Linear Algebra,complex variable functions

**Course Description:**

This course introduces the topics involving: Linear Algebra, Complex variable functions, Ordinary

Differential Equations and their applications. The course starts with algebra of matrix, systems of

linear equations and with preliminary course on complex variable. It introduces the CR equation,

analytic function, Taylor and Laurent series expansions and determination of residues. Emphasis also

placed on the development of concepts and applications for first and second order ordinary differential

equations (ODE), systems of differential equations and Laplace transforms.

**Course Objectives:**

1. To solve the system of linear equations, and develop orthogonal transformation with emphasis on the role of eigen-values and eigen-vectors.

2. To analyze the function of complex variable and its analytic property with a review of elementary complex function.

3. To understand the Taylor and Laurent expansion with their use in finding out the residue and improper integral.

4. To identify important characteristics of ODE and develop appropriate method of obtaining solutions of ODE.

5. Explore the use of ODE as models in various applications to solve initial value problems by using

Laplace transform method.

**UNIT I: MATRICES**

Symmetric, Skew-symmetric and Orthogonal matrices, Determinants, System of linear equations,Inverse and rank of a matrix, Rank-nullity theorem, Eigen values and eigenvectors, Diagonalization of matrices, Cayley-Hamilton Theorem, and Orthogonal transformation.(12)

**UNIT II: COMPLEX VARIABLE – DIFFERENTIATION**

Differentiation, Cauchy-Riemann equations, Analytic function, Harmonic functions, finding harmonicconjugate, Elementary analytic functions (exponential, trigonometric, logarithm) and their

properties.(12)

**UNIT III: COMPLEX VARIABLE – INTEGRATION**

Contour integrals, Cauchy-Goursat theorem (without proof), Cauchy integral formula (without proof),Liouville’s and Maximum-Modulus theorem (without proof); Taylor’s series, Zeros of analyticfunctions, Singularities, Laurent’s expansion (without proof), Residues, Cauchy Residue theorem (without proof), Evaluation of definite integral involving sine and cosine, Evaluation of certain improper integrals using the Bromwich contour.(12)

**UNIT IV: FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS**

Exact, Linear and Bernoulli’s, Equations not of first degree: equations solvable for p, equations solvable for x, equations solvable for y and Clairaut’s type.(12)

**UNIT V: ORDINARY DIFFERENTIAL EQUATIONS OF HIGHER ORDERS**

Second order linear differential equations with variable coefficients, Method of variation of parameters, Laplace Transform, Inverse Laplace transform, Bromwich contour method,and its applications to solve ordinary differential equations.(12)

**Text books:**

1. Higher Engineering Mathematics by Dr. B.S. Grewal, 42nd Edition, Khanna Publishers.

2. Complex variables and applications by R. V Churchill and J. W. Brown, 8th edition, 2008,

McGraw-Hill.

3. Differential Equations with applications and historical notes by G.F. Simmonssecond edition,

McGraw Hill, 2003.

**References:**

1. Elementary linear Algebra by Stephen Andrilli and David Hecker, 4th Edition, Elsevier, 2010

2. Ordinary and partial differential equations. By M.D. Raisinghania, 2013. S. Chand Publishing.

3. Linear Algebra and its Applications by D.C. Lay, 3rd edition, Pearson Education, Inc.

**Course outcomes**

Students are able to

1. Solve the systems of linear equations occurring in engineering system.

2. Determine harmonic function, velocity potential and stream lines in fluid flow systems.

3. Evaluate a contour integral and definite integral involving exponential, sine and cosine functions.

4. Find general solutions to first and second order homogeneous differential equations by algebraic

and computational methods.

5. Determine the solution of ODE of second and higher order.

ELECTRICAL ENGINEERING

**Course Description:**

The laboratory facilitates the students to deal with electrical instruments which further strengthen the

concepts & operation of various AC & DC circuits, and machines, and their characteristics. The lab

also reinforce the concepts discussed in class with a hands-on approach which enable the students to

gain significant experience with electrical instruments such as ammeter, voltmeter, digital

multimeters, oscilloscopes, tachometer, switches, fuses and power supplies.

**Course Objectives:**

1. To provide hands on experience in setting up simple electrical circuits (DC and AC).

2. To get exposure to handle different electrical equipment’s.

3. To measure various electrical parameters with different measuring instruments.

4. To get hands on experience in operating DC and AC machines.

5. To understand the operation of basic converters and various components of LT Switchgear.

**LIST OF LABORATORY EXPERIMENTS/DEMONSTRATIONS:**

**DEMONSTRATIONS:**

1. Basic safety precautions. Introduction and use of measuring instruments – voltmeter, ammeter,

multi-meter, oscilloscope. Study of passive components – resistors, capacitors and inductors.

