ANNA UNIVERSITY COIMBATORE
B.E/B.TECH.DEGREE EXAMINATIONS:SEPTEMBER 2009
REGULATIONS-2007
THIRD SEMESTER
070030004-ENGINEERING MATHEMATICS 111
(COMMON TO CIVIL/AERONAUTICAL/CSE/IT)
TIME:3 Hours Max.Marks:100
PART-A
ANSWER ALL THE QUESTIONS
1.Form partial differential equation by eliminating the arbitary constants from z=ax+by+a
2.solve p+q=4.
3.solve(D-6DD'+9d')z=0
4.findthe P.I of(D-4DD')z=e
5.state the dirichlet's conditions for the existence of Fourier series for f(x).
6.write the formulae for Fourier constants for f(x)in the interval (-1,2).
7.obtain the sine series fo the unity in (0,3).
8.if f(x)=|x| expanded as a Foutrier series in 09.Explain the method of separation of variables.
10.state the assumptions made in the derivation of one dimentional wave equation.
11.state one dimentional heat equation with the initial boundary conditions.
12.when the ends of the road 20 cm are maintained at the temperature 283k and 293k respectively until steady state prevailed.determine the steady state temperature of the rod.
13.state the Fourier integral theorem
14.find the sine transform of e power -x.
15.state shifting theorem on fourier transform.
16.state convolution theorem for fourier transform.
17.prove that z(a power n)=z/z-a
18.find Z(sinat)
19.find Z power -1[z power 2/(z-a) power 2.
20.state the final value theorem on Z transforms
PART-B
(5x12=60 marks)
21.a)form partial differential equation dy eliminating the arbitary functions f and g in z=x square f(y)+y square g(x)
b)find the singular integral of z=px+qy+2 root of pq.
22.a)solve p square + q square =x square + y square.
b)solve(D cube-4D square D'+ 4DD')z=6 sin(3x+6y)
23.find the fourier series of f(x)=x in (0,pie)
24.a)obtain the half range cosine series for f(x)=cosax in -pie25.A string is stretched and fastened to two points l apart.Motion is started displacing the string into the form of the curve y=k(lx=x square) and then released from rest in this position.find the displacement y(x,t).
26.find the steady state temperature distribution in a square plate bounded by the lines x=0,y=0,x=20,y=20,.it's surfaces are in sulated satisfying the boundary conditions U(0,y)=U(20,y)=U(x,20)=x(20-x).
27.a)find the fourier transform of f(x)={x,|x| 0,|x|>a}
b)evaluate integral 0 to infinity dx/(x square + a square )(x square + b square) using transforms
28.solve the difference equation using Z transform method:
y base n+2-3 base n+1 + 2y base n=n2 power n givwn that y(0)=0,y(1)=0.
KEYWORDS:ENGINEERING MATHEMATICS 111,2007 ANNA UNIVERSITY CHENNAI B.E COMPUTER SCIENCE ENGINEERING MATHEMATICS 111 QUESTION PAPER,ANNA UNIVERSITY QUESTION PAPER,ANNA UNIVERSITY,ANNA UNIVERSITY CHENNAI,ANNA UNIVERSITY COIMBATORE,ANNA UNIVERSITY TRICHY,ANNA UNIVERSITY TIRUNELVELI,ANNA UNIVERSITY MADURAI,ANNA UNIVERSITY SYLLABUS,ANNA-UNIVERSITY RESULTS,ANNA UNIVERSITY DISTANCE EDUCATION,ANNA UNIVERSITY MBA-CENTRE FOR DISTANCE EDUCATION,ANNA UNIVERSITY SCHEDULE OF EXAMINATIONS,ANNA UNIVERSITY ADMISSION,ANNA UNIVERSITY COURSES,ANNA UNIVERSITY ACADEMIC,ANNA UNIVERSITY DEPARTMENTS,ANNA UNIVERSITY RESEARCH,ANNA UNIVERSITY MAIL,ANNA UNIVERSITY QUESTION PAPERS,ANNA UNIVERSITY COUNSELLING DATES,ANNA UNIVERSITY RE-EVALUATION RESULTS
B.E/B.TECH.DEGREE EXAMINATIONS:SEPTEMBER 2009
REGULATIONS-2007
THIRD SEMESTER
070030004-ENGINEERING MATHEMATICS 111
(COMMON TO CIVIL/AERONAUTICAL/CSE/IT)
TIME:3 Hours Max.Marks:100
PART-A
ANSWER ALL THE QUESTIONS
1.Form partial differential equation by eliminating the arbitary constants from z=ax+by+a
2.solve p+q=4.
