Notes

F–6192 Sub. Code
7BMAA3


U.G. DEGREE EXAMINATION, NOVEMBER 2021

Mathematics

Allied : ANCILLARY MATHEMATICS — III

(CBCS – 2017 onwards)

Time : 3 Hours Maximum : 75 Marks

Section A (10 × 2 = 20)
Answer all questions.

1. Form the differential equation by eliminating the
constants a and b from z = axy + b .

z = axy + b &¼¸¢x
©õÔPÒ a ©ØÖ® b I }UQ
ÁøPUöPÊa \©ß£õk Aø©UP.

2. Define : Particular integral.
Áøμ¯Ö : ]Ó¨¦z öuõøP.

3. Give an example of a first Order partial differential
equation.
•uÀ Á›ø\ £Sv ÁøPUöPÊ \©ß£õmiØS J¸
GkzxUPõmk u¸P.

4. Find the general Solution of zp + x = 0 .
zp + x = 0 &ß ö£õxz wºÄ PõsP.

5. Define : Laplace Transform.
Áøμ¯Ö : »õ¨»õì E¸©õØÓ®.

, s
6. Prove : L(cos ax ) = .
s + a2
2


s
{ÖÄP : L(cos ax ) = .
s + a2
2



dy
7. Write the Newton’s forward difference formula for .
dx
dy
&ØPõÚ {³mhÛß •ß÷ÚõUS ÷ÁÖ£õmk `zvμzøu
dx
GÊxP.

d2 y
8. Write the Newton’s backward difference formula for .
dx 2
d2 y
&ØPõÚ {³mhÛß ¤ß÷ÚõUS ÷ÁÖ£õmk
dx 2
`zvμzøu GÊxP.

9. Define : Gamma Function.
Áøμ¯Ö : Põ©õ \õº¦.

10. Prove : Γ(n + 1) = n! .
{ÖÄP Γ(n + 1) = n! .

Section B (5 × 5 = 25)

Answer all questions choosing either (a) or (b).

11. (a) Form the differential equation by eliminating the
function from z = f ( x 2 − y 2 ) .

z = f ( x 2 − y 2 ) &¼¸¢x \õºø£ }UQ ÁøPUöPÊa
\©ß£õk Aø©UP.

Or



2 F–6192