2. Demonstration of voltage and current relationships (line-line voltage, phase-to-neutral voltage,

line and phase currents). In star and delta connections.

3. Demonstration of cutout sections of transformer and DC & AC machines.

4. Demonstration of induction machine. Motor operation and generator operation of an induction

machine driven at super-synchronous speed.

5. Familiarization of (i) different types of cables/wires and switches and their uses, (ii) different

types of fuses & fuse carriers; MCB, ELCB, MCCB their ratings and uses (components of LT

switchgear).

**EXPERIMENTS:**

1. Wiring of a simple circuit for controlling (1) a lamp/fan point, (2) Staircase or Corridor Winding.

2. Wiring of a power circuit for controlling an electrical appliance (16A Socket).

3. Verification of Kirchhoff’s current and voltage laws (KCL & KVL).

4. Verification of superposition theorem

5. Sinusoidal steady state response of R-L, and R-C circuits (impedance calculation and verification).

6. Measurement of voltage, current and power in a single phase circuit using voltmeter, ammeter and

wattmeter. Also, calculate the power factor of the circuit.

7. Measurement of active power for star and delta connected balanced loads (single wattmeter

method).

8. Open-circuit and short-circuit test on a single phase transformer.

9. Speed control of separately excited DC motor.

10. Wiring of a power distribution arrangement using single phase MCB distribution board with

ELCB, main switch and energy meter (or residential house wiring).

11. Regulated power supply for generating a constant DC Voltage.

12. Fabrication of a given electronic circuit on a PCB and test the same.

**Course Outcomes:**

Upon successful completion of the course, the students are expected to

1. Get an exposure to common electrical components and their ratings.

2. Make electrical connections by wires of appropriate ratings.

3. Understand the usage of common electrical measuring instruments.

4. Understand the basic characteristics of transformers and electrical machines.

5. Get an exposure to the working of various power electronic converters.

**Course Description:**

Physics Practical course is meant for making the students to gain practical knowledge to co relate with

the theoretical studies. It covers experiments on Principles of Mechanics and Optics, Measurement of

Magnetic field and studying Resonance using LCR Circuit.

**Course Objectives:**

1. Elucidate the concepts of Physics through involvement in the experiment by applying theoretical

knowledge.

2. Illustrate the basics of mechanics, waves and optics to analyze the behavior and characteristics of

various materials for its optimum utilization.

3. Develop an ability to apply the knowledge of physics experiments in the later studies.

**LIST OF EXPERIMENTS:** (Any 10 Out of 18)

1. Spring constant – Coupled Pendulums.

2. Study of resonance effect in series and parallel LCR circuit.

3. Determination of radius of curvature of a curved surface – Newton’s Rings.

4. Wavelength of a laser – Diffraction Grating

5. Wavelength of the spectral lines – Diffraction Grating.

6. Magnetic field along the axis of a current carrying coil – Stewart Gees’ Apparatus

7. Ferroelectric hysteresis (B-H Curve).(ECE)

8. Thickness of a given wire – Wedge Method.

9. Determination of Planck’s constant. (EEE, CSE, CSIT, CST)

10. Dispersive power of prism – Spectrometer.

11. Frequency of the tuning fork – Melde’s apparatus.

12. Energy gap of a material of p-n junction. (EEE, CSE, CSIT, CST)

13. Width of single slit – Diffraction due to Single Slit.

14. Measurement of e/m of electron (Helical Coil method) (ECE)

15. Biot -Savart Law with Helmholtz Coil. (ECE)

16. The Wheatstone Bridge. (ECE)

17. Determination of particle size using Laser.

18. Torsional Pendulum. (ME & Civil)

**Course Outcomes:**

Upon successful completion of this course, the students should be able to:

1. Apply the scientific process in the conduct and reporting of experimental investigations.

2. Understand measurement technology, usage of new instruments and real time applications in

engineering studies.

3. Verify the theoretical ideas and concepts covered in lecture by doing hands on in the experiments.

4. Know about the characteristics of various materials in a practical manner and gain knowledge

about various optical technique methods.

5. Acquire and interpret experimental data to examine the physical laws.

**Reference Books:**

1. Physics Laboratory Manual

2. Optics, A. Ghatak, 4th Edition, Tata McGraw-Hill, New Delhi 2011.

3. Fundamentals of Optics, F. A. Jenkins and H. E. White, 4th edition, McGraw-Hill Inc., 1981.

4. Engineering Mechanics, 2nd ed. — MK Harbola

5. Introduction to Electrodynamics- David J Griffiths

**Course Description:**

Python is a language with a simple syntax, and a powerful set of libraries. It is an interpreted

language, with a rich programming environment. While it is easy for beginners to learn, it is widely

used in many scientific areas for data exploration. This course is an introduction to the Python

programming language for students without prior programming experience. This course provides

knowledge on how to implement programs in python language and to solve computational problems

using the various programming constructs including data structures, functions, string handling

mechanisms and file handling concepts.

