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K L Deemed to be University
Department of Computer Science and Engineering-Honors -- KLHYD
Course Handout
2022-2023, Even Sem
Course Title :MATHEMATICS FOR ENGINEERS
Course Code :22MT2102
L-T-P-S Structure : 2-1-0-0
Pre-requisite :
Credits :3
Course Coordinator :Krushnachandra Panigrahy
Team of Instructors :
Teaching Associates :
Syllabus :(A)Introduction to Advanced Matrix Algebra: 2 hours Decomposition, Complex Matrices (B)Calculus: 16 hours
(a) Differential and Integral Calculus: Taylor’s series for function of two variables, Maxima and Minima for functions of
two variables, Evaluation of double and triple integrals , Change of order of Integration, Change of Variables, in polar,
cylindrical and spherical coordinates. 4 hours (b) Vector Calculus: Scalar and vector point functions, Gradient, Directional
Derivative, Divergence and Curl, Evaluation of line integrals , Introduction to Greens and Stoke’s theorems and their
applications. 4 hours (c) Ordinary Differential Equations: Solution of first order equations and their Applications, Newton
law of cooling, Growth and Decay, Solution of Second and higher order Differential equations . 4 hours . (C) Laplace
Transforms: Laplace and Inverse Laplace transforms and their properties. 5 hours (D) Fourier Series: Definition, Dirchelt
conditions, Fourier series for simple functions. 4 hours (E) Partial Differential Equations: Formation of PDE, Solution of
first order linear equations – Lagrange’s method, Solution of second order PDE by separation of variables . Laplace’s
equation in two dimensions. 4 hours (F) Probability and Random Variables: Probability , Addition, Multiplication and
Baye’s theorems. Random variables , Probability Distributions – Binomial, Poisson and Gaussian distributions, Introduction
to Markov process. 9 hours (G) Complex Variables : Complex functions- Exponential, Logarithmic and Trigonometric
functions , Analytic function , Cauchy - Riemann equations , Introduction to Milne Thomson method . 6 hours (H)
Algebraic Structures: Introduction to Structure of Algebras, Semi groups, Monoids and Groups, Homomorphism’s, Normal
subgroups and congruence Relations, Rings. 4 hours
Text Books :1. Erwin Kreyszig, Advanced Engineering Mathematics, John Willey & Sons, 10th edition, 2010, New Delhi,
India. 2. R.E.Walpole, R.H.Myers, S.L.Myes, Keying Ye, Probability and Statistics for Engineers and Scientists, , Pearson’s
Publications , 9th edition, 2012, USA.
Reference Books :1. B.S.Grewal, Higher Engineering ,Mathematics, 43rd Edition, Khanna Publishers, New Delhi,India 2.
Mott, J.L., Kandel, A. and Baker, T.P., Discrete Mathematics for Computer Scientists and Mathematicians, Prentice Hall of
India Private Ltd, 1986, India. 3. Tremblay J P and Manohar R, Discrete Mathematical Structures with Applications to
Computer Science, Tata McGraw Hill publishers, 1st edition, 2001, India.
Web Links :Sno Topic Web link CO-1 1 Natural law of growth and decay
https://www.maplesoft.com/applications/view.aspx?sid=1591&view=html http://www.swl.k12.oh.us/Downloads/5-
6%20Growth%20and%20Decay.pdf https://www.coursehero.com/file/25852617/5E3-Law-of-Natural-Growthpdf/ 2
Modeling and Solution of RL and RC circuits http://www.ee.nthu.edu.tw/~sdyang/Courses/Circuits/Ch07_Std.pdf
https://nptel.ac.in/courses/108105053/pdf/L-10(GDR)(ET)%20((EE)NPTEL).pdf
http://aries.ucsd.edu/najmabadi/CLASS/MAE140/NOTES/dynamic-2.pdf https://x-engineer.org/graduate-
engineering/electronics/circuits/rl-circuit-detailed-mathematical-analysis/ 3 Modeling problems on Newton’s law of cooling
https://www.math24.net/newtons-law-cooling/ https://math.stackexchange.com/questions/1360386/newtons-law-of-
cooling- example http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html CO-2 7 Modeling and solution
of LCR circuits with electromotive force https://www.intmath.com/differential-equations/5-rl-circuits.php
http://www.phys.ufl.edu/courses/phy2054/s09/lectures/2054_ch21A.pdf https://www.ijser.org/researchpaper/A-
MATHEMATICAL-MODELING-OF-GROWTH-DECAY-OF-ELECTRIC-CURRENT.pdf
https://www.simiode.org/resources/4148/download/2011-Harwood-Modeling_a_RLC_Circuit.pdf 8 Modeling and Solution
of vibration on springs
https://www.brown.edu/Departments/Engineering/Courses/En4/Notes/vibrations_free_damped/vibrations_free_damped.htm
http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx
http://www.sharetechnote.com/html/DE_Modeling_Example_SpringMass.html
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http://www.math.utah.edu/~gustafso/2250forcedOscillations.pdf CO-3 9 Fourier series Introduction and Problems