3.solve(D-6DD'+9d')z=0
4.findthe P.I of(D-4DD')z=e
5.state the dirichlet's conditions for the existence of Fourier series for f(x).
6.write the formulae for Fourier constants for f(x)in the interval (-1,2).
7.obtain the sine series fo the unity in (0,3).
8.if f(x)=|x| expanded as a Foutrier series in 09.Explain the method of separation of variables.
10.state the assumptions made in the derivation of one dimentional wave equation.
11.state one dimentional heat equation with the initial boundary conditions.
12.when the ends of the road 20 cm are maintained at the temperature 283k and 293k respectively until steady state prevailed.determine the steady state temperature of the rod.
13.state the Fourier integral theorem
14.find the sine transform of e power -x.
15.state shifting theorem on fourier transform.
16.state convolution theorem for fourier transform.
17.prove that z(a power n)=z/z-a
18.find Z(sinat)
19.find Z power -1[z power 2/(z-a) power 2.
20.state the final value theorem on Z transforms
PART-B
(5x12=60 marks)
21.a)form partial differential equation dy eliminating the arbitary functions f and g in z=x square f(y)+y square g(x)
b)find the singular integral of z=px+qy+2 root of pq.
22.a)solve p square + q square =x square + y square.
b)solve(D cube-4D square D'+ 4DD')z=6 sin(3x+6y)
23.find the fourier series of f(x)=x in (0,pie)
24.a)obtain the half range cosine series for f(x)=cosax in -pie25.A string is stretched and fastened to two points l apart.Motion is started displacing the string into the form of the curve y=k(lx=x square) and then released from rest in this position.find the displacement y(x,t).
26.find the steady state temperature distribution in a square plate bounded by the lines x=0,y=0,x=20,y=20,.it's surfaces are in sulated satisfying the boundary conditions U(0,y)=U(20,y)=U(x,20)=x(20-x).
27.a)find the fourier transform of f(x)={x,|x| 0,|x|>a}
b)evaluate integral 0 to infinity dx/(x square + a square )(x square + b square) using transforms
28.solve the difference equation using Z transform method:
y base n+2-3 base n+1 + 2y base n=n2 power n givwn that y(0)=0,y(1)=0.
KEYWORDS:ENGINEERING MATHEMATICS 111,2007 ANNA UNIVERSITY CHENNAI B.E COMPUTER SCIENCE ENGINEERING MATHEMATICS 111 QUESTION PAPER,ANNA UNIVERSITY QUESTION PAPER,ANNA UNIVERSITY,ANNA UNIVERSITY CHENNAI,ANNA UNIVERSITY COIMBATORE,ANNA UNIVERSITY TRICHY,ANNA UNIVERSITY TIRUNELVELI,ANNA UNIVERSITY MADURAI,ANNA UNIVERSITY SYLLABUS,ANNA-UNIVERSITY RESULTS,ANNA UNIVERSITY DISTANCE EDUCATION,ANNA UNIVERSITY MBA-CENTRE FOR DISTANCE EDUCATION,ANNA UNIVERSITY SCHEDULE OF EXAMINATIONS,ANNA UNIVERSITY ADMISSION,ANNA UNIVERSITY COURSES,ANNA UNIVERSITY ACADEMIC,ANNA UNIVERSITY DEPARTMENTS,ANNA UNIVERSITY RESEARCH,ANNA UNIVERSITY MAIL,ANNA UNIVERSITY QUESTION PAPERS,ANNA UNIVERSITY COUNSELLING DATES,ANNA UNIVERSITY RE-EVALUATION RESULTS