**Course Objectives:**

1. Learn Python programming constructs.

2. Implement Python programs with conditional structures and loops.

3. Use functions for structuring Python programs.

4. Handle compound data using Python lists, tuples, and dictionaries.

5. Manipulate data using files handling in Python.

**UNIT-I**

Introduction: Algorithms, building blocks of algorithms (flow chart), History of Python, features of

Python Programming, Running Python Scripts, Variables, Assignment, Keywords, Input-Output,

Indentation. Data Types – Integers, Strings, Boolean.

a) Develop a flowchart for the various arithmetic operations on numbers.

b) Develop a flowchart to check whether the number is positive or negative.

c) Develop a flowchart for finding whether a given number is even or odd.

d) Develop a flowchart for finding biggest number among three numbers.

e) Develop a flowchart for displaying reversal of a number.

f) Develop a flowchart to print factorial of a number using function.

g) Develop a flowchart to generate prime numbers series up to N using function.

h) Develop a flowchart to check given number is palindrome or not using function.

i) Alexa travelled 150 kms by train. How much distance in miles she actually covered?

(12)

**UNIT-II**

Operators and Expressions: Operators- Arithmetic Operators, Comparison (Relational) Operators,

Assignment Operators, Logical Operators, Bitwise Operators, Membership Operators, Identity

Operators, Expressions and order of evaluations .Control Flow – if, if-elif-else, for,

while,break,continue,pass.

a) Swapping of two number with and without using temporary variable.

b) If the age of Ram, Sam, and Khan are input through the keyboard, write a python program to

determine the eldest and youngest of the three.

c) Develop a program that performs arithmetic operations (Addition, Subtraction, Multiplication,

and Division) on integers. Input the two integer values and operator for performing arithmetic

operation through keyboard. The operator codes are as follows:

For code ‘+’, perform addition.

For code ‘-‘, perform subtraction.

For code ‘*’, perform multiplication.

For code ‘/’, perform division.

d) Implement the python program to generate the multiplication table.

e) Implement Python program to find sum of natural numbers

f) If the first name of a student is input through the keyboard, write a program to display the

vowels and consonants present in his/her name.

g) The marks obtained by a student in 5 different subjects are input through the keyboard. Find

the average and print the student grade as per the MITS examination policy as shown below.

% OBTAINED GRADE

90 – 100 O (Outstanding)

80 – 89 A+ (Excellent)

70 – 79 A (Very Good)

60 – 69 B+ (Good)

50 – 59 B (Above)

45 – 49 C (Average)

40 – 44 P (Pass)

< 40 F (Fail)

h) Implement Python Script to generate prime numbers series up to N.

i) Given a number x, determine whether it is Armstrong number or not. Hint: For example, 371

is an Armstrong number since 3**3 + 7**3 + 1**3 = 371. Write a program to find all

Armstrong number in the range of 0 and 999.

(12)

**UNIT-III**

Data Structures Lists – Operations, Slicing, Methods; Tuples, Sets, Dictionaries, Sequences.

Comprehensions. Functions – Defining Functions, Calling Functions, Passing Arguments, variable in

python-Global and Local Variables.

a) Write a Python script to

create a list

access elements from a list

slice lists

change or add elements to a list

delete or remove elements from a list

b) Write a Python script to read the values from a list and to display largest and smallest numbers

from list.

c) Write a Python script to compute the similarity between two lists.

d) Write a Python script to read set of values from a Tuple to perform various operations.

e) Write a Python script to perform basic dictionary operations like insert, delete and display.

f) Write a Python program to count the occurrence of each word in a given sentence.

g) Define a dictionary named population that contains the following data.

Keys Values

Shanghai 17.8

Istanbul 13.3

Karachi 13.0

Mumbai 12.5

h) Write a Python script to create Telephone Directory using dictionary and list to perform basic

functions such as Add entry, Search, Delete entry, Update entry, View and Exit.

