Get premium membership and access revision papers, questions with answers as well as video lessons.

Acmp 203: Mathematical Methods Of Computer Scientists Question Paper

Acmp 203: Mathematical Methods Of Computer Scientists

Course:Bachelor Of Science In Computer Science

Institution: Chuka University question papers

Exam Year:2013

CHUKA

UNIVERSITY

UNIVERSITY EXAMINATIONS

SECOND YEAR EXAMINATION FOR THE AWARD OF DEGREE OF
BACHELOR OF SCIENCE (COMPUTER SCIENCE)

ACMP 203: MATHEMATICAL METHODS OF COMPUTER SCIENTISTS

STREAMS: B.SC (COMP. SCI) Y2S2 TIME: 2 HOURS

DAY/DATE: WEDNESDAY 7/8/2013 2.30 P.M. – 4.30 P.M.
INSTRUCTIONS:

Answer Question ONE (Compulsory) and any other two Questions.
Adhere to the instructions on the answer booklet.
Do not write on the question paper.

QUESTION ONE – COMPULSORY

Given that and g(x)=1/(x+1), evaluate

(i)
(ii) f^(-1) (x) [4 marks]

Find of the function [3 marks]

Evaluate

[2 marks]

Evaluate the gradient (dy/dx) of the function y=?tan?^(-1) (v(x-1)) [4 marks]

Using an integrating factor, solve the differential equation

( dy)/dx-2xy=x [3 marks]

Find the angle between the vectors a=i-2j+4k and b=-4i+j-2k. [3 marks]
Solve the system of linear equations using row reduction.

?-x?_1+x_2+?2x?_3=2

?3x?_1-x_2+x_3=6

?-x?_1+?3x?_2+?4x?_3=4

[3 marks]
Evaluate the determinant of the matrix

(¦(1&3&-2@4&-5&6@0&0&2)) [2 marks]

Evaluate the characteristic polynomial of the matrix

(¦(2&2&1@1&3&1@1&2&2)) [3 marks]

Using the ratio test, show that the series

is convergent. [2 marks]

QUESTION 2

Find the cross product a × b given that
a=i+3j-Rand

b=2i-j+R [4 marks]

Test the consistency of the system below. If found consistent solve it.

?-x?_1+?2x?_2-?3x?_3=4

?2x?_1-?4x?_2+?6x?_3=-8

? x?_1-?2x?_2+?3x?_3=-4 [5 marks]

Find the eigen values and eigen vectors of the matrix A below.

A=(¦(1&0&-1@1&2&1@2&2&3)) [11 marks]

QUESTION 3

(i) Use the trapezoidal rule with n = 5 to approximate to 4dp.

?_1^2¦dx/x [6 marks]

(ii) Evaluate the exact integral hence obtain the error of approximation. [4 marks]

(i) Define an exact differential equation. [2 marks]

(ii) Prove that the differential equation

(?5x?^4+?3x?^2 y^2-?2xy?^3 )dx+(?2x?^3 y-?3x?^2 y^2-?5y?^4 )dy=0

is exact hence solve it. [4 marks]

Find the particular solution of the differential equation

dy/dx=xy,y(0)=1 [4 marks]

QUESTION 4

(i) State four properties/characteristics of affine transformation. [4 marks]

(ii) Give examples of Affine transformations. [1 mark]

Evaluate the image co-ordinates of a 2 x 2 square centred at the origin after undergoing a rotation of 45o about its centre then a translation which moves the centre of the square to the point (3, 2) in 3D. [5 marks]

Prove that the series

is divergent

using the root test. [3 marks]

Using the ratio test, prove that the series

is divergent. [7 marks]

QUESTION 5

Evaluate the following limits

[3 marks]

[3 marks]

[3 marks]

(i) Prove that dy/dx of y=?Sin?^(-1) x=1/v(?1-x?^2 ) [4 marks]

(ii) Given that? y=2?^3x, evaluatedy/dx. [4 marks]

Apply the ratio test to the power series

to find the radius of convergence and the interval of convergence. [3 marks]

----------------------------------------------------------------------------------------------------------

Acmp 203: Mathematical Methods Of Computer Scientists Question Paper

More Question Papers

Popular Exams