CIVIL ENGINEERING CIVIL & STRUCTURAL ENGINEERING. Mathematics Syllab… · Sub.Code : Basic Engineering Mathematics I L T P - 3 1 0 Credits :04. Department of Mathematics For students

Department of Mathematics

For students admitted in 2017-2021 batch Page 1

CIVIL ENGINEERING

&

CIVIL & STRUCTURAL ENGINEERING

(For students admitted in 2017-2021 batch)



Semester – I(For students admitted in 2017-2021 batch)

Aim:

The student will acquire basic knowledge and understand the key facts in fields of matrices,integral and differential calculus.

Unit I: Numerical Solution of Algebraic, Transcendental Equation

Solution of algebraic and transcendental equations - Bisection method – Method ofsuccessiveapproximation-Method of false position (Regula-Falsi Method) - Newton-Raphson method-Honer’s method-Secant method. Matlab applications.

Unit II: Eigen Values, Eigen Vectors

Rank of matrix – Elementary transformation – Elementary matrices-solution of linear systemof equations-Cramer’s rule-Matrix inversion method-Consistency of linear system ofequations; Linear Transformations – Linear dependence of vectors – Eigen values and Eigenvectors – Properties of Eigenvalues – Cayley Hamilton theorem (without proof). Matlabapplications

Unit III: Differential Calculus and Different Ial Equation

Function of two or more variables – Partial derivatives – Total derivative – Taylor’sexpansion – Maxima and Minima of functions of two variables – Jacobians –Homogenousfunctions - Euler’s theorem for homogeneous function Operator D – Rules for findingComplementary function – Inverse operator – Rules for finding particular Integral – Workingprocedure to solve the equation. - Method of undetermined coefficients.

Unit IV: Linear Differential Equations

Method of variation of parameters- Equations reducible to linear equations with constantcoefficients: Cauchy's homogeneous linear equation , Legendre's linear equation - Lineardependence of solutions - Simultaneous linear equations with constant coefficients

Unit V: Vector Differentiation

Differentiation of vectors - Curves in space - Velocity and acceleration – Scalar and vectorpoint functions –vector operator Del- Del applied to scalar point functions : Gradient - Delapplied to vector point functions : Divergence and curl - Physical interpretation of divergenceand curl-irrotational and solenoidal vectors – Del applied twice to point functions - Delapplied to products of point functions-Conservative vector field.

Sub.Code : Basic Engineering Mathematics I L T P - 3 1 0 Credits :04



Note: Questions are to be set on problem solving and not on the theoretical aspects.

Prescribed Text Book:Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers, 2011

References1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-Wesley PublishingCompany, 7th Edition,20033. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.



Semester – II(For students admitted in 2017-2021 batch)

Aim:

To provide students with mathematical knowledge in developing their skills in applyingmathematical concepts to support their concurrent and subsequent engineering subjects.

Unit I: Numerical Solution of Simultaneous Equations

Solution of linear simultaneous equations - Direct methods of solution: Gauss eliminationmethod , Inversion of a matrix using Gauss –Elimination method- Gauss – Jordan method –Method of Factorization-Crout’s method, Iterative methods of solution : Jacobi’s method ,Gauss – Seidel method.

Unit II: Orthogonal Reduction

Orthogonal transformation-Reduction to diagonal form – Similarity matrices – Powers of amatrix - Reduction of quadratic form to canonical form – Nature of a quadratic form –Hermitian, Skew Hermitian and Unitary matrices – Outline of applications of Eigen valuesand Eigen vectors in engineering

Unit III: Integral Calculus and Its Applications

Reduction formulae – reduction formulae [without proof] and Bernoulli’s formula. Definiteintegrals, length of the curve. Double integrals - Change of order of integration - Doubleintegrals in polar coordinates - Areas enclosed by plane curves - Triple integrals – Volume asdouble integrals - Volume as triple integral.

Unit IV: Beta and Gamma Functions

Change of variables in double integrals and Triple integrals – Area of a curved surface. Betafunction - Gamma function –Reduction formula for G(n) – Relation between Beta and Gammafunctions – Outline of applications of multiple integrals

Unit V: Vector Integration

Integration of vectors - Line integral-circulation-work - Surface integral - Green's theorem inthe plane (without proof) - Stoke's theorem (without proof) - Volume integral - Gaussdivergence theorem (without proof) - Irrotational fields – Outline of applications of vectorcalculus in engineering.