https://www.math.psu.edu/tseng/class/Math251/Notes-PDE%20pt2.pdf
https://www.stewartcalculus.com/data/CALCULUS%20Early%20Transcendentals/upfiles/FourierSeries5ET.pdf
http://exampleproblems.com/wiki/index.php/Fourier_Series http://www.cse.salford.ac.uk/physics/gsmcdonald/H-
Tutorials/Fourier-series-tutorial.pdf https://www.slideshare.net/mohammadimran85/solved-numerical-problems-of-fourier-
series 10 Half range Fourier series https://en.wikipedia.org/wiki/Half_range_Fourier_series http://documents.routledge-
interactive.s3.amazonaws.com/9780415662840/answers/UEM_Sol_to_Exerc_Chap_103.pdf
https://www.intmath.com/fourier-series/4-fourier-half-range-functions.php
https://www.math.ubc.ca/~peirce/M257_316_2012_Lecture_14.pdf 11 Solution of ODE using Fourier series
http://www.sosmath.com/fourier/fourier6/fourier6.html http://www.staff.ul.ie/burkem/Teaching/fsnotes07.pdf 12 Matrix
algebra http://ibgwww.colorado.edu/~carey/p7291dir/handouts/matrix.algebra.pdf
https://www.mathsisfun.com/algebra/matrix-introduction.html https://byjus.com/maths/what-are-matrices/ 14 LU
decomposition method https://www.geeksforgeeks.org/l-u-decomposition-system-linear-equations/
https://en.wikipedia.org/wiki/LU_decomposition http://www.math.ohiou.edu/courses/math3600/lecture12.pdf 15 Jacobi
method and Gauss seildal iteration method https://www3.nd.edu/~zxu2/acms40390F12/Lec-7.3.pdf
https://www.maa.org/press/periodicals/loci/joma/iterative-methods-for-solving-iaxi-ibi-jacobis-method
Course Rationale :The students will be recognized by the end of its course that the mathematics is based on relatively few
basic concepts and involves powerful unifying principles. The course provides a firm grasp on the interrelations among
theory, computing and experimentation. It provides proficiency in differential calculus, integral calculus, vector calculus for
translating physical problems into a mathematical form by modeling appropriate partial differential equations. The solution
of the problems requires selection of a suitable numerical tool and graphical representation of the results for interpretation.
Course Objectives :To provide a profound knowledge in engineering mathematics and necessary proficiency in solving the
application oriented problems

COURSE OUTCOMES (COs):

Blooms
CO Taxonomy
Course Outcome (CO) PO/PSO
NO Level
(BTL)
Apply differential and integral calculus to find maxima & minima of
CO1 functions, evaluate the integrals and solve the ordinary differential PO1 3
equations.
Demonstrate the Fourier series and Laplace transforms and solve the
CO2 PO1 3
Partial differential equations.
CO3 Describe probability , Random Variables and Distributions PO1 3
Explain complex variables, analytic functions and introduction to
CO4 PO1 3
stochastic process and Algebraic structures.

COURSE OUTCOME INDICATORS (COIs)::

Outcome Highest
COI-1 COI-2 COI-3
No. BTL
Btl-3
Btl-2
Determine the maxima and
Explain Taylor’s series
Btl-1 minima for a function of two
forfunction of two variables.
Recall the concept of partial variables and its applications.
Illustrate the procedure for
derivatives, Define line, double Compute the area, volume, mass
evaluation of double integral by
CO1 3 and triple integrals, gradient, and moment of inertia through
change of order of integration
directional derivative of a scalar double integral and volume of
and change of variables in
functions, divergence and curl of solids by triple integrals. Apply
multiple integrals. Explain the
vector functions. Green’s, and Stokes’s theorems
line, surface and volume
for computing the line and
integrals over the region.
volume integrals.
CO2 3 Btl-1 Btl-2 Btl-3
Define Fourier series and Describe expansion of periodic Apply Laplace and inverse
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Laplace transforms and state functions as Fourier series, solve Laplace transform technique to
their properties. ordinary differential equations solve ODE.
and Partial differential equations.
Btl-2
Btl-3
Btl-1 Illustrate the concept of
Determine the density function
CO3 3 Recall the concepts of probability, random variables and
by using continuous random
Probability and standard results. probability distributions with real
variable.
world problems.
Btl-2
Describe the complex functions, Btl-3
Btl-1
tests and construction of analytic Apply Milne-Thompson method
Define complex numbers,
CO4 3 function and also illustrate to compute Flux function, stream
variables and algebraic
algebraic structures like groups, function and the complex
structures.
semi groups, subgroups, Rings potential function.
and their properties.