Dept. of Mechanical Engineering Page 27

i) Implement Python script to display power of given numbers using function.

j) Implement a Python program that takes a list of words and returns the length of the longest

one using function. (12)

**UNIT-IV**

String Handling -Modules: Creating modules, import statement, from.import statement, name

spacing-Files and Directories

a) Implement Python program to perform various operations on string using string libraries.

b) Implement Python program to remove punctuations from a given string.

c) Write a Python program to change the case of the given string (convert the string from lower

case to upper case). If the entered string is “computer”, your program should output

“COMPUTER” without using library functions.

d) Implement Python program to capitalize each word in a string. For example, the entered

sentence “god helps only people who work hard” to be converted as “God Helps Only People

Who Work Hard”

e) Write a Python script to display file contents.

f) Write a Python script to copy file contents from one file to another.

g) Write a Python script to combine two text files contents and print the number of lines,

sentences, words, characters and file size.

h) Write a Python commands to perform the following directory operations.

List Directories and Files

Making a New Directory

Renaming a Directory or a File

Removing Directory or File

(12)

**UNIT-V**

Python packages, Introduction to PIP, Installing Packages via PIP(Numpy, Pandas etc.., Using

PythonPackages.

Brief Tour of the Standard Library – Dates and Times, Data Compression, Turtle Graphics.

(10)

a) Create a package named Cars and build three modules in it namely, BMW, Audi and Nissan.

Illustrate the modules using class. Finally we create the __init__.py file. This file will be placed

inside Cars directory and can be left blank or we can put the initialization code into it.

b) Write a python script to display following shapes using turtle.

(12)

**Course Outcomes:**

At the end of the course, students will be able to

1. Understand problem solving techniques and their applications

2. Understand the syntax and semantics of python.

3. Demonstrate the use of Python lists and dictionaries.

4. Demonstrate the use of Python File processing, directories.

5. Describe and apply object-oriented programming methodology and Standard Library.

**Text Book:**

1. Allen B. Downey, “Think Python: How to Think Like a Computer Scientist’’, 2nd edition,

Updated for Python 3, Shroff/O’Reilly Publishers, 2016 (http://greenteapress.com/wp/thinkpython/)

2. Guido van Rossum and Fred L. Drake Jr, “An Introduction to Python – Revised and

updated for Python 3.2, Network Theory Ltd., 2011.

**References:**

1. Charles Dierbach, “Introduction to Computer Science using Python: A Computational Problem-

Solving Focus, Wiley India Edition, 2013.

2. John V Guttag, “Introduction to Computation and Programming Using Python’’, Revised and

expanded Edition, MIT Press , 2013.

3. Kenneth A. Lambert, “Fundamentals of Python: First Programs”, CENGAGE Learning, 2012.

4. Paul Gries, Jennifer Campbell and Jason Montojo, “Practical Programming: An Introduction to

Computer Science using Python 3”, Second edition, Pragmatic Programmers,LLC,2013.

5. Robert Sedgewick, Kevin Wayne, Robert Dondero, “Introduction to Programming in Python: An

Inter-disciplinary Approach, Pearson India Education Services Pvt. Ltd., 2016.

**Course Description:**

This course equips the students with a basic understanding of Electrical circuits and machines for

specific applications. In specific, the course covers basic of DC circuit & its analysis, introduction to

single-phase and three-phase AC Systems, magnetic circuits, transformers, DC & AC electrical

machines, basic converters and Components of LT Switchgear.

**Course Objectives:**

1. To learn the basics of the D.C. circuit analysis.

2. To have an idea about single-phase and three-phase A.C. electrical circuits.

3. To gain knowledge about basic magnetic circuits and transformers.

4. To learn the construction and operation of D.C. and A.C. machines.

5. To understand the operation of basic rectifiers and various components of LT Switchgear.

**UNIT I: DC CIRCUIT ANALYSIS**

Electrical circuit elements (R, L and C), voltage and current sources, Series and parallel resistive

circuits, Kirchhoff’s current and voltage laws, Nodal and Mesh analysis of simple circuits with dc

excitation. Source Transformation, Star-Delta Transformation, Superposition Theorem.

(9)

**UNIT II: AC CIRCUIT ANALYSIS**

Representation of sinusoidal waveforms, peak and rms values, phasor representation, real power,

reactive power, apparent power, power factor. Analysis of single-phase ac circuits consisting of R, L,

C, RL, RC, RLC combinations. Three phase balanced circuits, voltage and current relations in star and

delta connections. (9)

**UNIT III: MAGNETIC MATERIALS AND TRANSFORMERS**

Magnetic materials, B-H characteristics, ideal and practical transformer, principle of operation, emf

equation, equivalent circuit, losses in transformers, regulation and efficiency. (9)

**UNIT IV: DC AND AC MACHINES**

Construction, working, emf equation of DC generator, methods of excitation, speed control of dc

motor. Generation of rotating magnetic fields, construction and working of a three-phase induction

motor.Introduction of Single-phase induction motor. Introduction to Alternators.

