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CE3361 Surveying and Levelling Laboratory

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CE3361 Surveying and Levelling Laboratory

Anna University – CE3361 Surveying and Levelling Laboratory Regulation 2021 Syllabus, Lab Manual, Important Questions, Question Paper with Answers, Previous Year Question Paper.

OBJECTIVES:

 At the end of the course the student will possess knowledge about survey field techniques

LIST OF EXPERIMENTS: CE3361 Surveying and Levelling Laboratory

Chain Survey Lab Manual

1. Study of chains and its accessories, Aligning, Ranging, Chaining and Marking Perpendicular
offset
2. Setting out works – Foundation marking using tapes single Room and Double Room
Compass Survey
3. Compass Traversing – Measuring Bearings & arriving included angles

Levelling – Study of levels and levelling staff

4. Fly levelling using Dumpy level &Tilting level
5. Check levelling

Theodolite – Study of Theodolite CE3361 Surveying and Levelling Laboratory

6. Measurements of horizontal angles by reiteration and repetition and vertical angles
7. Determination of elevation of an object using single plane method when base is Accessible/inaccessible.

Tacheometry – Tangential system – Stadia system

8. Determination of Tacheometric Constants
9. Heights and distances by stadia Tacheometry
10. Heights and distances by Tangential Tacheometry

Total Station – Study of Total Station, Measuring Horizontal and vertical angles

11. Traverse using Total station and Area of Traverse
12. Determination of distance and difference in elevation between two inaccessible points
using Total station

COURSE OUTCOMES CE3361 Surveying and Levelling Laboratory

On completion of the course, the student is expected to
CO1 Impart knowledge on the usage of basic surveying instruments like chain/tape, compass
and levelling instruments
CO2 Able to use levelling instrument for surveying operations
CO3 Able to use theodolite for various surveying operations
CO4 Able to carry out necessary surveys for social infrastructures
CO5 Able to prepare planimetric maps

Syllabus	Click Here
Lab Manual	Click Here
Important Questions	Click Here

REFERENCES: CE3361 Surveying and Levelling Laboratory Lab Manual

1. T. P. Kanetkarand S. V. Kulkarni, Surveying and Levelling, Parts 1 & 2, Pune Vidyarthi Griha
Prakashan, Pune, 24th Reprint, 2015.
2. Dr. B. C. Punmia, Ashok K. Jainand Arun K Jain, Surveying Vol. I & II, Lakshmi Publications
Pvt Ltd, New Delhi, 17th Edition, 2016.
3. James M. Anderson and Edward M. Mikhail, Surveying, Theory and Practice, Seventh
Edition, McGraw Hill 2001
4. Bannisterand S. Raymond, Surveying, Seventh Edition, Longman 2004 a. David Clark,
Plane and Geodetic Surveying for Engineers, Volume I, Constable and Company Ltd,
London, CBS, 6th Edition, 2004.
5. David Clark and James Clendinning, Plane and Geodetic Surveying for Engineers, VolumeII,
Constable and Company Ltd, London, CBS, 6th Edition, 2004.
6. S. K. Roy, Fundamentals of Surveying, Second Edition, Prentice ‘Hall of India 2004
7. K. R. Arora, Surveying Vol. I & II, Standard Book house, Eleventh Edition, 2013.

Anna University Regulation 2021 Study Materials

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CE3351 Surveying and Levelling

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CE3351 Surveying and Levelling Study Materials

Anna University – CE3351 Surveying and Levelling Regulation 2021 Syllabus, Notes, Important Questions, Question Paper with Answers, Previous Year Question Paper.

UNIT I FUNDAMENTALS OF CONVENTIONAL SURVEYING CE3351 Surveying and Levelling Syllabus

Definition – Classifications – Basic principles – Equipment and accessories for ranging and chaining
– Methods of ranging – Well conditioned triangles – Chain traversing – Compass – Basic principles
– Types – Bearing – System and conversions – Sources of errors and Local attraction – Magnetic
declination – Dip – compass traversing – Plane table and its accessories – Merits and demerits –
Radiation – Intersection – Resection – Plane table traversing.

