Electrical and Electronics - Lingaya's University

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B.Tech. Electrical & Electronics Engineering (Regular)system of equations; linear and orthogonaltransformations; Eigen values and Eigen vectors;properties of Eigen values; Cayley - Hamiltontheorem and its applications.2. INFINITE SERIES: Convergence and divergence;comparison; D' Alembert's ratio; Integral; Raobes;De Morgan‘s & Bertrand‘s; logarithmic and Cauchyroot tests; alternating series; absolute andconditional convergence.3. APPLICATIONS OF DIFFERENTIATION: Taylor'sand Maclaurin's series; asymptotes; curvature.4. PARTIAL DIFFERENTIATION: Functions of two ormore variables; partial derivatives; total differentialand differentiability; derivatives of composite andimplicit functions; Jacobian‘s; higher order partialderivatives.5. APPLICATION OF PARTIAL DIFFERENTIATION:Homogeneous functions; Euler's theorem; Taylor'sseries for functions of two variables (without proof);maxima-minima of function of two variables;Lagrange's method of undetermined multipliers;differentiation under integral sign.6. FOURIER SERIES: Euler‘s formula; conditions for aFourier expansion; change of interval; Fourierexpansion of odd and even function; Fourierexpansion of square wave; rectangular wave; sawtoothedwave; half and full rectified wave functions;half range sine and cosine series.7. ORDINARY DIFFERENTIAL EQUATIONS & ITSAPPLICATIONS: Exact differential equations;equations reducible to exact differential equations;applications of differential equations of first order andfirst degree to simple electric circuits; Newton's law ofcooling; heat flow and orthogonal trajectories.TEXT BOOKKreyszig F., "Advanced Engineering Mathematics", 9thEdition, John Wiley, 2006REFERENCE BOOKS1. Jeffery, ―Engineering Mathematics‖, AcademicPress/Elsevier.2. Sastry, S. S., ―Engineering Mathematics Part-I‖,2nd Edition, Prentice Hall of India3. Jain, R. K. and Iyengar, S. R. K., ―AdvancedEngineering Mathematics‖ 3rd Edition, NarosaPublishing House4. Greenberg, D., Michael., ―Advanced Engg.Mathematics‖, 2nd Edition, Dorling Kindersley IndiaPvt. Ltd.MA-102 APPLIED MATHEMATICS-IIL T P Cr5 1 0 4OBJECTIVETo acquaint the students with the various concepts andtools of applied mathematics which will be very basic andthe very soul and guide of various engineering subjects.1. DIFFERENTIAL EQUATIONS OF HIGHERORDER AND ITS APPLICATION: Lineardifferential equations of second and higher order;complete solution; complementary function andparticular integral; method of variation of parametersto find differential particular integral; Cauchy's andLegendre's linear equations; simultaneous linearequations with constant coefficients; applications oflinear differential equations to simple pendulum;oscillatory electric circuits.2. LAPLACE TRANSFORMS AND ITSAPPLICATIONS: Laplace transforms ofelementary functions; properties of Laplacetransforms; existence conditions; transforms ofderivatives; transforms of integrals; multiplicationby t; division by t.3. EVALUATION OF INTEGRALS BY LAPLACETRANSFORMS: Laplace transform of unit stepfunction; unit impulse function and periodicfunction; Inverse transforms; convolution theorem;application to linear differential equations andsimultaneous linear differential equations withconstant coefficients.4. FOURIER TRANSFORMS: Fourier integraltransforms; shifting theorem (both on time andfrequency axes); Fourier transforms of derivatives;Fourier transforms of integrals; convolutiontheorem; Fourier transform of Dirac-delta function.5. CURVE TRACING: Applications of single integrationto find volume of solids and surface area of solids ofrevolution; double integral; change of order ofintegration; double integral in polar coordinates.6. APPLICATIONS OF MULTIPLE INTEGRALS:Applications of double integral to find areaenclosed by plane curves and volume of solids ofrevolution; triple integral; volume of solids; changeof variables; beta and gamma functions andrelationship between them.7. VECTOR CALCULUS: Differentiation of vectors;scalar and vector point functions; gradient of ascalar field and directional