(9)

**UNIT V: RECTIFIERS AND ELECTRICAL INSTALLATIONS**

PN junction diode, half wave, full wave and bridge rectifiers.Components of LT Switchgear: switch

fuse unit (SFU), MCB, ELCB, MCCB, types of wires and cables, earthing. (9)

**Course Outcomes:**

Upon successful completion of the course, students will be able to

1. To understand and analyze basic DC electric circuits.

2. To measure and analyze various electrical quantities of single phase and three AC electric circuits.

3. To develop magnetic circuits to experiment and analyze the transformers.

4. To study the working principles of electrical machines.

5. To create power converters for domestic applications with LT switchgear.

**Text Books:**

1. E. Hughes, “Electrical and Electronics Technology”, Pearson, 2010.

2. D. P. Kothari and I. J. Nagrath, “Basic Electrical Engineering”, Tata McGraw Hill, 2010.

3. D. C. Kulshreshtha, “Basic Electrical Engineering”, McGraw Hill, 2009.

4. L. S. Bobrow, “Fundamentals of Electrical Engineering”, Oxford University Press, 2011.

5. V. D. Toro, “Electrical Engineering Fundamentals”, Prentice Hall India, 1989.

**References:**

1. Abhijit Chakrabarti, “Circuit Theory : Analysis and Synthesis”, Dhanpat Rai & Co., 2014

2. J.B. Gupta, “Theory & Performance of Electrical Machines”, S. K. Kataria& Sons, 2013.

3. John Bird, “Electrical Circuit Theory and Technology”, Fourth edition, Elsevier Ltd., 2010.

**Course Description:** Engineering Physics for Civil and Mechanical Engineersis a physics course

which provides fundamental knowledge to understand the concepts of mechanics, waves and

oscillations, interference, diffraction, and lasers.

**Course Objectives:**

1. Expose students to the fundamental principles and laws of mechanics in Physics to understand the

types of motion.

2. Demonstrate the ability to identify and apply the appropriate analytic, numerical, and

mathematical reasoning, to situations of the physical world.

3. Analyze the concepts of mechanics, oscillations, waves and optics to prepare the students for

advanced level courses.

4. Expose students to theoretical and mathematical aspects of interference and diffraction of light for

testing of materials.

5. Adaptability to new developments in science and technology.

**UNITI: MECHANICS OF PARTICLES**

Velocity and Acceleration, Motion in one dimension, several dimensions, formal solution of

kinematical equations. Polar Co-ordinates, velocity and acceleration in polar coordinates. Newton’s

Laws, applications of Newton’s laws (Constraint equations, Block on string, Conical Pendulum,

Block and Wedge). (12)

**UNITII: MOMENTUM & WORK ENERGY**

Momentum, law of conservation of linear momentum, flow of mass, Rocket Equation, Rocket in free

space and in a gravitational field. Integrating equation of motion in one-dimension-work energy

theorem, orbital velocity and escape velocity,Potential energy, Potential energy of a uniform force

field, potential energy of an inverse square force, stability, conservation laws and particle collisions.

**UNITIII: WAVES AND OSCILLATIONS**

Simple Harmonic Motion, damped harmonic oscillations, forced harmonic oscillations, resonance,

and quality factor. Superposition of vibrations along same direction (equal frequency) and in

perpendicular directions, Lissajous figures. Transverse waves, solution of wave equation, velocity of a

transverse wave along a stretched string, modes of vibration of stretched string, standing waves,

standing wave ratio. (12)

**UNITIV: INTERFERENCE & DIFFRACTION**

Interference of light by division of wavefront- Young’s double slit experiment, expression for fringe

width, intensity distribution graph, interference of light by division of amplitude- interference in thin

film by reflection, Newton’s rings experiment, Michelson interferometer, applications of Interference

(colours of thin films). Diffraction, Farunhofer diffraction due to single slit, double slit and,

Diffraction grating (N-slit),applications of Diffraction (List only)

(12)

**UNITV: LASERS**

Introduction to Lasers, characteristics of Laser, interaction of radiation with matter-spontaneous and

stimulated emission, Einstein’s coefficients; amplification of light by population inversion, excitation

mechanism, types of lasers: solid-state lasers – ruby laser, gas lasers – He-Ne Laser, semiconductor pn

junction diode laser;applications of lasers.

(12)

**Course Outcomes:**

Upon successful completion of this course, the students should be able to:

1. Describe and explain the fundamental physical principles and laws of Mechanics in Physics.

2. Explain the concepts conservation of momentum, energy, and predict the future state of a system

based on its present state.

3. Apply the physical principles of waves together with logical and mathematical reasoning, to

situations of the physical world of vibrations.

4. Define and evaluate the fundamentals of materials testing using Interference and Diffraction

techniques.