Sub.Code : Basic Engineering Mathematics II L T P - 3 1 0 Credits :04



Prescribed Text Book:Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers, New Delhi,2011.

ReferencesErwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-Wesley PublishingCompany, 7th Edition,20033. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.



Semester – III(For students admitted in 2017-2021 batch)

Aim:

To enable the students in applying mathematical methods in various engineering fields bymaking them to understand the method of Fourier series and Fourier Transform and Z-Transform.

Unit I: Interpolation and Numerical Solution of Ordinary Differential Equations

Interpolation with equal intervals – Newton’s forward interpolation formula – Newton’sbackward interpolation formula - Interpolation with unequal intervals: Lagrange’sinterpolation formula, Newton’s divided difference formula. Picard’s method – Taylor seriesmethod - Modified Euler’s method – Runge’s method – Runge-Kutta method – Predictor-corrector methods: Milne’s method, Outline of applications of numerical solutions of ordinarydifferential equations in engineering.

Unit II: Fourier Series

Euler’s Formulae (Without Proof) – Condition for Fourier expansion – Functions havingpoints of discontinuity – Change of interval – Expansions of even and odd functions – HalfRange series – Parseval’s formula (without proof) – Root mean square value (without proof) –Typical waveforms (Definition Only): Square wave form, Saw toothed waveform, Modifiedsaw toothed waveform, Triangular waveform, Half wave rectifier, Full wave rectifier - Outlineof applications of Fourier series in engineering

Unit III: Laplace Transforms and Its Applications

Transforms of elementary functions : 1,tn , eat , sin at, cos at, sinh at, cosh at - Properties ofLaplace transforms: Linearity Property, First shifting property, Change of scale property –Transforms of derivatives - Transforms of integrals - Multiplication by tn - Divisionby t - Evaluation of integrals by Laplace transform - Inverse transforms: Method of partialfractions – Other methods of finding inverse - Convolution theorem (Without proof) -Unit step function – Unit Impulse Function - Application to differential equations –Outline of applications of Laplace transforms in engineering.

Unit IV: Z – Transform and Its Applications

Standard z-transforms of 1, – Linearity property – Damping rule – Shifting rules –Multiplication by n - Initial and final value theorems (without proof) – inverse z –transforms –Convolution theorem (without proof) – Convergence of z-transforms – Two sided z-transform

Sub.Code : Engineering Mathematics III L T P - 3 1 0 Credits :04



– Evaluation of inverse z-transforms: Power series method, Partial fraction method, inversionintegral method – Application to difference equations – Outline of applications of z-transformin engineering

Unit V: Fourier Transforms and Its Applications

Fourier integral theorem (without proof) - Fourier Sine and Cosine integrals – Complex formof Fourier integral - Fourier integral representation of a function - Fourier transform – Fouriersine and Cosine transforms – Properties of Fourier Transforms: Linear property, Change ofscale property, Shifting property - Parseval’s identity for Fourier transforms (without proof) –Application of transforms to boundary value problems: Heat conduction, Vibrations of astring, Transmission lines.


Prescribed Text Book:Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers, New Delhi,2011.References

Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-Wesley PublishingCompany, 7th Edition,20033. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.



Semester – IV(For students admitted in 2017-2021 batch)

Aim:

To provide a definite idea about complex functions and their applications. To solve seriessolution of differential equation, higher order partial differential equations and differenceequation.

Unit I: Analytic FunctionsLimit and continuity of a complex function - Derivative of a complex function: CauchyRiemann equations – Analytic functions – Harmonic functions - Orthogonal system –Applications to flow problems – Geometric representation of a complex function - Standardtransformations: Translation, Magnification and rotation, Inversion and reflection, Bilineartransformation - Conformal transformation – Special conformal transformations :

Outline of applications of analytic functions in engineering

Unit II: Complex IntegrationIntegration of complex functions – Cauchy’s theorem (without proof) – Cauchy’s integral

formula (without proof) – Taylor’s series (without proof)– Laurent’s series (without proof) –Zeros and Singularities of an analytic function – Residues – Residue theorem (without proof)– Calculation of residues – Evaluation of real definite integrals: Integration around the unitcircle, Integration around a small semi-circle, Integration around rectangular contours,Indenting the contours having poles on the real axis – Outline of applications of complexintegration in engineering.