UNIT II LEVELLING CE3351 Surveying and Levelling Notes

Level line – Horizontal line – Datum – Benchmarks – Levels and staves – Temporary and permanent
adjustments – Methods of leveling – Fly leveling – Check leveling – Procedure in leveling – Booking
– Reduction – Curvature and refraction – Reciprocal leveling – Precise leveling – Contouring.

UNIT III THEODOLITE SURVEYING CE3351 Surveying and Levelling Important Questions

Horizontal and vertical angle measurements – Temporary and permanent adjustments – Heights and
distances – Tacheometric surveying – Stadia Tacheometry – Tangential Tacheometry –
Trigonometric leveling – Single Plane method – Double Plane method.

UNIT IV CONTROL SURVEYING AND ADJUSTMENT CE3351 Surveying and Levelling Question Paper

Horizontal and vertical control – Methods – Triangulation – Traversing – Gale‘s table –
Trilateration – Concepts of measurements and errors – Error propagation and Linearization –
Adjustment methods – Least square methods – Angles, lengths and levelling network.

UNIT V MODERN SURVEYING CE3351 Surveying and Levelling Question Bank

Total Station: Digital Theodolite, EDM, Electronic field book – Advantages – Parts and accessories
– Working principle – Observables – Errors – COGO functions – Field procedure and
applications.GPS: Advantages – System components – Signal structure – Selective availability
and antispoofing receiver components and antenna – Planning and data acquisition – Data
processing – Errors inGPS – Field procedure and applications.

Syllabus	Click Here
Notes	Click Here
Important Questions	Click Here
Previous Year Question Paper	Click Here
Question Bank	Click Here

TEXTBOOKS: CE3351 Surveying and Levelling

1. Dr. B. C. Punmia, Ashok K. Jain and Arun K Jain, Surveying Vol. I & II, Lakshmi Publications
Pvt Ltd, New Delhi, Sixteenth Edition, 2016.
2. T. P. Kanetkarand S. V. Kulkarni, Surveying and Levelling, Parts 1 & 2, Pune Vidyarthi Griha
Prakashan, Pune, 2008.

REFERENCES:

1. R. Subramanian, Surveying and Levelling, Oxford University Press, Second Edition, 2012.
2. James M. Anderson and Edward M. Mikhail, Surveying, Theory and Practice, Seventh
Edition, Mc Graw Hill 2001.
3. Bannister and S. Raymond, Surveying, Seventh Edition, Longman 2004.
4. S. K. Roy, Fundamentals of Surveying, Second Edition, Prenticeˆ Hall of India2010.
5. K. R. Arora, Surveying Vol I & II, Standard Book house, Twelfth Edition 2013.
6. C. Venkatramaiah, Textbook of Surveying, Universities Press, Second Edition, 2011.

Anna University Regulation 2021 Study Materials

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CE3303 Water Supply and Wastewater Engineering

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CE3303 Water Supply and Wastewater Engineering Study Materials

Anna University – CE3303 Water Supply and Wastewater Engineering Regulation 2021 Syllabus, Notes, Important Questions, Question Paper with Answers, Previous Year Question Paper.

UNIT I WATER SUPPLY – CE3303 Water Supply and Wastewater Engineering SYLLABUS

Estimation of surface and subsurface water resources – Predicting demand for water- Impurities of
water and their significance – Physical, chemical and bacteriological analysis -Waterborne diseases
– Standards for potable water. Intake of water: Pumping and gravity schemes.

UNIT II WATER TREATMENT – CE3303 Water Supply and Wastewater Engineering NOTES

Objectives – Unit operations and processes – Principles, functions, and design of water treatment
plant units, aerators of flash mixers, Coagulation and flocculation – Clarifloccuator – Plate and tube
settlers – Pulsator clarifier – sand filters – Disinfection – softening, removal of iron and manganese –
Defluoridation – Softening – Desalination process – Residue Management – Construction, Operation
and Maintenance aspects

UNIT III WATER STORAGE AND DISTRIBUTION – CE3303 Water Supply and Wastewater Engineering IMPORTANT QUESTIONS

Storage and balancing reservoirs – types, location and capacity. Distribution system: layout,
hydraulics of pipe lines, pipe fittings, valves including check and pressure reducing valves, meters,
analysis of distribution systems, leak detection, maintenance of distribution systems, pumping
stations and their operations – House service connections.

