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SCIENCE & HUMANITIES
Course File
.
Department: SCIENCE AND HUMANITIES
Name of the Subject: MATHEMATICAL METHODS
Subject Code: 51002
JOGINPALLY B.R. ENGINEERING COLLEGE
YENKAPALLY(V),MOINABAD(M),R.R.DIST,HYDERABAD
Year:2009-2010
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Department of
SCIENCE &
HUMANITIES
Course File
1. Department: S&H
2. Name of the Subject: Mathematical Methods
3. Subject Code: 51002
JOGINPALLY B.R. ENGINEERING COLLEGE
YENKAPALLY(V),MOINABAD(M),R.R.DIST,HYDERABAD
Department of
SCIENCE &
Course Status Paper(Target, Course Plan,
objectives, Guidelines
Year: 2010-2011
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HUMANITIES etc.)
Target:
1. Percentage Pass: __________98%______________
2. Percentage above 70% of marks: 90%____________
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
3. On completion of the course the student shall be able to:
Understand the importance of Mathematics in EngineeringCourse.
To apply the mathematical knowledge and logical thinking inother subjects
4. Method of Evaluation:
3.1. Continuous Assessment Examination: Yes
3.2. Assignments: Yes
3.3. Questions in class room: Yes
3.4. Quiz as per University Norms: Yes
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3.5. Others: Assigning some technical topics to student to write usingthe all possible resources in the college.
5. List out any new topic(s) or any innovation you would like to
introduce in teaching the 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 numericalsimulation, an indispensable tool in the design and control of industrialprocesses.
5. To develop an understanding of the basic principles governing theconditions of rest and motion of particles and rigid bodies subjected tothe action of forces; to develop the ability to analyze and solve problemsin a simple and logical manner
Expected
date of completion of the course and remarks, if any:
Unit Number: 1 30/10/2010
Unit Number: 2 11/11/2010
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Unit Number: 3
Unit Number: 4
Unit Number: 5
Unit Number: 6
Unit Number:7
Unit Number: 8
Remarks (if any):
Schedule of instruction
Unit No: 1
S.No
Date Numberof Hours
Subject Topics Reference
120/10/10
1 Introduction to Matrices, and system of Equations.
Dr Iyengar etal. S Chand.
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2 21/10/10 1 Definition of Rank of a Matrix and problemsto illustrate to find the rank of a given
matrix
-do-
3 22/10/10,
23/10/10
2 Finding the rank of a matrix using Echelon
Form and Normal Form
-do-
4 25/10/10 1 Numerical problems illustrating the
previous methods
-do-
5 26/10/10
27/10/10
2 Consistence of a system of equations:
Necessary and Sufficient Conditions.
-do-
6 28/10/10 1 Solving the System of Equations using
various matrix methods
-do-
7 29/10/10
30/10/10
1 LU-Decomposition theorem -do-
Unit No: 2
S. No Date Number
of Hours
Subject Topics Reference
1 1 Introduction to the concept of
Characteristic equation and its roots.
Dr Iyengar et al.
S Chand.
2 1 Problem of finding Eigen values and
Eigen vectors.
-do-
3 1 Statement and Proof of Cayley
Hamilition Theorem and Problems
-do-
5 1 Finding inverse and powers of a
matrix using Cayley-Hamiliton
Theorem.
-do-
6 1 Diagonalization of a matrix. -do-
7 1 Properties of Eigen Values and EigenVectors.
-do-
Unit No: 3
S. No Date Numberof
Hours
Subject Topics Reference
1 1 Introduction to Complex
matrices.
Dr Iyengar et al.
2 1 Basic Properties of Hermitian,
Skew-Hermitian and UnitaryMatrices.
-do-
3 1 On Eigen values andEigenvectors of Hermitian, Skew-
Hermitian and Unitary Matrices.
-do-
4 1 Canonical Forms. -do-
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5 2 Explaining the concept of converting to canonical form by
orthogonal Transformation
-do-
6 1 Singular Value Decomposition -do-
7 1 Problems. -do-
8 1 Revision to first internal exams. -do-
Unit No: 4
S. No Date Numberof
Hours
Subject Topics Reference
1 1 Introduction to Numerical
methods to find the roots ofAlgebraic and Transcendental
equations.
Dr Iyengar et al.
2 1 Bisection method --do--
3 1 Method of False position: Theoryand Problems
-do-
4 3 Iteration method (Fixed point
Iteration method): Theory andProblems
-do-
5 1 Newton-Raphson method:Theory and Problems
-do-
6 2 Introduction to Finite differenceoperators, and relation between
them.
-do-
7 1 Introduction to Interpolation:
Newton forward interpolationformula: Problems
-do-
8 1 Newton Backward interpolationformula: Problems
-do-
9 1 Gauss Central forward andbackward formulae: Problems
-do-
10 3 Lagranges General Interpolationformula and Newton Divided
Difference interpolation formula:Problems.
-do-
11 2 Spline Interpolation: Theory andProblems
-do-
Unit No: 5
S.No
Date Numberof Hours
Subject Topics Reference
1 2 Introduction to Curve fitting:Method of Least square
approximation.
Dr. Iyengar et al.S Chand Company.
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2 1 Fitting a straight line to agive data using Least square
method
3 1 Fitting a Parabola to a give
data using Least Squaremethod.
4 1 Fitting different type of exponential curves to give
data using Least squaremethod.
5 1 Introduction to Numericaldifferentiation and
Integration.
6 1 Trapezoidal Rule:
Introduction with problems
7 1 Simpsons 1/3 and 3/8th rules
with Problems
8 1 Gaussian Integration.
Unit No: 6
S.