PROGRAM OUTCOMES & PROGRAM SPECIFIC OUTCOMES (POs/PSOs)

Po
Program Outcome
No.
Engineering Knowledge:Apply the knowledge of mathematics, science, engineering fundamentals, and an
PO1
engineering specialization to the solution of complex engineering problems.
Problem Analysis: Identify, formulate, review research literature, and analyse complex engineering problems
PO2
reaching substantiated conclusions using first principles of mathematics, natural sciences and engineering sciences
Design/Development of Solutions: Design solutions for complex engineering problems and design system
PO3 components or processes that meet the specified needs with appropriate consideration for the public health and
safety, and the cultural, societal, and environmental considerations
Conduct Investigations of Complex Problems:Use research-based knowledge and research methods including
design of experiments, analysis and interpretation of data, and synthesis of the information to provide valid
PO4
conclusions for complex problems that cannot be solved by straightforward application of knowledge, theories and
techniques applicable to the engineering discipline.
Modern Tool Usage:Create, select, and apply appropriate techniques, resources, and modern engineering and IT
PO5
tools including prediction and modelling to complex engineering activities with an understanding of the limitations.
The Engineer and Society:Apply reasoning informed by the contextual knowledge to assess societal, health, safety,
PO6
legal and cultural issues and the consequent responsibilities relevant to the professional engineering practice.
Environment and Sustainability:Understand the impact of the professional engineering solutions in societal and
PO7
environmental contexts, and demonstrate the knowledge of, and need for sustainable development
Ethics: Apply ethical principles and commit to professional ethics and responsibilities and norms of the engineering
PO8
practice
Individual and Team Work: Function effectively as an individual, and as a member or leader in diverse teams, and
PO9
in multidisciplinary settings.
Communication:Communicate effectively on complex engineering activities with the engineering community and
PO10 with society at large, such as, being able to comprehend and write effective reports and design documentation,
make effective presentations, and give and receive clear instructions
Project Management and Finance: Demonstrate knowledge and understanding of the engineering and management
PO11 principles and apply these to one’s own work, as a member and leader in a team, to manage projects and in
multidisciplinary environments.
Life-long Learning: Recognize the need for, and have the preparation and ability to engage in independent and
PO12
lifelong learning in the broadest context of technological change.
PSO1 An ability to design and develop software projects as well as Analyze and test user requirements.
PSO2 An Ability to gain working Knowledge on emerging software tools and technologies.

Lecture Course DELIVERY Plan:

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Teaching-
Book No[CH
Sess.No. CO COI Topic Learning EvaluationComponents
No][Page No]
Methods

Explain Course Handout ,Solving ALM,End Semester

COI- system of non-homogeneous linear Exam,Home
1 CO1 T1[20]849 Chalk,PPT,Talk
1 equations by using LU Assignment,SEM-
Decomposition method EXAM1,Tutorial

ALM,End Semester
COI- Express functions of two variables as Exam,Home
2 CO1 R1[13][660] Chalk,PPT,Talk
1 Taylor’s series Assignment,SEM-
EXAM1,Tutorial

ALM,End Semester
COI- Determine extreme values for Exam,Home
3 CO1 R1[13][687] Chalk,PPT,Talk
2 functions of two variables Assignment,SEM-
EXAM1,Tutorial

ALM,End Semester
COI- Exam,Home
4 CO1 Evaluate double integrals R1[13][687] Chalk,PPT,Talk
2 Assignment,SEM-
EXAM1,Tutorial

ALM,End Semester
COI- Evaluation of double integrals by Exam,Home
5 CO1 R1[13][687] Chalk,PPT,Talk
2 change the order of integration Assignment,SEM-
EXAM1,Tutorial

ALM,End Semester
Evaluate triple integrals by change
COI- Exam,Home
6 CO1 of variables in cylindrical, polar and T1[13][647] Chalk,PPT,Talk
2 Assignment,SEM-
Spherical coordinates
EXAM1,Tutorial

ALM,End Semester
Determine the gradient, directional
COI- Exam,Home
7 CO1 derivative, divergence and curl of a T1[9][354] Chalk,PPT,Talk
2 Assignment,SEM-
vector and scalar point functions.
EXAM1,Tutorial

ALM,End Semester
COI- Compute the work done by a Force Exam,Home
8 CO1 T1[10][671] Chalk,LTC,Talk
3 field of a vector Assignment,SEM-
EXAM1,Tutorial

Apply Green’s Theorem to transform

ALM,End Semester
line integrals to surface integrals,
COI- Exam,Home
9 CO1 Apply Stokes’s Theorem to T1[10][433] Chalk,PPT,Talk
3 Assignment,SEM-
transform surface integrals to line
EXAM1,Tutorial
integral

Analytical method to solve the ALM,End Semester

COI- natural growth/decay phenomena, Exam,Home
10 CO2 T1[2][53] Chalk,PPT,Talk
1 Apply analytical methods to solve Assignment,SEM-
the Newton’s law of cooling EXAM1,Tutorial

