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RAMRAO ADIK INSTITUTE OF TECHNOLOGY
NERUL, NAVI MUMBAI
Department of Engineering Sciences
(Academic Year: - 2014-15)
Program :–B. E. (COMPUTER)
Name of the course: AM- IV
Year : 2015
Semester: IV
Name of Faculty : Mrs.Shilpa Bhangale, Mr. Mahadev Zende
Academic Year: 2014-15
Course outcomes:
CO1 : Students will apply the method of solving complex integration and
computing residues also to find contour integrals.
CO2 : Demonstrate ability to manipulate matrices and compute eigen values and
eigen vectors.
CO3 : Students can relate the two different data.
CO4: Students will recognize the role of probability theory in the applications of many
different fields.
CO5: Students will be able to represent and statistically analyze the data both
graphically and numerically.
CO6: Students will be able to analyze the solution of a linear optimization problem.
Program Outcomes:
Program outcomes are narrower statements that describe what students are expected to
know and be able to do by the time of graduation. These relate to the skills, knowledge,
and behaviors.
Engineering programs must demonstrate that their students attain the following outcomes:
Pa) an ability to apply knowledge of mathematics, science, and engineering,
Pb) an ability to design and conduct experiments, as well as to analyze and interpret data,
Pc) an ability to design a system, component, or process to meet desired needs within
realistic constraints such as economic, environmental, social, political, ethical, health and
safety, manufacturability, and sustainability,
Pd) an ability to function on multidisciplinary teams.
Pe) an ability to identify, formulates and s olve engineering problems,
Pf) an understanding of professional and ethical responsibility,
Pg) an ability to communicate effectively.
Ph) the broad education n e c e s s a r y to understand the impact of engineering s o l u t i o n s in
a global, economic, environmental, and societal context,
Pi) A recognition of the need for, an ability to engage in lifelong learning.
Pj) A knowledge of contemporary issues.
Pk) an ability to use the techniques, skills, and modern engineering tools necessary for
higher studies and engineering practices.
Pl) An ability to have leadership and management skills to accomplish a defined goal.
Mapping of CO’s with PO’s
Subject: Applied Mathematics IV
Credits: 5
Course code: CSC401
Course Outcomes
(Weightage-60%)
Theory Credits: 4
Program Outcomes
Pa
Pb
Pc
Pd
Pe
Pf
Pg
Ph
Pi
Pj
Pk
CO1
2
2
2
CO2
2
2
2
CO3
1
2
2
CO4
2
2
2
CO5
1
2
1
CO6
2
2
2
1
2
Course Outcomes
(Weightage-40%)
Theory Credit: 1
Pl
Program Outcomes
Pa
Pb
Pc
Pd
Pe
Pf
Pg
Ph
Pi
Pj
Pk
CO1
2
1
1
CO2
1
2
1
CO3
1
CO4
1
CO5
1
CO6
1
1
1
2
2
1
1
1
2
1
Pl
\
SYLLABUS AM-IV
Subject
Code
Subject Name
Teaching Scheme
Theo
ry
SEITC401
Subject
Code
Applied
Mathematics IV *
Pract.
04
Credits Assigned
Tutorial
--
Theory
01
Subject Name
Total
-
01
05
Examination Scheme
Internal assessment
Applied
Mathematics –IV*
Tutorial
04
Theory Marks
SEITC401
TW/
Pract.
Test1
Test2
20
20
Avg.
20
Term
Work
Practical Oral Total
End
Sem.
Exam
80
25
-
-
125
Detailed Syllabus:
Sr.No.
Details
Module 01
Complex Integration
1.1 Complex Integration – Line Integral, Cauchy’s Integral theorem for simply
connected regions, Cauchy’s Integral formula(without proof)
1.2 Taylor’s and Laurent’s series ( without proof)
1.3 Zeros, poles of f(z), Residues, Cauchy’s Residue theorem
1.4 Applications of Residue theorem to evaluate Integrals.
Module 02
Module 03
Matrices
2.1 Eigen values and eigen vectors
2.2 Cayley-Hamilton theorem(without proof)
2.3 Similar matrices, diagonalisable of matrix.
2.4 Derogatory and non-derogatory matrices ,functions of square matrix.
Correlation
Hrs
(10)
(08)
(04)
Module 04
Module 05
Module 06
3.1 Scattered diagrams, Karl Pearson’s coefficient of correlation, covariance,
Spearman’s Rank correlation.
3.2 Regression Lines.
Probability
4.1 Baye’s Theorem,
4.2 Random Variables:- discrete & continuous random variables, expectation,
Variance, Probability Density Function & Cumulative Density Function.
4.3 Moments, Moment Generating Function.
4.4 Probability distribution: binomial distribution, Poisson & normal distribution.
(For detail study)
Sampling theory
5.1 Test of Hypothesis, Level of significance, Critical region, One Tailed and two
Tailed test, Test of significant for Large Samples:-Means of the samples and test
of significant of means of two large samples.
5.2 Test of significant of small samples:- Students t- distribution for dependent
and independent samples.
5.3 Chi square test:- Test of goodness of fit and independence of attributes,
Contingency table.
Mathematical Programming
6.1 Types of solution, Standard and Canonical form of LPP, Basic and feasible
solutions, simplex method.
