHARSHINI PRIYA L

21 c5E DHEJESH 5 M NANDHA 22

28 c5E ELAKIYA K 21

29 c5E GNANA SEKARAN K 20

30 csE IEM'YA RECHAL JOHN 24

31 c5E JENIFER M 24

IOSIT MATHEW 24

33 csE KANNAN K 24

34 csE NIRMAL A 24

35 NONGTHOMBAM SOPHIA DEVI 22

36 c5E RAIAPRIYA MK 24

csE RAMYA KRISHNA D

38 CSE SAMINATHAN K 24

39 csE SANGEETHA A 22

40 SANTHIYA IV] 23

4t c5E SASIREKA N 24

42 SETHUBATHIS 24

43 csE SREEPRIYA ANAND 22

44 c5E SRIVIDHYA M 22

45 csE SUGANYA J @ 24

46 c5E SUKI VIKNESH S 22

47 csE sUNDARESAN P 23

4A csE THOMAS SUNNY 24

49 ECE ABILASH KRISHNAN T 21

50 ECE AKILAN R 19

ECE ANITHA R

52 ECE ARAVIND P

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