Unit III: Calculus of Variations

Functionals – Euler’s Equation - Solutions of Euler’s equation – Geodesics – Isoperimetricproblems – Several dependant variables – Functionals involving higher order derivatives –Approximate solution of boundary value problems: Rayleigh-Ritz method.

Unit IV: Partial Differential Equations

Formation of partial differential equations – Solution of a partial differential equation –Equations solvable by direct integration – Linear equations of first order – Non-linearequations of the first order – Charpit’s method - Homogeneous linear equations with constantcoefficients –Rules for finding complementary functions – Rules for finding particular integral– Solution of homogeneous linear equation of any order.

Sub.Code : Engineering Mathematics IV L T P - 3 1 0 Credits :04



Unit V: Applications of Partial Differential Equations

Method of separation of variables – Vibration of a stretched string: Wave equation – Solutionof Wave equation - D’Alembert’s solution of wave equation – One dimensional heat flow –Solution of heat equation – Two dimensional heat flow – Solution of Laplace equation:temperature distribution in long plates, Temperature distribution in finite plates.

Prescribed Text Book:

Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers, New Delhi,2011.

References

1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. N.P.Bali, Manish Goyal, A Text Book of Engineering Mathematics, Laksmi Publications,2010 reprint.3. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.



Semester – V(For students admitted in 2017-2021 batch)

Aim:

The student can acquire the basic concepts of probabilities and statistical techniques forsolving different kinds of engineering problems.

Unit I: Probability TheoryRandom experiment – Mathematical, statistical and axiomatic definitions of probability –Conditional probability – Independent events - Theorem of total probability – Theorem ofprobability of causes: Baye’s theorem – Bernoulli’s trials – De Moivre-Laplace approximation– Generalization of Bernoulli’s theorem multinomial distribution – Outline of applications ofprobability theory in engineering.

Unit II: Probability DistributionsBinomial distribution: Properties and constants of Binomial distribution – Fitting a Binomialdistribution - The multinomial distribution – Negative Binomial distribution – Poissondistribution: Properties and constants of Poisson distribution – Fitting a Poisson distribution –Hyper-geometric distribution – Normal distribution: Properties and constants of Normaldistribution – Fitting a normal curve – Outline of applications of theoretical distributions inengineering.

Unit III: Collection and Analysis of DataClassification and tabulation of data - Frequency tables - Graphical representation - Measures

of central tendency : Averages, mean, median, mode, Geometric and harmonic means -Measures of dispersion : Range, quartile deviation, Mean deviation, Standard deviation -Relative distribution - Moments - Skewness - Kurtosis - Linear correlation - Coefficient ofcorrelation - Grouped data : calculation of correlation coefficient - Rank correlation - Linearregression - Regression lines.

Unit IV: Testing of HypothesisTests of Hypothesis- Sampling distribution-Estimation and testing of hypothesis-Tests of

hypothesis and tests of significance- Critical region and level of significance- Errors in testingof hypothesis- One-tailed and Two-tailed tests-Critical values – procedure of testing ofhypothesisTests of significance for large samples–Tests of significance for small samples-Student’s tDistribution-Snedecor’s F-distribution-Chi-square distribution-Chi-square test ofGoodness of fit.

Sub.Code : Probability and Statistics L T P - 3 1 0 Credits :04



Unit V: Design of ExperimentsParameters and statistics – Sampling distribution – Tests of hypothesis and tests ofsignificance – Critical region and level of significance – Errors in testing of hypothesis – Onetailed and two tailed tests – Procedure for testing of hypothesis – Design of experiments –Completely randomized design: Analysis of variance for one factor of classification –Randomized block design: Analysis of variance for two factors of classification – Latin squaredesign: Analysis of variance for three factors of classification – Outline of applications ofdesign of experiments in engineering. Note: Questions are to be set on problem solving andnot on the theoretical aspects.