11 CO2 COI- Solution of LCR circuits, with and T1[2][53] Chalk,PPT,Talk ALM,End Semester
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Teaching-
Book No[CH
Sess.No. CO COI Topic Learning EvaluationComponents
No][Page No]
Methods
1 without e.m.f Exam,Home
Assignment,SEM-
EXAM1,Tutorial

ALM,End Semester
COI- Solution of LCR circuits, with e.m.f Exam,Home
12 CO2 T1[2][53] Chalk,PPT,Talk
1 and oscillations of a spring Assignment,SEM-
EXAM1,Tutorial

ALM,End Semester
Laplace transforms and Inverse
COI- Exam,Home
13 CO2 Laplace transforms and their T1[6][204] Chalk,PPT,Talk
2 Assignment,SEM-
properties
EXAM1,Tutorial

ALM,End Semester
COI- Apply Laplace Transform method to Exam,Home
14 CO2 T1[6][238] Chalk,PPT,Talk
2 solve ODE Assignment,SEM-
EXAM1,Tutorial

Expansion of even/ odd periodic

ALM,End Semester
function as Fourier series in interval
COI- Exam,Home
15 CO2 of width 2π. Identify the Half range T1[11][483] Chalk,PPT,Talk
3 Assignment,SEM-
Fourier series expansion for periodic
EXAM1,Tutorial
function

Formation of partial differential

equations by eliminating the ALM,End Semester
COI- arbitrary constants and functions, T1[12] [540], Exam,Home
16 CO2 Chalk,PPT,Talk
3 Solve the linear partial differential T1[12] [543] Assignment,SEM-
equations through Lagrange’s EXAM1,Tutorial
method

ALM,End Semester
COI- Exam,Home
17 CO2 Two dimensional heat flow equation T1[12][545] Chalk,PPT,Talk
3 Assignment,SEM-
EXAM1,Tutorial

End Semester Exam,Home

COI- Baye’s theorem and their
18 CO3 R1[2][72] Chalk,PPT,Talk Assignment,SEM-
1 applications
EXAM2,Tutorial

ALM,End Semester
Describe the different types of
COI- Exam,Home
19 CO3 random variables and their R1[3][83] Chalk,PPT,Talk
1 Assignment,SEM-
probability
EXAM2,Tutorial

ALM,End Semester
COI- Applications on Binomial and Exam,Home
20 CO3 R1[5][149] Chalk,PPT,Talk
2 Poisson distributions Assignment,SEM-
EXAM2,Tutorial

21 CO3 COI- Understand the importance of R1[6][187] Chalk,PPT,Talk ALM,End Semester

2 Exam,Home
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Teaching-
Book No[CH
Sess.No. CO COI Topic Learning EvaluationComponents
No][Page No]
Methods
normal distribution in real world Assignment,SEM-
problems EXAM2,Tutorial

ALM,End Semester
Stochastic process and Markov
COI- Exam,Home
22 CO3 chain,Construction of Transition R1[6][208] Chalk,PPT,Talk
3 Assignment,SEM-
Probability Matrix
EXAM2,Tutorial

ALM,End Semester
COI- Identify the behavior of the complex Exam,Home
23 CO4 T1[13][608] Chalk,PPT,Talk
1 valued function Assignment,SEM-
EXAM2,Tutorial

ALM,End Semester
COI- Exam,Home
24 CO4 Construct the analytic function T1[13][619] Chalk,PPT,Talk
1 Assignment,SEM-
EXAM2,Tutorial

ALM,End Semester
COI- Construct the analytic function by T1[13][625], Exam,Home
25 CO4 Chalk,PPT,Talk
1 Milne-Thomson method T1[13][607] Assignment,SEM-
EXAM2,Tutorial

ALM,End Semester
COI- Structure of Algebras, Semi groups, Exam,Home
26 CO4 R3[3][270] Chalk,PPT,Talk
2 Monoids and Groups Assignment,SEM-
EXAM2,Tutorial

ALM,End Semester
COI- Group Homomorphism’s, Exam,Home
27 CO4 R3[3][319] Chalk,PPT,Talk
2 congruence Relations Assignment,SEM-
EXAM2,Tutorial

ALM,End Semester
COI- Normal subgroups and Introduction Exam,Home
28 CO4 R3[3][335] Chalk,PPT,Talk
3 to Rings Assignment,SEM-
EXAM2,Tutorial

Lecture Session wise Teaching – Learning Plan

SESSION NUMBER : 1

Session Outcome: 1 Solving system of non-homogeneous linear equations by using LU Decomposition method

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
10 Explain Course Handout 1 Talk APPLICABLE -
--
10 LU Decomposition 2 Chalk --- NOT
APPLICABLE -

