6. Furnco manufactures tables and chairs. A table requires 40 board ft of wood, and a chair requires 30 board ft of wood. Wood may be purchased at a cost of $1 per board ft, and 40, 000 board ft of wo
Question: . Krazy Snacks Company plans to produce and market two special nut mixes during the upcoming Chri.
. Krazy Snacks Company plans to produce and market two special nut mixes during the upcomi
COMPLEX VARIABLES
Introduction
Complex numbers
Consider the equations
x 2 1 0
x 2 3 0
x 2 10 x 40 0
There is no real number x which satisfies these equations. To get solutions of
these equations the s
Fourier series
Preliminaries
Periodic functions:
A function
T such that
Note: If
f (t )
is said to be periodic with period if there exists a positive constant
f (t T ) f (t )
f (t )
for all
is period
COMPLEX VARIABLES
Introduction
Complex numbers
Consider the equations
x 2 1 0
x 2 3 0
x 2 10 x 40 0
There is no real number x which satisfies these equations. To get solutions of these
equations the s
COMPLEX INTEGRATION
Introduction: The advantage of complex integration is that certain complicated real
integrals can be evaluated and properties of analytic functions can be established.
Line Integra
Fourier Cosine and Sine transforms
Consider the Fourier cosine integral representation of a function f(x)
2
f ( x) f (t )cos st cos sx dtds ,
00
x0
2 2
f
(
t
)cos
st
dt
cos sx ds
0 0
2
Let Fc f ( x
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
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. I
DIFFERENTIAL EQUATIONS
Introduction:
An equation involving one or more derivatives of an unknown function is called a differential
equation. Differential equations arise in many physical phenomena and
Linear Algebra
Introduction to generalization of vector concept:
Vectors are generally used in many areas of physical and engineering sciences. The
need for a vector concept arose very naturally in ma
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 CR
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
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
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
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
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 co
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 Techno
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 de
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 pap
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
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
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 obj
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