Text Book1. Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers, NewDelhi, 2011.2. Veerarajan. T., Probability, Statistics and Random Processes, Third Edition, Tata McGraw-Hill Publishers, New Delhi 2008.

Reference Books

1 Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.3. Gupta S.P, Statistical Methods, 28th Edition, Sultan Chand &Sons., New Delhi, 1997.



ELECTRONICS AND COMMUNICATION

ENGINEERING





Aim:






Unit III: Differential Calculus and Differential Equation















Aim:











Integration of vectors - Line integral-circulation-work - Surface integral - Green's theorem inthe plane (without proof) - Stoke's theorem (without proof) - Volume integral - Gaussdivergence theorem (without proof) - Irrotational fields – Outline of applications of vectorcalculus in engineering.Note: Questions are to be set on problem solving and not on the theoretical aspects.





References1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-Wesley Publishing

Company, 7th Edition,20033. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,

2010.




Aim:









Standard z-transforms of 1, – Linearity property – Damping rule – Shifting rules –Multiplication by n - Initial and final value theorems (without proof) – inverse z –transforms –Convolution theorem (without proof) – Convergence of z-transforms – Two sided z-transform– Evaluation of inverse z-transforms: Power series method, Partial fraction method, inversion




integral method – Application to difference equations – Outline of applications of z-transformin engineering





References

1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-Wesley Publishing

Company, 7th Edition,20033. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,

2010.




Aim:


Unit I: Analytic FunctionsLimit and continuity of a complex function - Derivative of a complex function: Cauchy

Riemann equations – Analytic functions – Harmonic functions - Orthogonal system –Applications to flow problems – Geometric representation of a complex function - Standardtransformations: Translation, Magnification and rotation, Inversion and reflection, Bilinear

transformation - Conformal transformation – Special conformal transformations :


Unit II : Complex IntegrationIntegration of complex functions – Cauchy’s theorem (without proof) – Cauchy’s integral


Unit III: Series Solution of Differential EquationsValidity of series solution - Series solution when x=0 is an ordinary point - Frobeniusmethod (Series solution when x=0 is a regular singularity) - Bessel's equation (Besselsfunctions of the first and second kind) - Recurrence formulae for Jn(x) - Expansions for J0

and J1 : Value of J1/2 - Generating function for Jn(x) - Equations reducible to Bessel'sequation – Orthogonality of Bessel functions – Outline of applications of Bessel’s functionsin engineering.

Unit IV : Partial Differential EquationsFormation of partial differential equations – Solution of a partial differential equation –Equations solvable by direct integration – Linear equations of first order – Non-linearequations of the first order – Charpit’s method - Homogeneous linear equations with constantcoefficients –Rules for finding complementary functions – Rules for finding particular integral– Solution of homogeneous linear equation of any order.




Unit V: Difference Equations and Its ApplicationsFormation of difference equations – Linear difference equations – Rules for finding thecomplementary function – Rules for finding the particular integral – Simultaneous differenceequations with constant coefficients – Outline of other applications of difference equations in



References

1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. N.P.Bali, Manish Goyal, A Text Book of Engineering Mathematics, Laksmi Publications,

2010 reprint.3. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,

2010.




Aim: The student can acquire the basic concepts of probabilities and Random processtechniques for solving different kinds of engineering problems.



Unit III: Random ProcessesClassification of random processes – Methods of description of a random process –Special classes of random processes – Average values of random processes – Analyticalrepresentation of a random processes – Autocorrelation function and its properties –Cross correlation function and its properties - Outline of applications of random processesin engineering.

Unit IV: Ergodic Process

Ergodicity – Mean Ergodic process – Correlation Ergodic process – DistributionErgodic process – Power spectral density function and its properties – System in theform of convolution – Unit impulse response of the system – Outline of applications ofergodic process in engineering.

Unit V: Special Random ProcessesPoisson process – Probability law for the Poisson Process – Second order probabilityfunction of a homogeneous Poisson process – Mean and autocorrelation of the Poissonprocess – Properties of Poisson process - Markov process – Markov chain – ChapmanKolmogorov theorem (without proof) – Classification of states of a Markov chain -Outline of applications of Poisson and Markov processes in engineering.