UNIT IV PLANNING AND DESIGN OF SEWERAGE SYSTEM – CE3303 Water Supply and Wastewater Engineering QUESTION BANK

Characteristics and composition of sewage – Population equivalent – Sanitary sewage flow
estimation – Sewer materials – Hydraulics of flow in sanitary sewers – Sewer design – Storm drainage-
Storm runoff estimation – Sewer appurtenances – Corrosion in sewers – Prevention and control –
Sewage pumping-drainage in buildings – Plumbing systems for drainage

UNIT V SEWAGE TREATMENT AND DISPOSAL – CE3303 Water Supply and Wastewater Engineering QUESTION PAPER

Objectives – Selection of Treatment Methods – Principles, Functions, – Activated Sludge Process
and Extended aeration systems – Trickling filters – Sequencing Batch Reactor(SBR) – UASB -Waste
Stabilization Ponds – Other treatment methods – Reclamation and Reuse of sewage – Recent
Advances in Sewage Treatment – Construction, Operation and Maintenance aspects. – Discharge
standards-sludge treatment -Disposal of sludge

Syllabus	Click Here
Notes	Click Here
Important Questions	Click Here
Previous Year Question Paper	Click Here
Question Bank	Click Here

TEXTBOOKS – CE3303 Water Supply and Wastewater Engineering

1. Garg, S.K. Environmental Engineering, Vol.I Khanna Publishers, New Delhi, 2010.
2. Modi, P.N., Water Supply Engineering, Vol.I Standard Book House, New Delhi, 2016.
3. Garg, S.K., Environmental Engineering Vol.II, Khanna Publishers, New Delhi, 2015.
4. Duggal K.N., “Elements of Environmental Engineering” S. Chand and Co. Ltd., New Delhi,
2014.
5. Punmia, B.C., Jain, A.K., and Jain.A.K.., Environmental Engineering, Vol.II, Laxmi
Publications, 2010.

REFERENCES: CE3303 Water Supply and Wastewater Engineering

1. Punmia B.C, Ashok Jain and Arun Jain, Water Supply Engineering, Laxmi Publications (P)
Ltd., New Delhi 2010.
2. Manual on Water Supply and Treatment, CPHEEO, Ministry of Urban Development,
Government of India, New Delhi, 1999.
3. Syed R. Qasimand Edward M. Motley Guang Zhu, Water Works Engineering Planning,
Design and Operation, Prentice Hall of India Learning Private Limited, New Delhi, 2009.
4. Of Urban Development, Government of India, New Delhi, 2013.
5. Metcalf and Eddy –Waste water Engineering – Treatment and Reuse, Tata Mc. Graw – Hill
Company, New Delhi, 2010.
6. Syed R.Qasim “Waste water Treatment Plants”, CRCPress,WashingtonD.C.,2010
7. Gray N.F, “Water Technology”, Elsevier India Pvt.Ltd. New Delhi, 2006.

Anna University Regulation 2021 Study Materials

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CE3302 Construction Materials and Technology

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CE3302 Construction Materials and Technology Study Materials

Anna University – CE3302 Construction Materials and Technology Regulation 2021 Syllabus, Notes, Important Questions, Question Paper with Answers, Previous Year Question Paper.

UNIT I STONES – BRICKS – CONCRETE BLOCKS – LIME CE3302 CONSTRUCTION MATERIALS AND TECHNOLOGY SYLLABUS

Stone as building material – Criteria for selection – Tests on stones – Bricks – Classification – Manufacturing of clay bricks – Tests on bricks – Compressive strength – Water Absorption – Efflorescence – Lime – Preparation of lime mortar – Concrete hollow blocks – Lightweight concrete blocks.

UNIT II OTHER MATERIALS CE3302 CONSTRUCTION MATERIALS AND TECHNOLOGY NOTES

Timber – Market forms – Plywood – Veneer – False ceiling materials – Steel – Mechanical treatment – Aluminum – Uses – Market forms – Glass – Ceramics – Refractories – Composite Materials – Types and applications – FRP – Fibre textiles – Geomembranes and Geotextiles for earth reinforcement.