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--
--- NOT
Solving system of non-homogeneous linear equations by using LU
25 3 Chalk APPLICABLE -
Decomposition method
--
--- NOT
5 Summarize the session 1 Talk APPLICABLE -
--

SESSION NUMBER : 2

Session Outcome: 2 Express functions of two variables as Taylor’s series

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
--- NOT
20 Express functions of two variables as Taylor’s series 2 Talk APPLICABLE -
--
--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
--- NOT
20 Problems on Taylor’s series expansion for function of two variables 1 Chalk APPLICABLE -
--

SESSION NUMBER : 3

Session Outcome: 3 Determine extreme values for functions of two variables

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
--- NOT
20 Determine extreme values for functions of two variables 2 Talk APPLICABLE -
--
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
--- NOT
20 Problems on extrema for functions of two variables 3 Chalk APPLICABLE -
--

SESSION NUMBER : 4

Session Outcome: 4 Evaluate double integrals

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods

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--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
--- NOT
20 Evaluate double integrals 2 Talk APPLICABLE -
--
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
--- NOT
20 Problems on double integrals 3 Chalk APPLICABLE -
--

SESSION NUMBER : 5

Session Outcome: 5 Evaluation of double integrals by change the order of integration

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
--- NOT
Evaluation of double Evaluate double integrals by change the order
20 2 Talk APPLICABLE -
of integration
--
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
--- NOT
20 Solving the problems 3 Chalk APPLICABLE -
--

SESSION NUMBER : 6

Session Outcome: 6 Evaluate triple integrals by change of variables in cylindrical, polar and Spherical coordinates

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
--- NOT
Evaluate triple integrals by change of variables in cylindrical, polar
20 2 Talk APPLICABLE -
and Spherical coordinates
--
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
--- NOT
20 Solving the problems 3 Chalk APPLICABLE -
--

SESSION NUMBER : 7

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Session Outcome: 7 Determine the gradient, directional derivative, divergence and curl of a vector and scalar point
functions.

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
--- NOT
Determine the gradient, directional derivative, divergence and curl
20 2 Talk APPLICABLE -
of a vector and scalar point functions.
--
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
--- NOT
20 Solving the related problems 3 Chalk APPLICABLE -
--

SESSION NUMBER : 8

Session Outcome: 8 Compute the work done by a Force field of a vector

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
--- NOT
20 Compute the work done by a Force field of a vector 2 Talk APPLICABLE -
--
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
--- NOT
20 Solving the related application problems 3 Chalk APPLICABLE -
--

SESSION NUMBER : 9

Session Outcome: 9 Apply Green’s Theorem to transform line integrals to surface integrals, Apply Stokes’s Theorem to
transform surface integrals to line integral

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Apply Green’s Theorem to transform line integrals to surface --- NOT
20 integrals, Apply Stokes’s Theorem to transform surface integrals to 3 Chalk APPLICABLE -
line integral --
--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
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--- NOT
20 Solving the related application problems 3 Chalk APPLICABLE -
--

SESSION NUMBER : 10

Session Outcome: 10 Analytical method to solve the natural growth/decay phenomena, Apply analytical methods to solve
the Newton’s law of cooling

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Apply analytical method to solve the natural growth/decay --- NOT
20 phenomena, Apply analytical methods to solve the Newton’s law of 3 Chalk APPLICABLE -
cooling --
--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
--- NOT
20 Solving the related application problems 3 Chalk APPLICABLE -
--

SESSION NUMBER : 11

Session Outcome: 1 Solution of LCR circuits, with and without e.m.f

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
--- NOT
20 Solution of LCR circuits, with and without e.m.f 2 Talk APPLICABLE -
--
--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
--- NOT
20 Solving the related application problems 3 Chalk APPLICABLE -
--

SESSION NUMBER : 12

Session Outcome: 2 Solution of LCR circuits, with e.m.f and oscillations of a spring

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--

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Quiz/Test
20 Solution of LCR circuits, with e.m.f and oscillations of a spring 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 13

Session Outcome: 3 Laplace transforms and Inverse Laplace transforms and their properties

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Laplace transforms and Inverse Laplace transforms and their Quiz/Test
20 2 Talk
properties Questions
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Solving problems on Laplace transforms and Inverse Laplace Quiz/Test
20 3 Chalk
transforms Questions

SESSION NUMBER : 14

Session Outcome: 4 Apply Laplace Transform method to solve ODE

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Apply Laplace Transform method to solve ODE 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 15

Session Outcome: 5 Expansion of even/ odd periodic function as Fourier series in interval of width 2π. Identify the Half
range Fourier series expansion for periodic function

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--

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Expansion of even/ odd periodic function as Fourier series in

Quiz/Test
20 interval of width 2π. Identify the Half range Fourier series 2 Talk
Questions
expansion for periodic function
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 16

Session Outcome: 6 Formation of partial differential equations by eliminating the arbitrary constants and functions, Solve
the linear partial differential equations through Lagrange’s method