No
Date Number
of Hours
Subject Topics Reference
1 1 Introduction to solve Differentialequations with initial conditions.
Dr. Iyengar et al.S Chand company
2 2 Taylor series method: theory and
problems
-do-
3 2 Picards method: Theory and Problems -do-
4 2 Eulers method: Theory and Problems -do-
5 2 Modified Eulers method: Theory andProblems
-do-
6 1 Runge-Kutta Method (Fourth order):
Theory and Problems
-do-
7 1 Predictor-Corrector methods: Milnes
Method: Problems
-do-
8 1 Adam-Bashforth-Moulton Method:
Problems
-do-
9 1 Conclusions and Revision -do-
Unit No: 7
S. No Date Number
of Hours
Subject Topics Reference
1 1 Introduction of Fourier Series Dr Iyengar et al.S Chand Company
2 1 Definitions and Problems -do-
3 1 Dirichlets Conditions and EulersFormulae
-do-
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4 1 Fourier Sine and Cosine Series -do-
5 1 Half Range Fourier Series -do-
6 1 Fourier Series of a Function over
an interval a to +a
-do-
7 1 Fourier Sine and Cosine Series -do-
8 1 Half-Range Fourier Series -do-
Unit No: 8
S. No Date Number
of Hours
Subject Topics Reference
1 1 Introduction to Partial Differential
Equations
Dr. Iyengar et al.
S Chand Company
2 1 Formation of Partial Differential
Equations
-do-
3 1 Lagranges method to findgeneral solution of PDE -do-
4 1 Complete integral of some
special Partial differentialequations.
-do-
5 1 Char pits method to solvenonlinear partial differential
equations
-do-
6 1 Method of Separation of Variable. -do-
7 1 Solution of Heat equation -do-
8 2 Solution of Wave equation -do-
9 1 Solution of Laplace equation -do-10 2 problems -do-
This Assignment/Tutorial is concerned to Unit Number: 1
(Please write the questions/problems/exercises. Which you would like to give to thestudents)
Q1. Define Rank of a matrix. Find the Rank of the following matrix using the Normal form
=
134813748
3124
5312
A
Q2. Test for the Consistence of the following equations and solve them if possible23;932;42 ==+=++ zyxzyxzyx
Q3.Determine the value of for which the following set of equations may posses non-
trivial solution and solve them in each case
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042;0324;03 =++==+ zyxzyxzyx
This Assignment/Tutorial is concerned to Unit Number: 2
(Please write the questions/problems/exercises. Which you would like to give to thestudents)
Q1. Diagonalize the matrix
=
344
120
111
A and hence find A4.
Q2. Show that the matrix
=
210
321
221
A satisfies its characteristic equation. Hence find
A-1.
Q3.Verify the sum of eigen values is equal to its trace of A for the matrix
=
1312
6204
2210
A and find the corresponding eigen vectors.
This Assignment/Tutorial is concerned to Unit Number: 3
(Please write the questions/problems/exercises. Which you would like to give to thestudents)
Q1. Find a matrix P which diagonalize the matrix associated with the quadratic form
xyzxyzzyx 222353 222 +++ and reduce its to canonical form
Q2. Show that the eigen values of Hermitian matrix are real
Q3. Find the nature of the quadratic form, index and signature
yzxzxyzyx 61045210222
+++
This Assignment/Tutorial is concerned to Unit Number: 4(Please write the questions/problems/exercises. Which you would like to give to the
students)
Q1. Find the real root of 2=xxe using Regula False method and approximate with Newton
Raphson method.
Q2. Find f(22) form the following table using Gauss forward formula
x 20 25 30 35 40 45
f(x) 354 332 291 260 231 204
Q3.Construct difference table for the following data:
X 0.1 0.3 0.5 0.7 0.9 1.1 1.3
F(x) 0.003 0.067 0.148 0.248 0.370 0.518 0.697
This Assignment/Tutorial is concerned to Unit Number: 5
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(Please write the questions/problems/exercises. Which you would like to give to thestudents)
Q1. Derive normal equations to fit the straight line y=a+bx
Q2. Fit a parabola to the following data using least square method
X 10 15 20 25 30 35y 35.3 32.4 29.2 26.1 23.2 20.5
Q3. Evaluate +
1
01 x
dxtaking h=0.25 using Cubic spline.
This Assignment/Tutorial is concerned to Unit Number: 6
(Please write the questions/problems/exercises. Which you would like to give to thestudents)
Q1. Using Runge-Kutta Method to evaluate y(0.1) and y(0.2), given that
1)0(; =+= yyx
dx
dy.
Q2.Given 1)0(;sin =+= yyxdx
dycompute y(0.2) and y(0.4) with h=0.2 using Eulers
modified method
Q3. Find y(0.2) using Picards method given that 1)0(, == yxydx
dyusing Picards method of
successive approximation with stepsize h=0.1
This Assignment/Tutorial is concerned to Unit Number: 7(Please write the questions/problems/exercises. Which you would like to give to the
students)
Q1. Find the half-range Cosine and Sine series of f(x)=(x-1)2
in the interval 0
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S.No. Quiz Test MaximumMarks
Best Marks Worst Marks Remarks
1 Quiz Test 1 10
2 Quiz Test 2 10
3 Quiz Test 3 10
4 Quiz Test 4 10
5 Quiz Test 5 10
* 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 the course 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 beincluded in the course file.
5. A record of the best and worst marks achieved by the students in every quiz tests
must be maintained properly.
6. A detailed / brief course material / lecture notes if prepared may be submitted in the
HODs office.
7. Xerox copies of at least 5 answer sheets, after duly signed by the student on
verification of the evaluated answer script.
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