Reg.No
MANIPAL INSTITUTE OF TECHNOLOGY
MANIPAL UNIVERSITY, MANIPAL - 576 104
IV SEMESTER B.E DEGREE END SEMESTER MAKEUP EXAMINATION JULY 2013
MAT 212 : Engineering Mathematics IV (COMP/IT)
(REVISED CREDIT SYSTEM - 2011)
Time : 3 Hrs.
Max.Marks : 50
Note
Elementary Matrix Theory
Definition
A matrix A of order (or size) m n is a rectangular array of mn elements
arranged in m rows and n columns. The element in the i th row and j th
column is called the (i, j ) -entry of the matrix and is denoted by aij .
a
4. NUMERICAL METHODS-I
Introduction:
Most of the problems of engineering, physical and economical sciences can be
formulated in terms of system of equations, ordinary or partial differential
equations. In majority of the cases, the solutions to these prob
NUMERICAL METHODS II
Solution of Algebraic and Transcendental Equations
Preliminaries :
A problem of great importance in science and engineering
determining the roots/zeros of an equation of the form f(x) = 0.
is that of
A polynomial equation of the form
BIOLOGY FOR ENGINEERS ASSIGNMENT NO.3
1
After the Biology for Engineers class, near the staircase of NLH in MIT, students discovered a
colony containing amazing never before seen glow-in-the-dark ants. Few students very
curious to know how this trait is i
DEPARTMENT OF MATHEMATICS
MAT-1101 ENGINEERING MATHEMATICS - 1
(I Semester Common for all Branches)
No. of Lecture hours per week : 4 Hrs.
Total Hours : 50 Hrs.
Matrix Algebra:
Matrices, Elementary column and row transformations, Inverse of a matrix by el
A Report on Sewage
Treatment Plant
Located at End Point, Manipal
Submitted to:
Submitted by:
Prof. Maddodi
Sachin agarwal
Dept. of Civil Engineering,
Section P, Roll no 55,
Manipal Institute of Technology.
Regt no 140906696
GENERAL OUTLINES OF SEWAGE
TREA
III SEM B.TECH - MECH/IP/MT/Auto/Aero
ASSIGNMENT IV
f . dr
1. Evaluate
2
x=z , z= y
2
given
f =( 3 x2 y ) i+ ( y +2 z ) jx 2 k
the curve being
from ( 0,0,0 ) to ( 1,1,1 ) .
2. Find the directional derivative of
3
2
2
=4 x z 3 x y z
at (2, -1, 2) in the
d
MANIPAL INSTITUTE OF TECHNOLOGY
MANIPAL UNIVERSITY, MANIPAL - 576 104
First Semester B.E Degree end Semester Examination
MAT 1101:Engineering Mathematics I
( Comman to all branches)
Model question paper
(Revised Credit System - 2014)
Time: 3 Hrs.
Max.Mark
III sem Mech/IP/ Auto/Aero/MT
Engg.Mathematics III - ASSIGNMENT 1
1 Solve
'
y =y
y (1 ) =1.1752, y ( 2 )=10.0179, h=0.25
with
by finite difference
method. Is the system of linear equations so obtained tridiagonal?
(What is the method of solution?) Compare
III SEM B.TECH - MECH/IP/MT/Auto/Aero
ASSIGNMENT III
1. Sketch the odd and even periodic extension of the function
cfw_
t
f ( x )= e 0<t< 1 .
0 1<t < 2
Also obtain the two half range expansion of the
function.
2. Expand f ( x )=
cfw_
kx 0 x
l
2
l
k ( lx
V-ASSIGNMENT
(Mech/Aero/IP/Auto/Mechatronics)
1. Prove that
is conservative force
F (y 2 cosx z 3 )i (2ysinx 4)j (3xz 2 2)k
field, find the scalar potential for
and find the work done in moving an object
F
in this field from (0,1,-1) to (/2,-1, 2).
2. Ver
III SEM B.TECH - MECH/IP/MT/Auto/Aero
ASSIGNMENT II
1. Solve by the method of finite differences:
With
,
y (1) 0 y(2) 2
x y xy ( x 3) y 0
2
2
2. Solve
3. Solve
4. Solve
,
,
, and
,
h 0.25
.
,
2u 0 0 x, y 4 u ( x,0) 0 u ( x,4) 6 u (0, y ) u (4, y) 1
u 8