UNIT III CONSTRUCTION PRACTICES & SERVICE REQUIREMENTS CE3302 CONSTRUCTION MATERIALS AND TECHNOLOGY IMPORTANT QUESTIONS

Types of Foundations – Shallow and Deep Foundations – Stone Masonry – Brick Masonry – Plastering and Pointing – Cavity Walls – Diaphragm Walls – Formwork – Centering and Shuttering – Shoring – Scaffolding – Underpinning – Roofing – Flooring – Joints in concrete – Contraction/Construction/Expansion joints – Fire Protection – Thermal Insulation – Ventilation and Air conditioning – Acoustics and Sound Insulation – Damp Proofing.

UNIT IV CONSTRUCTION EQUIPMENTS CE3302 CONSTRUCTION MATERIALS AND TECHNOLOGY QUESTION PAPER

Selection of equipment for earthwork excavation, concreting, material handling and erection of structures – Dewatering and pumping equipment.

UNIT V CONSTRUCTION PLANNING CE3302 CONSTRUCTION MATERIALS AND TECHNOLOGY QUESTION BANK

Introduction to construction planning – Scheduling for activities – Critical path method (CPM) and PERT network modelling and time analysis – Case illustrations.

Syllabus	Click Here
Notes	Click Here
Important Questions	Click Here
Previous Year Question Paper	Click Here
Question Bank	Click Here

TEXTBOOKS CMT NOTES

1. Varghese.P.C, Building Materials, Second Edition PHI Learning Ltd., 2015.
2. Arora S.P and Bindra S.P Building construction, Dhanpat Rai and sons,2013.

OBJECTIVES: CMT IMPORTANT QUESTIONS

To introduce students to various construction materials and the techniques that are commonly used in civil engineering construction.

REFERENCES: CMT QUESTION PAPER

1. Varghese.P.C, Building Construction, Second Edition PHI Learning ltd., 2016.
2. Punmia ,B.C Building construction , Laxmi publication (p)ltd..,2008.
3. Peurifoy R.L., Schexnayder,C.J., Shapira A., Schmitt.R., Construction Planning Equipment
and Methods, Tata McGraw-hill, 2011.
4. Srinath L.S.,PERT and CPM -Principles and applications, Affliated East West Press 2001

Anna University Regulation 2021 Study Materials

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CE3301 Fluid Mechanics

CE3301 Fluid Mechanics Study Materials

Anna University – CE3301 Fluid Mechanics Regulation 2021 Syllabus , Notes , Important Questions, Question Paper with Answers Previous Year Question Paper.

UNIT I FLUIDS PROPERTIES AND FLUID STATICS CE3301 Fluid Mechanics Syllabus

Scope of fluid mechanics – Definitions of a fluid – Methods of analysis – Continuum hypothesis – System and Control volume approach – Reynold’s transportation theorem – Fluid properties – Fluid statics – Manometry – Forces on plane and curved surfaces – Buoyancy and floatation – Stability of floating bodies.

UNIT II BASIC CONCEPTS OF FLUID FLOW CE3301 Fluid Mechanics Notes

Kinematics: Classification of flows – Streamline, streak-line and path-lines – Stream function and velocity potentials – Flownets; Dynamics : Application of control volume to continuity, energy and momentum – Euler’s equation of motion along a stream line – Bernoulli’s equation – Applications to velocity and discharge measurements – Linear momentum equation – Application to Pipe bends – Moment of momentum equation.

UNIT III DIMENSIONAL ANALYSIS AND MODEL STUDIES CE3301 Fluid Mechanics Important Questions

Fundamental dimensions – Dimensional homogeneity – Rayleigh’s method and Buckingham Pi theorem – Dimensionless parameters – Similitude and model studies – Distorted and undistorted models.

UNIT IV INCOMPRESSIBLE VISCOUS FLOW CE3301 Fluid Mechanics Question Bank

Reynolds experiment – Laminar flow in pipes and between parallel plates – Development of laminar and turbulent flows in pipes – Darcy-Weisbach equation – Moody diagram – Major and minor losses of flow in pipes – Total energy line – Hydraulic grade line – Siphon – Pipes in series and parallel – Equivalent pipes.

UNIT V BOUNDARY LAYERS CE3301 Fluid Mechanics Question Paper

Definition of boundary layers – Laminar and turbulent boundary layers – Displacement, momentum and energy thickness – Momentum integral equation – Applications – Separation of boundary layer – Drag and Lift forces.

