A 0800MAT201122102 Pages: 3

Reg No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Third Semester B.Tech Degree Examination December 2021 (2019 scheme)

Course Code: MAT201
Course Name: Partial Differential equations and Complex analysis

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all questions. Each question carries 3 marks Marks
1 Find the partial differential equation by eliminating arbitrary functions 1 वात (3)

g from z = f(x) + g(y)

2 0522 _ (3)
Solve 77 = XY

3 Write the three possible solutions of one dimensional wave equation. (3)
4 Write any two assumptions used in the derivation of one dimensional heat (3)
equation.
5 ९, #0 (3)
Test the continuity at 2 = 0 of f(z) = | [2 '
0, z=0
6 Check whether f (7) = Z is an analytic function? (3)
7 5٢٢ 9 — dz, where ௦ is the circle |z|= 4 (3)
8 Find the Taylor series expansion of e” about z = 7. (3)
9 Give example of (a) removable singularity (b) pole (c) essential singularity (3)
10 Find the Laurent series expansions of ۳ नत्या about 2 = 0 (3)
PART 13
Answer any one full question from each module. Each question carries 14 marks
Module 1
11 (൮ Solve y2p—xyq = xz 7
(0) ऽग by the method of separation of variables ன + =0, u(x, 0) = 4€ ॐ 7
12 (a) Find the complete integral of px + ‏رو‎ = pq using Charpit’s method. 7

(b) Form the partial differential equation corresponding to family of spheres

with center on z-axis and radius a.

Page 10/3