Sub.Code : Probability and Random Processes L T P - 3 1 0 Credits :04





Reference Books

1.Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.3. Gupta S.P, Statistical Methods, 28th Edition, Sultan Chand &Sons., New Delhi, 1997.4. Stochastic Processes, J.Medhi, New Age International Publishers, 3rd Edition, 2009



ELECTRICAL AND ELECTRONICS

ENGINEERING





Aim:






Unit III: Differential Calculus and Differential Equations


Unit-IV: Linear Differential Equations








Prescribed Text Book:Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers,New Delhi, 2011.





Aim:

To provide students with mathematical knowledge in developing their skills in applying

mathematical concepts to support their concurrent and subsequent engineering subjects.




















Aim:







Transforms of elementary functions : 1,tn , eat , sin at, cos at, sinh at, cosh at - Properties ofLaplace transforms: Linearity Property, First shifting property, Change of scale property –Transforms of derivatives - Transforms of integrals - Multiplication by tn - Divisionby t - Evaluation of integrals by Laplace transform - Inverse transforms: Method of partialfractions – Other methods of finding inverse - Convolution theorem (Without proof) -Unit step function – Unit Impulse Function - Application to differential equations –











References

1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-Wesley PublishingCompany, 7th Edition,20033. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.




Aim:


Unit I: Analytic FunctionsLimit and continuity of a complex function - Derivative of a complex function: CauchyRiemann equations – Analytic functions – Harmonic functions - Orthogonal system –Applications to flow problems – Geometric representation of a complex function - Standardtransformations: Translation, Magnification and rotation, Inversion and reflection, Bilinear



Unit II: Complex IntegrationIntegration of complex functions – Cauchy’s theorem (without proof) – Cauchy’s integralformula (without proof) – Taylor’s series (without proof)– Laurent’s series (without proof) –Zeros and Singularities of an analytic function – Residues – Residue theorem (without proof)– Calculation of residues – Evaluation of real definite integrals: Integration around the unitcircle, Integration around a small semi-circle, Integration around rectangular contours,Indenting the contours having poles on the real axis – Outline of applications of complexintegration in engineering.

Unit III: Series Solution Of Differential EquationsValidity of series solution - Series solution when x=0 is an ordinary point - Frobeniusmethod (Series solution when x=0 is a regular singularity) - Bessel's equation (Besselsfunctions of the first and second kind) - Recurrence formulae for Jn(x) - Expansions for J0


Unit IV: Partial Differential EquationsFormation of partial differential equations – Solution of a partial differential equation –Equations solvable by direct integration – Linear equations of first order – Non-linearequations of the first order – Charpit’s method - Homogeneous linear equations with constantcoefficients –Rules for finding complementary functions – Rules for finding particular integral– Solution of homogeneous linear equation of any order.




Unit V: Difference Equations and Its ApplicationsFormation of difference equations – Linear difference equations – Rules for finding thecomplementary function – Rules for finding the particular integral – Simultaneous differenceequations with constant coefficients – Outline of other applications of difference equations in



References






Unit I: Probability TheoryRandom experiment – Mathematical, statistical and axiomatic definitions of probability –Conditional probability – Independent events - Theorem of total probability – Theorem ofprobability of causes: Baye’s theorem – Bernoulli’s trials – De Moivre-Laplace approximation– Generalization of Bernoulli’s theorem multinomial distribution – Outline of applications ofprobability theory in engineering





Unit V: Special Random Processes

Poisson process – Probability law for the Poisson Process – Second order probabilityfunction of a homogeneous Poisson process – Mean and autocorrelation of the Poissonprocess – Properties of Poisson process - Markov process – Markov chain – ChapmanKolmogorov theorem (without proof) – Classification of states of a Markov chain -Outline of applications of Poisson and Markov processes in engineering.