Syllabus	Click Here
Notes	Click Here
Important Questions	Click Here
Previous Year Question Paper	Click Here
Question Bank	Click Here

TEXTBOOKS: CE3301 Fluid Mechanics Study materials

1. Modi P.N and Seth Hydraulics and Fluid Mechanics including Hydraulic Machines Standard
Book House New Delhi. 2015.
2. Streeter, V.L. Wylie, E. B. and Bedford K.W, Fluid Mechanics. (9th Ed.) Tata McGraw Hill,
New Delhi, 1998.

REFERENCES:

1. S K Som; Gautam Biswas and S Chakraborty, Introduction to Fluid Mechanics and Fluid
Machines, Tata McGraw Hill Education Pvt. Ltd., 2012.
2. Pani B S, Fluid Mechanics: A Concise Introduction, Prentice Hall of India Private Ltd, 2016.
3. Jain A. K. Fluid Mechanics including Hydraulic Machines, Khanna Publishers, New Delhi,
2014.
4. Narayana Pillai N. Principles of Fluid Mechanics and Fluid Machines, (3rd Ed.) University
Press (India) Pvt. Ltd. 2009.

Anna University Regulation 2021 Study Materials

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ME3351 ENGINEERING MECHANICS

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ME3351 Engineering Mechanics Study Materials

Anna University – ME3351 Engineering Mechanics Regulation 2021 Syllabus , Notes , Important Questions, Question Paper with Answers Previous Year Question Paper.

UNIT I STATICS OF PARTICLES ME3351 Engineering Mechanics Syllabus

Fundamental Concepts and Principles, Systems of Units, Method of Problem Solutions, Statics of Particles -Forces in a Plane, Resultant of Forces, Resolution of a Force into Components, Rectangular Components of a Force, Unit Vectors. Equilibrium of a Particle- Newton’s First Law of Motion, Space and Free-Body Diagrams, Forces in Space, Equilibrium of a Particle in Space.

UNIT II EQUILIBRIUM OF RIGID BODIES ME3351 Engineering Mechanics Notes

Principle of Transmissibility, Equivalent Forces, Vector Product of Two Vectors, Moment of a Force about a Point, Varignon’s Theorem, Rectangular Components of the Moment of a Force, Scalar Product of Two Vectors, Mixed Triple Product of Three Vectors, Moment of a Force about an Axis, Couple – Moment of a Couple, Equivalent Couples, Addition of Couples, Resolution of a Given Force into a Force -Couple system, Further Reduction of a System of Forces, Equilibrium in Two and Three Dimensions – Reactions at Supports and Connections.

UNIT III DISTRIBUTED FORCES ME3351 Engineering Mechanics Important Questions

Centroids of lines and areas – symmetrical and unsymmetrical shapes, Determination of Centroids by Integration , Theorems of Pappus-Guldinus, Distributed Loads on Beams, Centre of Gravity of a Three-Dimensional Body, Centroid of a Volume, Composite Bodies , Determination of Centroids of Volumes by Integration. Moments of Inertia of Areas and Mass – Determination of the Moment of Inertia of an Area by Integration, Polar Moment of Inertia , Radius of Gyration of an Area , Parallel-Axis Theorem , Moments of Inertia of Composite Areas, Moments of Inertia of a Mass – Moments of Inertia of Thin Plates , Determination of the Moment of Inertia of a Three-Dimensional Body by Integration.

UNIT IV FRICTION ME3351 Engineering Mechanics Question Papers

The Laws of Dry Friction, Coefficients of Friction, Angles of Friction, Wedge friction, Wheel Friction, Rolling Resistance, Ladder friction.

UNIT V DYNAMICS OF PARTICLES ME3351 Engineering Mechanics Question Banks

Kinematics – Rectilinear Motion and Curvilinear Motion of Particles. Kinetics- Newton’s Second Law of Motion -Equations of Motions, Dynamic Equilibrium, Energy and Momentum Methods -Work of a Force, Kinetic Energy of a Particle, Principle of Work and Energy, Principle of Impulse and Momentum, Impact of bodies.