5. Identify the working elements of different lasers and estimate laser operation parameters.

**Text Books:**

1. An Introduction to Mechanics, by D. Kleppner and R. Kolenkow, Tata McGraw-Hill Edition,

2007.

2. H. J. Pain, “The physics of vibrations and waves”, Wiley, 2006.

3. A. Ghatak, “Optics”, McGraw Hill Education, 2012.

4. O. Svelto, “Principles of Lasers”, Springer Science & Business Media, 2010.

**Reference Books:**

1. Physics Vol I & II, Halliday/Resnick/Krane 5th Edition, John Wiley, 2003.

2. Berkeley Physics Course Volume I, Tata-McGraw Hill.

3. Engineering Mechanics, 2nd ed. — MK Harbola

4. Introduction to Mechanics — MK Verma

5. Theory of Vibrations with Applications — WT Thomson

**Course Description**

The course introduces the concepts of single variable and multivariable calculus with the view of its

applications in various engineering fields. It prepares the students to develop various methods of

finding derivatives and integrals; understanding of concepts related to continuous functions and enrich

their experience in critical analysis.

**Course Objectives**

1. To introduce the basic concepts of definite integrals and its applications, Beta and Gamma

functions,

2. To acquire knowledge on mean value theorems in calculus.

3. To illustrate various techniques of testing the convergence of infinite series and introduces the

functions of sine and cosine series.

4. To familiarize the knowledge of limit, continuity and derivatives, extreme values in multivariable.

5. To emphasize the role of Double and Triple integrals in dealing with area and volume of the

regions.

**UNIT I:INTEGRALCALCULUS**

Definite integrals; Applications of definite integrals to evaluate area and length of curves, surface

areas and volumes of revolutions; Beta and Gamma functions and their properties. (12)

**UNIT II: DIFFERENTIAL CALCULUS**

Rolle’s theorem ,Mean value theorems, Taylor’s and Maclaurin theorems with remainders (without

proofs);indeterminate forms, Maxima and minima.(12)

**UNIT III: SEQUENCE AND SERIES**

Sequence and Series, their Convergence and tests for convergence; Power series, Taylor’s series,

series for exponential, trigonometric and logarithmic functions; Fourier series: Half rangesine and

cosine series, Parseval’s theorem.(12)

**UNITIV:MULTIVARIABLE DIFFERENTIAL CALCULUS**

Limit, continuity and partial derivatives, directional derivatives, total derivative; Tangent plane and

normal line; Maxima, minima and saddle points; Method of Lagrange multipliers.(12)

**UNITV: MULTIVARIABLE INTEGRAL CALCULUS**

Multiple Integration: Double integrals (Cartesian and polar), change of order of integration in double

integrals, Change of variables (Cartesian to polar),Applications: areas and volumes (double

integration); triple integrals, curl and divergence, Green’s, Stokes and Gauss divergence theorems

(without proofs).(12)

**Course Outcomes**

At the end of the course, the students should be able to

1. Evaluate the definite integrals, Beta and Gamma functions and calculate length of curve and

underlying area.

2. Relate the results of mean value theorems in calculus to Engineering problems.

3. Use the power series and Fourier series for ascertaining the stability and convergence of various

techniques.

4. Apply the functions of several variables to evaluate the rates of change with respect to time and

space variables in engineering.

5. Compute the area and volume by interlinking them to appropriate double and triple integrals.

**Text Books**

1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 42th Edition, 2012.

2. G. B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano, Thomas’ Calculus Pearson

education 11th Edition, 2004.

R**eference Books**

1. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, 9th Edition, Pearson, Reprint,

2002.

2. Erwin kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, 2006.

3. Veerarajan T., Engineering Mathematics for first year, Tata McGraw-Hill, New Delhi, 2008.

4. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th Reprint, 2010.

5. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.

6. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications,

Reprint, 2008.

**PART-A – ENGINEERING WORKSHOP**

Course Prerequisite: None

**Course Description:**

This course will provide students with a hands-on experience on various basic engineering

practices CSE and presenting the final product design.

**Course Objective**

1. Introduction to the use of Tools and Machinery in foundry, forging, tinsmith, carpentry,

welding, fitting, working, fabrication of plastic components, fabrication of polymer

composite materials, simple machine turning and wood turning, basic electrical

connections

2. Introduction of basic electrical engineering

3. Fabrication of final product design at end of the semester.

**LIST OF EXPERIMENTS**

1. Carpentry (Cross half lap Joint and Miter Joint)

2. Fitting (Square and‘V’ fit)

3. Sheet Metal – Tin smithy (Square tray)

4. Foundry (Solid and Split pattern)

5. Welding (Arc and Gas welding) – SingleV Butt Joint, T-fillet Joint

6. Plastic fabrication (Pen Stand)

7. Metrology (Internal and External dimension)

8. Introduction of Power Tools and CNC(Demo Only)

9. Introduction to 3D Printing (Demo Only)

Course Outcomes: On successful completion of this course, the student will be able to

1. Fabricate carpentry components with suitable joint and pipe connections including plumbing

works.

