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7/30/2019 Mathematics-I course file
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SCIENCE & HUMANITIES
Course File
.
Department: SCIENCE AND HUMANITIES
Name of the Subject: MATHEMATICS - I
Subject Code: 51002
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JOGINPALLY B.R. ENGINEERING COLLEGE
YENKAPALLY(V),MOINABAD(M),R.R.DIST,HYDERABAD
Department of
SCIENCE &
HUMANITIES
Course File Year:2009-2010
2. Department: S&H
3. Name of the Subject: Mathematics-1
4. Subject Code: 51002
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JOGINPALLY B.R. ENGINEERING COLLEGE
YENKAPALLY(V),MOINABAD(M),R.R.DIST,HYDERABAD
Department of
SCIENCE &
HUMANITIES
Course Status Paper(Target, Course Plan,
objectives, Guidelines
etc.)
Year: 2009-2010
Target:
1. Percentage Pass: __________90%_
2. Percentage above 70% of marks: 60%____________
Course Plan:
(Please write how you intend to cover the contents: that is, coverage of units
by lectures, guest lectures, design exercises, solving numerical problems,
demonstration of models, model preparation, or by assignments etc.)
a. Design exercises,b. Solving numerical problems,c. Model preparation by assignments etc
On completion of the course the student shall be able to:
To utilize the mathematical concepts in other subjects To apply the mathematical knowledge and logical thinking in
other subjects
4. Method of Evaluation:
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3.1. Continuous Assessment Examination: Yes / No
3.2. Assignments: Yes / No
3.3. Questions in class room: Yes / No
3.4. Quiz as per University Norms: Yes / No
3.5. Others: Make the students to solve the problems on the board(Please Specify)
5. List out any new topic(s) or any innovation you would like to
introduce in teachingthe subject in this semester:
6. Guidelines to study the subject:
1. Mathematics has played a fundamental role in the formulation ofmodern
Science since the very beginning; a scientific theory is a theory that has an
adequate mathematical model.
2. The Mathematics that can be applied today covers all the fields of the
mathematical science and not only some special topics; it concerns
Mathematics of all levels of difficulty and not only simple results and
arguments.
3. The sciences continue to require today new results from ongoing research
and
present multiple new directions of inquiry to the researchers, but the rhythm
of the
contemporary society makes the time lapse substantially shorter and the
request more urgent.
4. The capabilities of scientific computation have made numerical
simulation, an indispensable tool in the design and control of industrialprocesses.
5.To develop an understanding of the basic principles governing the
conditions of rest and motion of particles and rigid bodies subjected to the
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action of forces; to develop the ability to analyze and solve problems in a
simple and logical manner
Expected date of completion of the course and remarks, if any:
Unit Number: 1 30-9-09
Unit Number: 2 20-10-09
Unit Number: 3 6-11-09
Unit Number: 4 16-2-10
Unit Number: 5 5-3-10
Unit Number: 6 30-3-10
Unit Number:7 17-4-10
Unit Number: 8 6-5-10
Remarks (if any):
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Schedule of instruction
Unit No: 1
S.No
Date Numberof Hours
Subject Topics Reference
1 1 Sequences,Convergent,Divergent,Oscillatorysequences
S.Chand &Dr.C.Sankara
2 1 Bunded and Unbounded sequences,limit of asequence
S.Chand &Dr.C.Sankara
3 2 Infinite series:Properties of theseries,Geometric Series,Auxiliary Series(p-
Series),Series of positive terms
S.Chand &Dr.C.Sankara
4 3 Comparison test,DAlemberts Ratio test S.Chand &
Dr.C.Sankara5 2 Raabes Test S.Chand &
Dr.C.Sankara
6 1 Cauchys Root Test,Cauchys Integral Test S.Chand & Dr.C.Sankara
7 1 Alternating Series, Lebnitzs test S.Chand & Dr.C.Sankara
8 2 Absolute and Conditional Convergence S.Chand & Dr.C.Sankara
Unit No: 2S.
