COLLEGE OF ENGINEERING, PUNE
Compulsory Ph. D. Course in Mathematics
Tutorial 3 (Due on Thursday, September 24, 2015)
PART A
Q.1 Problem 13 of Tutorial 2 was withdrawn because its solution required something
more than merely finding an antiderivative. To

COLLEGE OF ENGINEERING, PUNE
Compulsory Ph. D. Course in Mathematics
Tutorial 2 (Due on Thursday, September 10, 2015)
PART A
Q.1 Find the general solution of the differential equation
d3 y
dy
3 + 2y = 0
3
dx
dx
(1)
Q.2 Show that if y = f1 (x) and y = f2

COLLEGE OF ENGINEERING, PUNE
Compulsory Ph. D. Course in Mathematics
Tutorial 5 (Due on Thursday, October 15, 2015)
PART A
Q.1 Suppose cfw_an
n=0 and cfw_bn n=0 are sequences of real numbers.
(a) Prove that 4(an bn ) = 4(an ) 4(bn ) where 4 is the (forwa

COLLEGE OF ENGINEERING, PUNE
Compulsory Ph. D. Course in Mathematics
Tutorial 1 (Due on Thursday, September 3, 2015)
PART A
Half the success in mathematics lies in supplying the right word at the right place.
By working too many numerical problems, there

COLLEGE OF ENGINEERING, PUNE
Compulsory Ph. D. Course in Mathematics
Tutorial 4 (Due on Thursday, October 1, 2015)
Parts A and B are optional. They contain problems on some transform techniques
including some interesting applications of recurrence relatio

COLLEGE OF ENGINEERING, PUNE
Compulsory Ph. D. Course in Mathematics
Tutorial 6 (Due on Thursday, November 5, 2015)
Q.1 Let V be the vector space of all polynomials of degree 4 or less. Define T : V V
by T (p(x) = p00 (x). Put differently, T = D2 where D