2. Practice the welding equipment to join the structures

3. Effective the basic machining operations

4. Create the models using sheet metal and plastic works.

5. Illustrate the operations of foundry, fitting and smithy

6. Fabrication product in composite material and product in plastic material

7. Conduct experiment basic electrical wire connection

8. Design and fabrication of final product design

Suggested Text/Reference Books:

1. Hajra Choudhury S.K., Hajra Choudhury A.K. and Nirjhar Roy S.K., “Elements of

Workshop Technology”, Vol. I 2008 and Vol. II 2010, Media promoters and publishers

private limited, Mumbai.

2. Kalpakjian S. And Steven S. Schmid, “Manufacturing Engineering and Technology”, 4th

edition, Pearson Education India Edition, 2002.

3. Gowri P. Hariharan and A. Suresh Babu, “Manufacturing Technology – 1” Pearson

Education, 2008.

4. Roy A. Lindberg, “Processes and Materials of Manufacture”, 4th edition, Prentice Hall

India, 1998. (v) Rao P.N., “Manufacturing Technology”, Vol. I and Vol. II, Tata

McGrawHill House, 2017.

Mode of Evaluation: Continuous Internal Evaluation, Practical Examination (Project show).

PART – B- IT WORKSHOP

Course Prerequisite: None

**Course Description:**

This course helps the students to understand the basic components of a computer, installation of

operating systems, working on productivity tools Word power, point excel. Also it gives a basic

understanding of using Google tools and various emails setting in Gmail.

**Course Objectives:**

1. The course focuses on enhancing student knowledge in computer peripherals and assembling.

2. To install operating system on computers and create new email account.

3. To understand basic software like WinRAR, WinZip, PDF readers and web browser.

4. To provide technical training to the students on Google tools like forms, calendar, drive, translate

and Photo.

5. To make the students to install software like JDK, Turbo C compiler ,and .net

** LIST OF EXPERIMENTS**

1. Components of Computer & Assembling a Computer:

Learning about the different parts of the computer and its advancement

Processor

Memory – Types

Motherboard

Peripheral interfaces – I/O devices

Learn about the proper connectivity among the devices inside the PC

Assembling the different parts of the computer inside the cabinet

2. Install Operating System

Partition the disk drive based on the capacity and the OS to be installed using utility tools

Install Windows

Install Linux or Ubuntu – use command line installation

3. Basic PC Troubleshooting

Awareness on the possible issues in a computer

Troubleshooting the problems using the available tools

Removal and repair of existing software

Identification of suitable Device driver for Hardware Devices.4. Learning Basic Software:

Installation of Productivity tools like WinRAR, WinZip, and PDF Reader.

Installation of Image Editor and Web browsers.

Basic Software installation in Linux based system.

Connect the Printer and Scanner Devices perform printing and scanning operation.

5. Productivity Tools (Office 365):

Generate, manipulate, search, aligning content using MS Word.

Creation of Excel sheet with various column and rows applying various Excel formulas.

Create Presentation and Visualization – graphs, charts, 2D, 3D.

Create a database template using MS Access.

Draw flowchart using the Drawing tools – Google Quick draw,sketchup,

6. Introduction to Google Tools

Design a Google form and collect a response date among students using Google Form.

Schedule One day of your activities using Google Calendar.

Store and Retrieve Date from cloud storage using Google Drive.

Translate the English language sentence to Telugu sentence using Google Translate

Organizing photo and editing photo using Google Photos.

7. Exploring Email

Creation, Composing and Sending the E-mail.

Use High Priority setting to categories the mail.

Create a Folder in different Categories and move the received mail to Folder.

Unsubscribing unwanted emails

Enable settings for automatic reply

Technical Stack :Windows 7 / UbantuOs – Winrar, Winzip,PDF reader, Office Package.

**Course Outcomes:**

Upon successful completion of the course, students will be able to

1. Attain complete knowledge of a computer hardwares

2. Install Operating Systems and troubleshooting using Utility software.

3. Able to do document task through MS.office .

4. Attain technically strong usage of Google Tools and Email handling .

5. Able to install basic computer engineering software.

**Course Objectives:**

1. To make the student understand problem solving techniques and their applications

2. Students will be able to understand the syntax and semantics of C programming language

3. Develop algorithms for manipulating linked lists, stacks, queues, searching and sorting.

**LIST OF EXPERIMENTS**

1. a) Write a C program to swap the two numbers.

b) Write a C Program to find the eligibility of admission for a Professional course based on the

following criteria:

Marks in Maths >=65

Marks in Physics >=55

Marks in Chemistry>=50

OR

Total in all three subject >=180

2. a) Write a C program to list all the factorial numbers less than or equal to an input number n.