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Formation of partial differential equations by eliminating the
Quiz/Test
20 arbitrary constants and functions, Solve the linear partial 2 Talk
Questions
differential equations through Lagrange’s method
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 17

Session Outcome: 7 Two dimensional heat flow equation

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Two dimensional heat flow equation 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 18

Session Outcome: 8 Baye’s theorem and their applications

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
5 Attendance/Recap; Poll/Pop Question 1 Talk --- NOT
APPLICABLE -
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--
--- NOT
20 Baye’s theorem and their applications 1 Talk APPLICABLE -
--
--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
--- NOT
20 Solving related problems 3 Chalk APPLICABLE -
--

SESSION NUMBER : 19

Session Outcome: 9 Describe the different types of random variables and their probability

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Describe the different types of random variables and their Quiz/Test
20 2 Talk
probability Questions
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 20

Session Outcome: 10 Applications on Binomial and Poisson distributions

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Applications on Binomial and Poisson distributions 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 21

Session Outcome: 1 Understand the importance of normal distribution in real world problems

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
5 Attendance/Recap; Poll/Pop Question 1 Talk --- NOT
APPLICABLE -
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--
Understand the importance of normal distribution in real world Quiz/Test
20 2 Talk
problems Questions
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 22

Session Outcome: 2 Stochastic process and Markov chain

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Stochastic process and Markov chain 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 23

Session Outcome: 3 Identify the behavior of the complex valued function

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Identify the behavior of the complex valued function 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
--- NOT
20 Solving the related application problems 2 Chalk APPLICABLE -
--

SESSION NUMBER : 24

Session Outcome: 4 Construct the analytic function

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
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Quiz/Test
20 Construct the analytic function 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 25

Session Outcome: 5 Construct the analytic function by Milne-Thomson method

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Construct the analytic function by Milne-Thomson method 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 2 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 26

Session Outcome: 6 Structure of Algebras, Semi groups, Monoids and Groups

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Structure of Algebras, Semi groups, Monoids and Groups 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 2 Chalk
Questions

SESSION NUMBER : 27

Session Outcome: 7 Group Homomorphism’s, congruence Relations

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Group Homomorphism’s, congruence Relations 2 Talk
Questions
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--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

SESSION NUMBER : 28

Session Outcome: 8 Normal subgroups and Introduction to Rings

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Normal subgroups and Introduction to Rings 2 Talk
Questions
--- NOT
5 Break out rooms/poll questions 1 Talk APPLICABLE -
--
Quiz/Test
20 Solving the related application problems 3 Chalk
Questions

Tutorial Course DELIVERY Plan:

List of Experiments supposed to finish in Open Lab Sessions:

Lab
session List of Experiments CO-Mapping
no

Determine solution of non-homogeneous linear equations by using LU Decomposition

1 method, Taylor’s series for functions of two variables & extreme values for functions of CO1
two variables

2 Evaluate double and triple integrals CO1

Scalar and vector point functions, Gradient, Directional Derivative, Divergence and Curl,
3 CO1
work done by a force field, surface integral, Greens theorem, Stokes theorem

Apply modeling an engineering problem as a first and second order ordinary differential
4 CO2
equation (ODE)

Laplace and Inverse Laplace transform of a function, Solutions of ODE by using Laplace
5 CO2
Transforms

Fourier series expansion for even and odd functions, Formation and Solution of partial
6 CO2
differential equations through Lagrange’s and method, Method of separation of variables

7 Apply Baye’s rule Binomial distribution to the engineering applications CO3

8 Apply Poisson, Normal Distribution distribution to the engineering applications CO3

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Lab
session List of Experiments CO-Mapping
no

9 Markov Process and Construction of Transition Probability Matrix CO3

10 Construct the analytic function CO4

11 Structure of Algebras, Groups CO4

12 Homomorphisms of Groups CO4

13 Revision Problems covering all CO's CO4

Tutorial Session wise Teaching – Learning Plan

SESSION NUMBER : 1

Session Outcome: 1 Determine solution of non-homogeneous linear equations by using LU Decomposition method,
Taylor’s series for functions of two variables & extreme values for functions of two variables

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Determine solution of non-homogeneous linear equations by using --- NOT
20 LU Decomposition method, Taylor’s series for functions of two 3 Chalk APPLICABLE -
variables & extreme values for functions of two variables --
--- NOT
25 Practice problems 3 Chalk APPLICABLE -
--

SESSION NUMBER : 2

Session Outcome: 2 Evaluate double and triple integrals

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Evaluate double and triple integrals 2 Talk
Questions
Quiz/Test
25 Practice problems 3 Chalk
Questions

SESSION NUMBER : 3

Session Outcome: 3 Scalar and vector point functions, Gradient, Directional Derivative, Divergence and Curl, work done
by a force field, surface integral, Greens theorem, Stokes theorem