Reference Books

1.Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.3. Gupta S.P, Statistical Methods, 28th Edition, Sultan Chand &Sons., New Delhi, 1997.4. Stochastic Processses, J.Medhi, New Age International Publishers, 3rd Edition, 2009



ELECTRONICS AND INSTRUMENTATION

ENGINEERING

&

MECHATRONICS ENGINEERING





Aim:





















Aim:









Change of variables in double integrals and Triple integrals – Area of a curved surface. Betafunction - Gamma function –Reduction formula for (n) – Relation between Beta and Gammafunctions – Outline of applications of multiple integrals












Aim:


Unit 1:Interpolation and Numerical Solution of Ordinary Differential Equations




Unit III: Laplace Transforms And Its Applications












References

1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-Wesley PublishingCompany, 7th Edition,20033. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.




Aim:


Unit I: Analytic Functions

Limit and continuity of a complex function - Derivative of a complex function: CauchyRiemann equations – Analytic functions – Harmonic functions - Orthogonal system –Applications to flow problems – Geometric representation of a complex function - Standardtransformations: Translation, Magnification and rotation, Inversion and reflection, Bilinear



Unit II: Complex Integration

Integration of complex functions – Cauchy’s theorem (without proof) – Cauchy’s integralformula (without proof) – Taylor’s series (without proof)– Laurent’s series (without proof) –Zeros and Singularities of an analytic function – Residues – Residue theorem (without proof)– Calculation of residues – Evaluation of real definite integrals: Integration around the unitcircle, Integration around a small semi-circle, Integration around rectangular contours,Indenting the contours having poles on the real axis – Outline of applications of complexintegration in engineering.

Unit III: Series Solution of Differential Equations

Validity of series solution - Series solution when x=0 is an ordinary point - Frobeniusmethod (Series solution when x=0 is a regular singularity) - Bessel's equation (Besselsfunctions of the first and second kind) - Recurrence formulae for Jn(x) - Expansions for J0







Unit V: Difference Equations and Its Applications

Formation of difference equations – Linear difference equations – Rules for finding thecomplementary function – Rules for finding the particular integral – Simultaneous differenceequations with constant coefficients – Outline of other applications of difference equations in



References











Unit V: Special Random ProcessesPoisson process – Probability law for the Poisson Process – Second order probabilityfunction of a homogeneous Poisson process – Mean and autocorrelation of the Poissonprocess – Properties of Poisson process - Markov process – Markov chain – ChapmanKolmogorov theorem (without proof) – Classification of states of a Markov chain -Outline of applications of Poisson and Markov processes in engineering.





Text Book1. Veerarajan. T., Probability, Statistics and Random Processes, Third Edition, Tata McGraw-Hill Publishers, New Delhi 2008.1. Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers, NewDelhi, 2011.

Reference Books

1.Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.3. Gupta S.P, Statistical Methods, 28th Edition, Sultan Chand &Sons., New Delhi, 1997.4. Stochastic Processses, J.Medhi, New Age International Publishers, 3rd Edition, 2009



Semester – VI(For students admitted in 2017-2021 batch)

Aim

To provide the students to understand mathematical techniques to model and analyze decision

problems with effective applications to real life in optimization of objectives.

Unit I: Linear Programming and Simplex Method

Mathematical formulation of the problem - Graphical solution method - Exceptional cases -General linear programming problem - Canonical and standard forms of linear programmingproblem - The simplex method - Computational procedure : The simplex algorithm - Artificialvariable techniques : Big M method, Two phase method - problem of degeneracy.

Unit II: Transportation, Assignment and Routing Problems

Mathematical formulation of the transportation problem - Triangular basis - Loops in atransportation table - Finding initial basic feasible solution (NWC, IBM and VAM methods) -Moving towards optimality - Degeneracy in transportation problems- Transportationalgorithm (MODI method) - Unbalanced transportation problems - Mathematical formulationof the assignment problem - Assignment algorithm : Hungarian assignment method - Routingproblems : Travelling salesman problem.

Unit III: Game Theory and Sequencing Problems

Two person zero sum games - Maxmin Minmax principle - Games without saddle points(Mixed strategies) - Solution of 2 X 2 rectangular games - Graphical method - Dominanceproperty - Algebraic method for m x n games - Matrix oddments method for m x n games -Problem of sequencing - Problems with n jobs and 2 machines - Problems with n jobs and kmachines - Problems with 2 jobs and k machines.

