PTU B.Tech Mechanical Engineering 5th Semester May 2019 70601 MATHEMATICS III Question Papers

FirstRanker.com

Roll No. [ [ [ L[ T[T [1] Total No. of Pages : 02
Total No. of Questions : 09

--- Content provided by‍ FirstRanker.com ---

--- Content provided by⁠ FirstRanker.com ---

INSTRUCTION TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt ANY FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt ANY TWO questions.

SECTION-A

--- Content provided by‌ FirstRanker.com ---

1. Write briefly :
   1. Expand mx — x in half range series in interval (0, ) upto first three terms.
   2. Find Laplace transform of £ &
   3. Find the inverse Laplace Transform of ( s J
   4. Describe the conditions required for the Fourier expansion.
   5. Express f(x) =x*+ 3x’ —x* + 5x — 2 in terms of Legendre polynomials.

   --- Content provided by‌ FirstRanker.com ---

   6. Evaluate J x'j (x)dx
   7. Form the partial differential equation z = (x + y) ¢ (x> = )*)
   8. Solve 22+ 2=0 given that x=0,z=¢ and ==1.
   9. Define harmonic function
   10. Check whether f(z) =./| xy| is analytic at origin or not?

   --- Content provided by​ FirstRanker.com ---

FirstRanker.com

SECTION-B

1. Obtain Fourier series to represent f'(x) = Z(n—x)z, 0
2. Solve the initial value problem y' =5y +4y=e€"y(0) =

--- Content provided by​ FirstRanker.com ---

3. Find the frobenius series solution about x = 0 of equation (1=x)y"=2xy +6y=0
4. Find bilinear transformation which maps the points z = 1, 7, —1 onto the points w=i, 0, —i. Hence find
   1. The image of |z | 1
   2. Solve (¥’ —yz)p + (0P —zx) q =2 —xp

   SECTION-C

   1. State and prove convolution theorem. Apply convolution theorem to evaluate _ s ' ——— ((52+a2)2]

   --- Content provided by⁠ FirstRanker.com ---

   2. Find the residue of f(z)= 3 zZ m at its poles and hence evaluate JDc f(z)dx where ¢ is circle | z| = 2.5
   3. Solve the Laplace equation a—lj+§:0 subject to the conditions X sin nmx u0,)=uxy)=ulx 0=0,ux a) = ]

   NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

   FirstRanker.com

   
   

   --- Content provided by‍ FirstRanker.com ---