LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – COMPUTER SCI. & APPL.
FIRST SEMESTER – NOVEMBER 2012
MT 1103 – MATHEMATICS FOR COMPUTER SCIENCE
Date : 03/11/2012 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
Answer ALL questions: (10X2 =20)
- Define Unitary Matrix.
- Write down the expansion of in terms of cosθ.
- If α and β are the roots of 2x2 + 3x +5 = 0, find α+β and αβ.
- Find partial differential coefficients of u = sin (ax + by + cz) with respect to x, y and z.
- Evaluate .
- Solve the differential equation (D2 +2D + 1)y = 0.
- Find the complete integral of
- Write the formula for Trapezoidal rule.
- Write Newton’s backward difference formula for first and second order derivatives.
Answer any FIVE questions: (5 x8 = 40)
- Test the consistency of the following system of equations and if consistent solve
2x-y-z = 2, x+2y+z = 2, 4x-7y-5z = 2.
- Show that
- What is the radius of curvature of the curve at the point (1,1).
- Show that .
- Evaluate: .
- Solve the equation.
- Find by Newton-Raphson method, the real root of, correct to three decimal places.
Answer any TWO questions: (2 x 20 = 40)
- Verify Cayley-Hamilton theorem for the matrix and hence find its inverse.
- (i) Evaluate: dx
(ii) Evaluate: .
- (a) Solve the equation .
(b) Solve q2 – p = y – x.
- (i) Solve upto 3 decimals by using Regula-flasi method.
(ii) Evaluate using Simpson’s 1/3rd rule with
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