MTH401 Final Term Subjective 2013

Rana Abubakar Khan

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MTH401 FINAL TERM PAPER SUBJECTIVE 2013

Q1. Define eigenvalue of multiplicity m? (2 marks)

Q2. Characteristic equation of the matirx (2 marks)

is

Q3. If the initial temperature of cooling body is (2 marks)

then write the differential equation of Newton Law of Cooling.

Q4. A (3 marks)

T In the equation state the conditions for ordinary and singular points if a2, a1, a0 are polynomials with

no common factor.

Q5. For the given system of differential equations (3 marks)

(D+1)x + (D-1)y= 2

3x + (D+2)y= -1

Write down its auxiliary equation for ‘x’.

Q6. Find eigen vector of (3 marks)

A= ,corresponding eigen value

Q7. a x y (3 marks)

a x y a x y Suppose that a dead body was discovered at midnight in a room when its temperature was 85° F. The temperature of the room is kept

constant at 70° F . Two hours later the temperature of the body dropped to 72° F, then find the value of using the following solution

of the initial value problem

Q8. Find the Eigen values and Eigen vector of the given matirx (5 marks)

Q9. Explain the Interval of convergence of (5 marks)

Q10. Find the eigenvalues of the following matrix. (5 marks)

k

70 , 98.6 dT

k T T

dt

k t

m m T t T T T e

A

n

n

n

n n

x · a · n