Unit IV: Inventory Control and Replacement

Types of inventory - Inventory decisions - Economic order quantity - Deterministic inventoryproblem - EOQ problem with price breaks - Multi item deterministic problem-Replacement ofequipment or asset that deteriorates gradually - Replacement of equipment that fails suddenly- Recruitment and promotion problem

Unit V: Network Scheduling

Network and basic components - Rules of network construction - Time calculations innetworks - Critical path method (CPM) - PERT - PERT calculations - Negative float andnegative Slack - Advantages of network (PERT/CPM).

Sub.Code : Operation Research L T P - 3 1 0 Credits :04



Unit VI*:Optimization Techniques

Multivariable Optimization Techniques with Inequality Constraints- Kuhn-Tucker Conditions-Multiobjective Optimization- Global Criterion Method-Introduction to Genetic Algorithm-Neural-Network-Based Optimization- Optimization of Fuzzy Systems

* Questions will not be asked from this unit in the university theory examination.

Text Books:1. Kanti Swarup, P.K.Gupta and Man Mohan, Operations Research, Eighth Edition, SultanChand & Sons, New Delhi, 1999.2. Singiresu S. Rao, Engineering Optimization, New Age International Publications, NewDelhi, Revised Third Edition, 2007 (Unit-VI)Reference Books:1. H.A.Taha, Operations Research, 9th Edition, Pearson, 20132. Richard Bronson, Operations Research, (Schaum's Outline Series, McGraw Hill Company,1982.3. J.K.Sharma, Operation Research (Theory and Applications), Mac Millen Ltd., 1997.



MECHANICAL ENGINEERING





Aim:





















Aim:

















ReferencesErwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-Wesley PublishingCompany, 7th Edition,20033. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.




Aim:


Unit 1:Interpolation And Numerical Solution of Ordinary Differential Equations















Prescribed Text Book:Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers, New Delhi,2011.ReferencesErwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-Wesley PublishingCompany, 7th Edition,20033. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.




Aim:


Unit I: Analytic FunctionsLimit and continuity of a complex function - Derivative of a complex function: Cauchy

Riemann equations – Analytic functions – Harmonic functions - Orthogonal system –Applications to flow problems – Geometric representation of a complex function - Standardtransformations: Translation, Magnification and rotation, Inversion and reflection, Bilinear



Unit II: Complex IntegrationIntegration of complex functions – Cauchy’s theorem (without proof) – Cauchy’s integral


Unit III: Calculus of Variations

Functionals – Euler’s Equation - Solutions of Euler’s equation – Geodesics – Isoperimetricproblems – Several dependant variables – Functionals involving higher order derivatives –Approximate solution of boundary value problems: Rayleigh-Ritz method.






Unit V: Applications of Partial Differential Equations

Method of separation of variables – Vibration of a stretched string: Wave equation – Solutionof Wave equation - D’Alembert’s solution of wave equation – One dimensional heat flow –Solution of heat equation – Two dimensional heat flow – Solution of Laplace equation:temperature distribution in long plates, Temperature distribution in finite plates.

Prescribed Text Book:Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers, New Delhi,2011.References1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. N.P.Bali, Manish Goyal, A Text Book of Engineering Mathematics, Laksmi Publications,2010 reprint.3. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.




Aim:

The student can acquire the basic concepts of probabilities and statistical techniques forsolving different kinds of engineering problems.



Unit III: Collection and Analysis Of DataClassification and tabulation of data - Frequency tables - Graphical representation - Measures

of central tendency : Averages, mean, median, mode, Geometric and harmonic means -Measures of dispersion : Range, quartile deviation, Mean deviation, Standard deviation -Relative distribution - Moments - Skewness - Kurtosis - Linear correlation - Coefficient ofcorrelation - Grouped data : calculation of correlation coefficient - Rank correlation - Linearregression - Regression lines.

Unit IV: Testing of HypothesisTests of Hypothesis- Sampling distribution-Estimation and testing of hypothesis-Tests of

hypothesis and tests of significance- Critical region and level of significance- Errors in testingof hypothesis- One-tailed and Two-tailed tests-Critical values – procedure of testing ofhypothesisTests of significance for large samples–Tests of significance for small samples-Student’s tDistribution-Snedecor’s F-distribution-Chi-square distribution-Chi-square test ofGoodness of fit.