No
Date Number
ofHours
Subject Topics Reference
1 1 Rolles Theorem S.Chand
2 1 Lagranges Mean Value Theorem
Altrnate form of Lagranges Mean Value
Theorem
S.Chand
3 1 Cauchys Mean Value Theorem S.Chand
4 1 Taylors Series,Taylors Theorem with
Lagranges form ofRemainder,Alternative Form
S.Chand
5 1 Maclaurins Series,Maclaurins Theorem
with Lagranges form of Remainder
S.Chand
6 1 Functions of Several variables S.Chand
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7 1 Jacobians,Properties S.Chand
8 1 Functional Dependence S.Chand
9 1 Taylors Theorem for Two Variables S.Chand
10 2 Maxima and Minima of a function of two
or more variables
S.Chand
11 1 Constrained Maxima and Minima:
Lagranges method of undeterminedmultipliers
S.Chand
Unit No: 3
S.No
Date Numberof
Hours
Subject Topics Reference
1 1 Curvature S.Chand & Dr.C.Sankaraiah
2 2 Formula for Radius of
Curvature,Circle ofcurvature
S.Chand &
Dr.C.Sankaraiah
3 2 Radius of curvature at theorigin
S.Chand &Dr.C.Sankaraiah
4 1 Pedal Eqution, Formula for
Radius of curvature for the
pedal eqn
S.Chand &
Dr.C.Sankaraiah
5 1 Centre of Curvature,Co-ordinates of centre of
curvature
S.Chand &Dr.C.Sankaraiah
6 2 Evolute,Properties of
evolutes
S.Chand &
Dr.C.Sankaraiah
7 2 Envelopes,Method of
finding envelope
S.Chand &
Dr.C.Sankaraiah
8 1 Curve Tracing S.Chand &
Dr.C.Sankaraiah
9 1 Curve tracing in Cartesian
form
S.Chand &
Dr.C.Sankaraiah
10 2 Curve Tracing in ParametricForm
S.Chand &Dr.C.Sankaraiah
11 2 Curve Tracing in Polar form S.Chand & Dr.C.Sankaraiah
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Unit No: 4
S.
No
Date Number
ofHours
Subject Topics Reference
1 1 To find the length of the arcof a curve in Cartesian co-
ordinates
S.Chand &Dr.C.Sankaraiah
2 1 Polar Co-ordinatesS S.Chand &
Dr.C.Sankaraiah
3 2 Volume of Revolution
4 3 Volume Formulae forParametric Eqn,Volume
Formulae in Polar Co-ordinates,Volume between
two solids
5 1 Surface Area of Revolution
6 1 Multiple IntegralsDouble Integral
7 1 Triple Integral
8 1 Double Integral in Polar
Form
9 1 Region of Integration
10 2 Change of order of
integration
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Unit No: 5
S.
No
Date Number
of
Hours
Subject Topics Reference
1 3 Differential EqnsIFirst
Order&First Degree)
Introduction:OrdinaryDifferential Eqns
Solution of adifferential Eqn
S.Chand &
Dr.C.Sankaraiah
2 1 Exact Differential Eqns
3 1 Integrating Factors
4 2 Eqns Reducible to exacteqns(methods to find
integrating factors)
5 1 Linear Eqns
6 2 Bernoullis Eqns
7 2 Applications-Orthogonal
Trajectories(CartesianForm,Polar Form)
8 2 Law of Natural Growthor Decay,Newtons Law
of Cooling
Unit No: 6
S.