6.2 Artificial variables, Big –M method (method of penalty).
6.3 Duality, Dual simplex method.
6.4 Non Linear Programming:-Problems with equality constrains and inequality
constrains
(No formulation, No Graphical method).
Term work:
Term work shall consist of minimum four SCILAB practicals and six tutorials.
SCILAB practicals :
08 marks
Tutorials :
12 marks
Attendance :
05 marks
Total :
25 marks
Recommended Books:
1. Higher Engineering Mathematics by Grewal B. S. 38th edition, Khanna Publication 2005.
2. Operation Research by Hira & Gupta,S Chand.
3. A Text Book of Applied Mathematics Vol. I & II by P.N.Wartilar &
J.N.Wartikar, Pune, Vidyarthi Griha Prakashan., Pune.
4. Probability and Statistics for Engineering, Dr. J Ravichandran, Wiley-India.
5. Mathematical Statistics by H. C Saxena, S Chand & Co.
Reference Books:
1.
2.
3.
4.
Advanced Engg. Mathematics by C. Ray Wylie & Louis Barrett.TMH International Edition.
Mathematical Methods of Science and Engineering by Kanti B. Datta, Cengage Learning.
Advanced Engineering Mathematics by Kreyszig E. 9th edition, John Wiley.
Operations Research by S.D. Sharma Kedar Nath, Ram Nath & Co. Meerat.
(08)
(08)
(10)
5. Engineering optimization (Theory and Practice) by Singiresu S.Rao, New Age International publication.
6. Probability by Seymour Lipschutz, McGraw-Hill publication.
Theory Examination:
Question paper will comprise of 6 questions, each carrying 20 marks. Total 4 questions need to be
solved. Q.1 will be compulsory, based on entire syllabus wherein sub questions of 2 to 3 marks will
be asked. Remaining question will be randomly selected from all the modules. Weightage of marks
should be proportional to number of hours assigned to each module.
LECTURE PLAN
Lecture
no.
Dates
Modules
Course
outcomes
Module 1 : Complex Integration
L-1
Complex integration – Line integral
CO1
L-2
Cauchy’s integral theorem for simply connected
regions, problems.
CO1
L-3
Cauchy’s integral formula, problems
CO1
L-4
Problems on above topics
CO1
L-5
Taylors series, related problems
CO1
L-6
Laurent series, related problems
CO1
L-7
Zeros, singularities, poles, residues
CO1
L-8
Cauchy’s residue theorem, related problems
CO1
L-9
Applications of residue theorem
CO1
L-9
Applications of residue theorem
CO1
L-10
Problems on above topics
CO1
Module 2 : Matrices
L-11
Eigen values and eigen vectors
CO2
L-12
Problems of eigen values and eigen vectors
CO2
L-13
Cayley Hamilton theorem with problems
CO2
L-14
Similar matrices, problems
CO2
L-15
Diagonalisable of matrix
CO2
L-16
Problems on above topics
CO2
L-17
Derogatory and non-derogatory matrices
CO2
Module 3 : Correlation
L-18
Scattered diagrams, Karl Pearson’s coefficient of
correlation
CO3
L-19
Covariance
CO3
L-20
Spearman’s Rank correlation, problems
CO3
L-21
Regression Lines
CO3
L-22
Problems on above topics
CO3
Module 4: Probability
L-23
Baye’s Theorem, problems
CO4
L-24
Random variables, discrete and continous r.v,
expectation
CO4
L-25
Variance ,Probability density function and
cumulative density function
CO4
L-26
Moments, problems based on moments
CO4
L--27
Problems on above topics
CO4
L-28
Moment generating function
CO4
L-29
Probability distribution- Binomial distribution
CO4
L-30
Poisson distribution
CO4
L-31
Normal distribution
CO4
L-32
Problems on above topics
CO4
Module 5 : Sampling Theory
L-33
Test of hypothesis, level of significance, critical
region, one tailed test, two tailed test
CO5
L-34
Test of significant for large samples :means of
samples
CO5
L-35
Test of significant of means of two large samples
CO5
L-36
Test of significant of small samples : tdistribution for dependent sample
CO5
L-37
t-distribution for independent samples
CO5
L-38
Chi-square test : test of goodness of fit
CO5
L-39
Test of independence of attributes
CO5
L-40
Problems on above topics
CO5
Module 6: Mathematical Programming
L-41
Types of solution, standard and canonical form of
LPP.
CO6
L-42
Basic and feasible solutions
CO6
L-43
Simplex method
CO6
L-44
Artificial variables, Big – M method(method of
penalty)
CO6
L-45
Duality problems
CO6
L-46
Dual simplex method Problems
CO6
L-47
Non linear programming problems with equality
constraints
CO6
L-48
Problems on above topic
CO6
L-49
Non linear programming :inequality constraints
CO6
L-50
Problems on above topics
CO6
LIST OF TUTORIALS AND SCILAB PRACTICALS
TUTORIAL NO.
1.
2.
3.
4.
5
6
7.
SCILAB
PRACTICALS
1.
2.
3.
TOPICS
Complex integration
Matrices
Correlation and regression
Probability
Sampling theory
Mathematical programming 1(LPP)
Mathematical programming2(NLPP)
TOPICS
Correlation
Binomial distribution
Poisson distribution
Course
outcomes
CO1
CO2
CO3
CO4
CO5
CO6
CO6
Course
outcomes
Co3
Co4
Co4