Sub.Code : Probability and Statistics L T P - 3 1 0 Credits :04



Unit V: Design Of ExperimentsParameters and statistics – Sampling distribution – Tests of hypothesis and tests ofsignificance – Critical region and level of significance – Errors in testing of hypothesis – Onetailed and two tailed tests – Procedure for testing of hypothesis – Design of experiments –Completely randomized design: Analysis of variance for one factor of classification –Randomized block design: Analysis of variance for two factors of classification – Latin squaredesign: Analysis of variance for three factors of classification – Outline of applications ofdesign of experiments in engineering. Note: Questions are to be set on problem solving andnot on the theoretical aspects.



Reference Books1 Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9th Edition,20062. Ramana.B.V. Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th reprint,2010.3. Gupta S.P, Statistical Methods, 28th Edition, Sultan Chand &Sons., New Delhi, 1997.



Semester – VII(For students admitted in 2017-2021 batch)

Aim:

To provide the students to understand mathematical techniques to model and analyze decision

problems with effective applications to real life in optimization of objectives.

Unit I: Linear Programming And Simplex MethodMathematical formulation of the problem - Graphical solution method - Exceptional cases -General linear programming problem - Canonical and standard forms of linear programmingproblem - The simplex method - Computational procedure : The simplex algorithm - Artificialvariable techniques : Big M method, Two phase method - problem of degeneracy.

Unit II: Transportation, Assignment and Routing Problems

Mathematical formulation of the transportation problem - Triangular basis - Loops in atransportation table - Finding initial basic feasible solution (NWC, IBM and VAM methods) -Moving towards optimality - Degeneracy in transportation problems- Transportationalgorithm (MODI method) - Unbalanced transportation problems - Mathematical formulationof the assignment problem - Assignment algorithm : Hungarian assignment method - Routingproblems : Travelling salesman problem.

Unit III: Game Theory and Sequencing Problems

Two person zero sum games - Maxmin Minmax principle - Games without saddle points(Mixed strategies) - Solution of 2 X 2 rectangular games - Graphical method - Dominanceproperty - Algebraic method for m x n games - Matrix oddments method for m x n games -Problem of sequencing - Problems with n jobs and 2 machines - Problems with n jobs and kmachines - Problems with 2 jobs and k machines.

Unit IV: Inventory Control and Replacement

Types of inventory - Inventory decisions - Economic order quantity - Deterministic inventoryproblem - EOQ problem with price breaks - Multi item deterministic problem-Replacement ofequipment or asset that deteriorates gradually - Replacement of equipment that fails suddenly- Recruitment and promotion problem

Sub.Code : Operation Research L T P - 3 1 0 Credits :04



Unit V: Network Scheduling

Network and basic components - Rules of network construction - Time calculations innetworks - Critical path method (CPM) - PERT - PERT calculations - Negative float andnegative Slack - Advantages of network (PERT/CPM).

Unit VI*: Optimization Techniques

Multivariable Optimization Techniques with Inequality Constraints- Kuhn-Tucker Conditions-Multiobjective Optimization- Global Criterion Method-Introduction to Genetic Algorithm-Neural-Network-Based Optimization- Optimization of Fuzzy Systems

* Questions will not be asked from this unit in the university theory examination.

Text Books:

1. Kanti Swarup, P.K.Gupta and Man Mohan, Operations Research, Eighth Edition, SultanChand & Sons, New Delhi, 1999.2. Singiresu S. Rao, Engineering Optimization, New Age International Publications, NewDelhiRevised Third Edition, 2007(Unit-VI)Reference Books:1. H.A.Taha, Operations Research, 9th Edition, Pearson, 20132. Richard Bronson, Operations Research, (Schaum's Outline Series, McGraw Hill Company,1982.3. J.K.Sharma, Operation Research (Theory and Applications), Mac Millen Ltd., 1997.

Documents

CIVIL ENGINEERING CIVIL & STRUCTURAL ENGINEERING. Mathematics Syllab… · Sub.Code : Basic Engineering Mathematics I L T P - 3 1 0 Credits :04. Department of Mathematics For students