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Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Scalar and vector point functions, Gradient, Directional Derivative,
Quiz/Test
20 Divergence and Curl, work done by a force field, surface integral, 2 Talk
Questions
Greens theorem, Stokes theorem
Quiz/Test
25 Practice Problem 3 Chalk
Questions

SESSION NUMBER : 4

Session Outcome: 4 Apply modeling an engineering problem as a first and second order ordinary differential equation
(ODE)

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Apply modeling an engineering problem as a first and second order Quiz/Test
20 2 Talk
ordinary differential equation (ODE) Questions
Quiz/Test
25 Practice problems 3 Chalk
Questions

SESSION NUMBER : 5

Session Outcome: 5 Laplace and Inverse Laplace transform of a function, Solutions of ODE by using Laplace Transforms

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Laplace and Inverse Laplace transform of a function, Solutions of Quiz/Test
20 2 Talk
ODE by using Laplace Transforms Questions
Quiz/Test
25 Practice problems 3 Chalk
Questions

SESSION NUMBER : 6

Session Outcome: 6 Fourier series expansion for even and odd functions, Formation and Solution of partial differential
equations through Lagrange’s and method, Method of separation of variables

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
20 Fourier series expansion for even and odd functions, Formation and 2 Talk Quiz/Test
Solution of partial differential equations through Lagrange’s and Questions
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method, Method of separation of variables

Quiz/Test
25 Practice problems 3 Chalk
Questions

SESSION NUMBER : 7

Session Outcome: 7 Apply Baye’s rule Binomial distribution to the engineering applications

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Apply Baye’s rule Binomial distribution to the engineering Quiz/Test
20 2 Talk
applications Questions
Quiz/Test
25 Practice problems 3 Chalk
Questions

SESSION NUMBER : 8

Session Outcome: 8 Apply Poisson, Normal Distribution distribution to the engineering applications

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Apply Poisson, Normal Distribution distribution to the engineering Quiz/Test
20 2 Talk
applications Questions
Quiz/Test
25 Practice problems 3 Chalk
Questions

SESSION NUMBER : 9

Session Outcome: 9 Markov Process and Construction of Transition Probability Matrix

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Markov Process and Construction of Transition Probability Matrix 2 Talk
Questions
Quiz/Test
25 Practice problems 3 Chalk
Questions

SESSION NUMBER : 10

Session Outcome: 10 Construct the analytic function

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods

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--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Construct the analytic function 2 Talk
Questions
Quiz/Test
25 Practice problems 3 Chalk
Questions

SESSION NUMBER : 11

Session Outcome: 1 Structure of Algebras, Groups

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Structure of Algebras, Groups 2 Talk
Questions
Quiz/Test
25 Practice problems 3 Chalk
Questions

SESSION NUMBER : 12

Session Outcome: 2 Homomorphisms of Groups

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Chalk APPLICABLE -
--
Quiz/Test
20 Homomorphisms of Groups 2 Talk
Questions
Quiz/Test
25 Practice problems 3 Talk
Questions

SESSION NUMBER : 13

Session Outcome: 1 Revision Problems covering all CO's

Teaching-
Active Learning
Time(min) Topic BTL Learning
Methods
Methods
--- NOT
5 Attendance/Recap; Poll/Pop Question 1 Talk APPLICABLE -
--
Quiz/Test
20 Revision 1 Talk
Questions
Quiz/Test
25 Revision Problems covering all CO's 1 Talk
Questions

Practical Course DELIVERY Plan: NO Delivery Plan Exists

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Practical Session wise Teaching – Learning Plan

No Session Plans Exists

Skilling Course DELIVERY Plan: NO Delivery Plan Exists

Skilling Session wise Teaching – Learning Plan

No Session Plans Exists

WEEKLY HOMEWORK ASSIGNMENTS/ PROBLEM SETS/OPEN ENDEDED PROBLEM-SOLVING EXERCISES etc:

Assignment Assignment
Week Topic Details co
Type No

COURSE TIME TABLE:

Hour 1 2 3 4 5 6 7 8 9
Day Component
Theory H-S2,H-S6 --- H-S3,H-S4 --- --- --- --- --- ---
Tutorial -- --- -- --- --- --- --- --- ---
Mon
Lab -- --- -- --- --- --- --- --- ---
Skilling -- --- -- --- --- --- --- --- ---
Theory H-S2 --- H-S3,H-S4 --- --- --- --- --- ---
Tutorial -- --- -- --- --- --- --- --- ---
Tue
Lab -- --- -- --- --- --- --- --- ---
Skilling -- --- -- --- --- --- --- --- ---
Theory H-S1 --- --- H-S6 --- --- --- --- ---
Tutorial H-S2 --- --- -- --- --- --- --- ---
Wed
Lab -- --- --- -- --- --- --- --- ---
Skilling -- --- --- -- --- --- --- --- ---
Theory H-S7 --- H-S1 --- --- -- --- --- ---
Tutorial -- --- H-S6 --- --- H-S4 --- --- ---
Thu
Lab -- --- -- --- --- -- --- --- ---
Skilling -- --- -- --- --- -- --- --- ---
Theory H-S5,H-S7 --- -- --- --- --- --- --- ---
Tutorial -- --- H-S1 --- --- --- --- --- ---
Fri
Lab -- --- -- --- --- --- --- --- ---
Skilling -- --- -- --- --- --- --- --- ---
Theory -- --- H-S5 --- --- -- --- --- ---
Tutorial H-S3 --- H-S7 --- --- H-S5 --- --- ---
Sat
Lab -- --- -- --- --- -- --- --- ---
Skilling -- --- -- --- --- -- --- --- ---
Theory -- -- -- -- -- -- -- -- --
Tutorial -- -- -- -- -- -- -- -- --
Sun
Lab -- -- -- -- -- -- -- -- --
Skilling -- -- -- -- -- -- -- -- --

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REMEDIAL CLASSES:

Supplement course handout, which may perhaps include special lectures and discussions that would be planned, and
schedule notified according

SELF-LEARNING:

Assignments to promote self-learning, survey of contents from multiple sources.

S.no Topics CO ALM References/MOOCS

DELIVERY DETAILS OF CONTENT BEYOND SYLLABUS:

Content beyond syllabus covered (if any) should be delivered to all students that would be planned, and schedule notified
accordingly.
Advanced Topics, Additional Reading, Research papers
S.no CO ALM References/MOOCS
and any

EVALUATION PLAN:

Evaluation Assessment Duration

Evaluation Component Weightage/Marks CO1 CO2 CO3 CO4
Type Dates (Hours)
End Semester
Weightage 40 10 10 10 10
Summative
End Semester Exam 180
Evaluation
Max Marks 100 25 25 25 25
Total= 40 %
In Semester Weightage 18 9 9
Semester in Exam-I 90
Summative Max Marks 50 25 25
Evaluation Weightage 18 9 9
Total= 36 % Semester in Exam-II Max Marks 50
90
25 25
Weightage 8 2 2 2 2
ALM 50
In Semester Max Marks 100 25 25 25 25
Formative Weightage 8 2 2 2 2
Tutorial 50
Evaluation Max Marks 100 25 25 25 25
Total= 24 % Weightage 8 2 2 2 2
Home Assignment and
10
Textbook Max Marks 100 25 25 25 25

ATTENDANCE POLICY:

Every student is expected to be responsible for regularity of his/her attendance in class rooms and laboratories, to appear in
scheduled tests and examinations and fulfill all other tasks assigned to him/her in every course
In every course, student has to maintain a minimum of 85% attendance to be eligible for appearing in Semester end
examination of the course, for cases of medical issues and other unavoidable circumstances the students will be condoned if
their attendance is between 75% to 85% in every course, subjected to submission of medical certificates, medical case file
and other needful documental proof to the concerned departments

DETENTION POLICY :

In any course, a student has to maintain a minimum of 85% attendance and In-Semester Examinations to be eligible for
appearing to the Semester End Examination, failing to fulfill these conditions will deem such student to have been detained
in that course.

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PLAGIARISM POLICY :

Supplement course handout, which may perhaps include special lectures and discussions

COURSE TEAM MEMBERS, CHAMBER CONSULTATION HOURS AND CHAMBER VENUE DETAILS:

Supplement course handout, which may perhaps include special lectures and discussions
Chamber
Delivery Sections Chamber Chamber Signature of
Consultation
Name of Faculty Component of of Consultation Consultation Course
Timings for each
Faculty Faculty Day (s) Room No: faculty:
day
MALLESH 1-MA,3-
MARDANPALLY L MA,5- - - - -
PEDDA MA
MALLESH 3-MA,5-
MARDANPALLY T MA,1- - - - -
PEDDA MA
2-MA,4-
KALYAN
L MA,7- - - - -
PALAPARTHI
MA
2-MA,4-
KALYAN
T MA,7- - - - -
PALAPARTHI
MA
Krushnachandra
L 6-MA - - - -
Panigrahy
Krushnachandra
T 6-MA - - - -
Panigrahy

GENERAL INSTRUCTIONS

Students should come prepared for classes and carry the text book(s) or material(s) as prescribed by the Course Faculty to
the class.

NOTICES

Most of the notices are available on the LMS platform.

All notices will be communicated through the institution email.

All notices concerning the course will be displayed on the respective Notice Boards.

Signature of COURSE COORDINATOR

(Krushnachandra Panigrahy)

Signature of Department Prof. Incharge Academics & Vetting Team Member

Department Of FED-HYD

HEAD OF DEPARTMENT:

Approval from: DEAN-ACADEMICS

(Sign with Office Seal) [object HTMLDivElement]
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