Syllabus	Click Here
Notes	Click Here
Important Questions	Click Here
Previous Year Question Paper	Click Here
Question Bank	Click Here

TEXTBOOKS: ME3351 Engineering Mechanics Questions and Answers

1. Beer Ferdinand P, Russel Johnston Jr., David F Mazurek, Philip J Cornwell,
SanjeevSanghi, Vector Mechanics for Engineers: Statics and Dynamics, McGraw Higher
Education., 11thEdition, 2017.
2. Vela Murali, “Engineering Mechanics-Statics and Dynamics”, Oxford University Press,
2018.

References:

1. Boresi P and Schmidt J, Engineering Mechanics: Statics and Dynamics, 1/e, Cengage
learning, 2008.
2. Hibbeller, R.C., Engineering Mechanics: Statics, and Engineering Mechanics: Dynamics,
13th edition, Prentice Hall, 2013.
3. Irving H. Shames, Krishna Mohana Rao G, Engineering Mechanics – Statics and Dynamics,
4thEdition, Pearson Education Asia Pvt. Ltd., 2005.
4. Meriam J L and Kraige L G, Engineering Mechanics: Statics and Engineering Mechanics:
Dynamics, 7th edition, Wiley student edition, 2013.
5. Timoshenko S, Young D H, Rao J V and SukumarPati, Engineering Mechanics, 5thEdition,
McGraw Hill Higher Education, 2013.

Anna University Regulation 2021 Study Materials

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MA3351 Transforms and Partial Differential Equations

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Post date August 24, 2022
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MA3351 Transforms and Partial Differential Equations

Anna University – MA3351 Transforms and Partial Differential Equations Regulation 2021 Syllabus , Notes , Important Questions, Question Paper with Answers Previous Year Question Paper.

UNIT I PARTIAL DIFFERENTIAL EQUATIONS MA3351 Transforms and Partial Differential Equations Syllabus

Formation of partial differential equations –Solutions of standard types of first order partial differential equations – First order partial differential equations reducible to standard types- Lagrange’s linear equation – Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types.

UNIT II FOURIER SERIES MA3351 Transforms and Partial Differential Equations Notes

Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series and cosine series – Root mean square value – Parseval’s identity – Harmonic analysis.

UNIT III APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS MA3351 Transforms and Partial Differential Equations Important Questions

Classification of PDE – Method of separation of variables – Fourier series solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two dimensional equation of heat conduction (Cartesian coordinates only).

UNIT IV FOURIER TRANSFORMS MA3351 Transforms and Partial Differential Equations Question Paper

Statement of Fourier integral theorem– Fourier transform pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.

UNIT V Z – TRANSFORMS AND DIFFERENCE EQUATIONS MA3351 Transforms and Partial Differential Equations Question Bank

Z-transforms – Elementary properties – Convergence of Z-transforms – – Initial and final value theorems – Inverse Z-transform using partial fraction and convolution theorem – Formation of difference equations – Solution of difference equations using Z – transforms.

Syllabus	Click Here
Notes	Click Here
Important Questions	Click Here
Previous Year Question Paper	Click Here
Question Bank	Click Here

TEXT BOOKS For MA3351 Transforms and Partial Differential Equations PDF

1. Grewal B.S.,“Higher Engineering Mathematics” 44thEdition, Khanna Publishers,New Delhi, 2018.
2. Kreyszig E, “Advanced Engineering Mathematics “, 10th Edition, John Wiley, New Delhi, India,
2016.

REFERENCES:

1. Andrews. L.C and Shivamoggi. B, “Integral Transforms for Engineers” SPIE Press, 1999.
2. Bali. N.P and Manish Goyal, “A Textbook of Engineering Mathematics”, 10th Edition, Laxmi
Publications Pvt. Ltd, 2015.
3. James. G., “Advanced Modern Engineering Mathematics”, 4thEdition, Pearson Education, New
Delhi, 2016.
4. Narayanan. S., Manicavachagom Pillay.T.K and Ramanaiah.G “Advanced Mathematics for
Engineering Students”, Vol. II & III, S.Viswanathan Publishers Pvt. Ltd, Chennai, 1998.
5. Ramana. B.V., “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd,
New Delhi, 2018.
6. Wylie. R.C. and Barrett . L.C., “Advanced Engineering Mathematics “Tata McGraw Hill Education
Pvt. Ltd, 6th Edition, New Delhi, 2012.