No
Date Number
of
Hours
Subject Topics Reference
1 2 Linear differential eqnsComplementary fn
S.Chand &Dr.C.Sankaraiah
2 1 Particular IntegralMethods of finding P.I
-do-
3 2 Cauchys Homogenious LinearEqn
-do-
4 1 Legendres Linear Eqn -do-
5 2 Linear Differential Eqns of
Second Order-Method of
-do-
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Variation of Parameters
6 2 Applications
Bending of Beams
-do-
7 1 Boundary Conditins -do-
8 1 Electrical Circuits -do-
9 1 Simple Harmonic Motion -do-
Unit No: 7
S.No
Date Numberof
Hours
Subject Topics Reference
1 1 Introduction of Laplace
Transforms
S.Chand &
Dr.C.Sankaraiah2 2 Linearity Property,First
shifting,Second
shifing,Change of Scale
Properties
-do-
3 2 Laplace Transform of
standard fns:Multiplication by t
Division by t
-do-
4 2 Laplace Transform of
Derivatives
-do-
5 2 Laplace Transform of Integrals
-do-
6 1 Laplace Transform of Periodic fns,L-T of unit step
fn
-do-
7 2 Inverse Laplace
Transforms:First shiftingtheorem,Second Shifting
theorem,Second shifting
theorem
-do-
8 2 Change of scaleproperty,Inverse Laplace
Transform of Derivatives
-do-
9 1 Inverse Laplace Transform
of Integrals
-do-
10 1 Multiplication by powers of
s
-do-
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11 1 Division by powers of s -do-
12 1 Convolution Theorem -do-
13 1 Application of L-Ts -do-
Unit No: 8
S.
No
Date Number
ofHours
Subject Topics Reference
1 2 Vector Differentiation S.Chand & Dr.C.Sankaraiah
2 2 Gradient of scalar Function -do-
3 1 The Divergence of a Vector
Function
-do-
4 2 Curl of a Vectorfunction,Laplacian Operator
-do-
5 2 Vector Integration -do-
6 2 Surface Integrals -do-
7 2 Volume Integrals -do-
8 2 Greens Theorem in the
Plane,Application of Greenstheorem
-do-
9 1 Gauss Divergence Theorem -do-
10 2 Stokes Theorem -do-
This Assignment/Tutorial is concerned to Unit Number: 1
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(Please write the questions/problems/exercises. Which you would like to giveto the students)
Q 1: Test for convergence the series n
xn(x>0)
Q 2: Find the interval of convergence of the series
7
x.
6
5.
4
3.
2
1
5
x.
4
3.
2
1
3
x.
2
1x
753
+++
Q 3: Test for the convergence of the series, )0x......(10
x
5
x
2
x1
32
>++++
Q 4:Test whether the series
= +1n 2 1nncos
converges absolutely
Q 5:Find the interval of convergence of the series .............)x1(2
1x1
12+
+
This Assignment/Tutorial is concerned to Unit Number: 2
(Please write the questions/problems/exercises. Which you would like to giveto the students)
Q 1:Show that8
1
335
1
3>
using Legranges mean value theorem.
Q 2:Find c of Cuachuys mean value theorem for f(x)= ,x g(x)=x
1in
[a,b] where 0++=
This Assignment/Tutorial is concerned to Unit Number: 3
(Please write the questions/problems/exercises. Which you would like to give
to the students)
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Q 1:Find the curvature at the point
2
a3,
2
a3of the curve axy3yx
33 =+ .
Q 2:If 2,1 are the radius of curvature of the curve at the extremities of
any chord of the cardioids r= )cos1(a which passes through the pole.
Show that9
a16,
22
2
2
1=
Q 3:Considering evolutes as the envelope of the normal find the evolutes of
the parabola. Is ax4y2=
Q 4:Find the envelope to the family of circles thoroughly the origin and
whose centres lies on the ellipse 1b
y
a
x
2
2
2
2
=+
Q 5:Trace the curve22 )a5x)(a2x(ay9 =
This Assignment/Tutorial is concerned to Unit Number: 4
(Please write the questions/problems/exercises. Which you would like to giveto the students)
Q 1:Find the length of the arc of the parabola ax4y2= cut off by its latus
rectum.
Q 2:Find the perimeter of the cardioid )cos1(ar += . Also show that the
upper half of the cardioid is bisected by the line x = /3.