A number N is called a factorial number if it is the factorial of a

Positive integer. For example, the first few factorial numbers are

1, 2, 6, 24, 120, …

*Note* – We do not list the factorial of 0.

b) Write a program that reads numbers which are in the range 0 to 100, till it encounters -1.

Print the sum of all the integers that you have read before you encountered -1

3. a) Given three points (x1, y1), (x2, y2) and (x3, y3), write a program to check if all the three

points fall on one straight line.

b) The digital root (also called repeated digital sum) of a number is a single digit value obtained by

an iterative process of summing digits. Digital sum of 65536 is 7, because 6+5+5+3+6=25 and

2+5 = 7. Write a program that takes an integer as input and prints its digital root.

4. a) Write a C program to find the series of prime numbers in the given range.

b) Write a C Program to Check Whether a Number is Palindrome or Not.

5. a) Write a c program to check whether a given number is a perfect number or not. (Perfect

number is a positive number which sum of all positive divisors excluding that number is equal to

that number. For example 6 is perfect number since divisor of 6 are 1, 2 and 3. Sum of its divisor

is 1 + 2+ 3 = 6)

b) Write a C function to find the kth occurrence of an integer n in a sequence of non-negative

integers, and then call your function from main.

Your function should be according to the following declaration:

int find(int n, int k);

sample example: input 3 2

1 1 3 2 3 -1

Output: 4

6. Write a C program to find Factorial, GCD, Fibonacci, (Using recursion)

7. Your program should take as input: dimension of a square matrix N, two matrices of

size N x N with integer values, and one operator symbol (+, – ,*). It must perform the

Corresponding operation given below

a) Matrix Addition b) Matrix Subtraction c) Matrix Multiplication

8. One needs to first input a set of N number of ALPHABETIC Strings each representing a name of

a student in an array studname [N] . Assume each string can be Max. 40 Characters long**.**

subsequently, one needs to input Marks obtained by those students in another array marks [N]

Assume that studname [I] i.e. ith student in the list of student names has obtained Marks [I] in the

Marks List. You need to find out and print the Max Marks obtained by a student and also print the

name of the student who has obtained this mark.

9. Implement the following searching techniques

a) Linear Search b) Binary Search

10 .a) Bubble sort is a sorting algorithm that works by repeatedly stepping through lists that need to

be sorted, comparing each pair of adjacent items and swapping them if they are in the wrong

order. This passing procedure is repeated until no swaps are required, indicating that the list is

sorted. Bubble sort gets its name because smaller elements bubble toward the top of the list.

Consider an array of size 10. It will be filled it by reading 10 integers. The final output will be

sorted output in Ascending Order.

b) Insertion sort is a sorting algorithm in which the elements are transferred one at a time to the right

position. Here the first element in the array is considered as sorted, even if it is an unsorted array.

Then each element in the array is checked with the previous elements, resulting in a growing

sorted output list. With each iteration, the sorting algorithm removes one element at a time and

finds the appropriate location within the sorted array and inserts it there. The iteration continues

until the whole list is sorted. First an array of size 10 will be taken. We will fill it by reading 10

integers. The final output will be sorted output in Ascending Order.

11 a) Write a C program to swap two integers using pointers. You have to write a swap function that

will accept the address of two integer and swap their values

b) Write a program in C to add two numbers using pointers. You have to write the fsum() function

which accepts the address of two variables and returns the sum of their values to the main

function.

12 Write a C program to compute internal marks of students for five different subjects using

Structures.

13 Implement the following Data Structures

a) Stack ADT b) queue ADT c) Circular queue ADT

14 a)Write a C program to implement all string operations (string length, string copy, string compare,

string concatenation and string reverse) without using standard string library functions.

b) Write a C program for reading a string and assigning its base address to the character pointer to

count characters are vowels or consonants.

15 a) Write a C program to copy the file contents from one file to another file (pass file names as

Command line arguments).

b) Write a C program to count no of lines, words and characters in a file.

**Course Outcomes:**

After completing this course the students should be able to

1. Understand problem solving techniques for a wide-range of problems.

2. Design and implement applications using functions and arrays.

3. Design and implement applications using Strings, Pointers and File processing.

4. Choose appropriate data structure depending on the problem to be solved.

5. Use appropriate searching and sorting technique to suit the application.