Q 3: Find the volume of the solid generated by revolving the ellipse x2/a2 +
y2/b2 = 1 about the major axis.
Q 4: Evaluate the dzdydxzxy2
taken through the positive octant of the
sphere x2 + y2 + z2 = a2
Q 5: Evaluate by transforming into polar co-ordinates dydxyxy 22a
0
xa
0
22
+
This Assignment/Tutorial is concerned to Unit Number: 5
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(Please write the questions/problems/exercises. Which you would like to giveto the students)
Q 1: Solve: (y2 2xy) dy = (x2 2xy)dy
Q 2: Solve: (x3y2 + xy) dx = dy
Q 3: Solve xdx
dy+ y = x3.y
Q 4: If the air is maintained at 300 C and the temperature of the body cools
down from 800 C to 600 C in 12 min. Find the temperature of body after 24mi
Q 5: Find the orthogonal trajectories of the family of the parabolas y 2 = 4ax
This Assignment/Tutorial is concerned to Unit Number: 6
(Please write the questions/problems/exercises. Which you would like to giveto the students)
Q 1: Solve: (D2 + 4D + 4 ) y = 18 cos hx
Q 2: Solve: ym + 2.yn yp 2y = 1 4y3
Q 3: Solve by the method of variation of parameters yn + 4y = tan 2x
Q 4: Solve: x2sin.e8y13dxdy6
dxyd x32
2=+
Q 5: Solve xsinxydx
yd2
2
=+ by the method of variation of parameters.
This Assignment/Tutorial is concerned to Unit Number: 7
(Please write the questions/problems/exercises. Which you would like to giveto the students)
Q 1: Find the laplace transforms of the following:
(i) tttet
3cos33sin2432
++(ii)sin(wt+ )
Q 2: If L[f(t)] = 3
2
)1(
15129
+
s
ss
, find L[f(3t)] using change of scale property
Q 3: Find the inverse Laplace transform of)2)(1(
4
++ ss
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Q 4:Using convolution theorem evaluate L-1
)4)(1( 22 ++ ss
s
Q 5:Using Laplace transform solve (D
2
+2D-3)y=sinx,y(0)=y(0)=0
This Assignment/Tutorial is concerned to Unit Number: 8
(Please write the questions/problems/exercises. Which you would like to giveto the students)
Q 1: Find the directional derivative of (xyz2+xz) at (1,1,1) in a direction of
the normal to the surface 3xy2+y=z at (0,1,1)
Q 2: Using Divergence theorem, evaluate ++s
zdxdyydzdxxdydz where
s:x2+y2+z2=a2
Q 3: Verify divergence theorem for 2x2yi-y2j+4xz2k taken over the region of
the first octant of the cylinder y2+z2=9 and x=0,x=2
Q 4:Verify Greens theorem for ++c
dyxdxyxy22
)( , where c is bounded by
y=x and y=x2
Q 5Apply Stokes theorem to evaluate ++
c
xdzzdyydx
. Where c is the curveof intersection of x2+y2+z2=a2 and x+z=a
Internal Quiz Marks
S.No.
Quiz Test Maximum
Marks
BestMarks
WorstMarks
Remarks
1Quiz Test
1
10
2Quiz Test
210
3Quiz Test
310
4Quiz Test4
10
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5Quiz Test
510
* indicate if any remedial tests were conducted, if any.
Please note:
1. The question papers in respect of quiz test 1, 2, 3, 4 and 5 of this
subject should be included in the course file.
2. Model question paper which you have distributed to the students in the
beginning of the semester for this subject should be included in thecourse file.
3. The list of seminar topics you have assigned, if any may also be
included here.
4. The J. N. T. University end examination question paper for this subject
must be included in the course file.
5. A record of the best and worst marks achieved by the students inevery quiz tests must be maintained properly.
6. A detailed / brief course material / lecture notes if prepared may besubmitted in the HODs office.
7. Xerox copies of at least 5 answer sheets, after duly signed by thestudent on verification of the evaluated answer script.
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