derivative; divergenceand curl of a vector field and their physicalinterpretations; integration of vectors; line integral;surface integral; volume integral; Green‘s, Stoke'sand Gauss‘ theorems (without proof) and theirsimple applications.TEXT BOOKKreyszig F., "Advanced Engineering Mathematics", 9thEdition, John Wiley, 2006REFERENCE BOOKS1. Ross, S. L., ―Differential Equation‖, Wiley IndiaPublishers2. Piaggio, H. T. H., ―Differential Equations‖, 1stEdition, CBS Publishers and Distributors,3. Jain, R. K. and Iyengar, S. R. K. ―AdvancedEngineering Mathematics‖, 3rd Edition, NarosaPublishing House4. Greenberg, D., Michael ―Advanced Engg.Mathematics‖, 2nd Edition, Dorling Kindersley IndiaPvt. Ltd.MA-202APPLIED NUMERICALMETHODSL T P Cr5 1 0 4OBJECTIVETo provide a foundation for numerical computing forscientific and engineering applicationsPRE-REQUISITEKnowledge of Basic Mathematics involvingdifferentiation, integration, differential equations, linearequations, etc.34
Lingaya’s University, Faridabad1. ERRORS IN NUMERICAL CALCULATIONS:Introduction; numbers and their accuracy;absolute; relative and percentage errors and theiranalysis; truncation errors; general formula; errorcalculation for inverse problem.2. SOLUTION OF NON-LINEAR EQUATIONS:Bisection method; Regula-Falsi method; Secantmethod; Newton-Raphson method; fixed pointmethod; initial approximation and convergencecriteria.3. SOLUTION OF LINEAR SYSTEMS: Gausselimination method; Gauss-Jorden method; UVfactorization, Jacobi‘s method; Gauss-Seidalmethod.4. INTERPOLATION & CURVE FITTING:Introduction to interpolation; Newton‘s forward andbackward formula; Sterling formula; Lagrangianpolynomials; divided differences; least squaresmethod.5. NUMERICAL DIFFERENTIATION ANDINTEGRATION: Derivatives from differencestables; numerical differentiation formulas, Newton-Cotes integration formulae; trapezodial rule;Simpson‘s rule; Bool‘s rule; Weddle‘s rule;Romberg‘s rule.6. SOLUTION OF DIFFERENTIAL EQUATIONS:Taylor‘s series method; Euler and modified Euler‘smethod; Runge-Kutta method; Milne‘s predictioncorrector method, Adams–Bashforth method.7. SOLUTION OF PARTIAL DIFFERENTIALEQUATIONS: Finite difference approximation;solution of Laplace equation (standard 5 pointformula) one-dimensional heat equation (Schmidtmethod, Cranck-Nicolson method; Dufort & Frankelmethod and wave equation.TEXT BOOKGrewal B. S., ―Numerical Methods in Engineering andSciences‖, Khanna PublisherREFERENCE BOOKS1. Curtis F, Gerald and Patrick, ―Applied NumericalAnalysis‖, 7th Edition, Addison Wesley2. Balagurusamy E., ―Numerical Methods‖, TataMcGraw Hill3. Sastry S. S., ―Introductory Methods of NumericalAnalysis‖, Prentice Hall of India4. Jain M. K., Iyenger S. R. K. and Jain R. K.―Numerical Methods for Scientific and Engg.Computations‖, Wiley Eastern5. Rao S. S., ―The Finite Element Method inEngg.‖, 2nd Edition, Pregamon Press/McGrawHill, 1989MA-252APPLIED NUMERICALMETHODS LABL T P Cr0 0 2 1LIST OF EXPERIMENTS1. To find the roots of non-linear equation usingBisection method.2. To find the roots of non-linear equation usingSecant method.3. To find the roots of non-linear equation usingNewton‘s method.4. To solve the system of linear equations usingGauss-Elimination method.5. To solve the system of linear equation usingGauss-Seidal iteration method.6. To find the values of function at a particular pointusing Newton‘s forward formula.7. To find the values of function at a particular pointusing Newton‘s backward formula.8. To find the values of function at a particular pointusing Lagrange‘s interpolation formula.9. To integrate numerically using Trapezoidal rule.10. To integrate numerically using Simpson‘s rule.11. To find the solution of o.d.e (ordinary differentialequation) by Euler‘s method.12. To find the solution of o.d.e by Runge-Kuttamethod.13. To find the numerical solution of Laplaceequation.14. To find the numerical solution of heat equation.15. To find the numerical solution of wave equation.REFERENCE BOOKS1. Curtis F, Gerald and Patrick, ―Applied NumericalAnalysis‖, 7th Edition, Addison Wesley2. Balagurusamy E., ―Numerical Methods‖, TataMcGraw Hill3. Sastry S. S., ―Introductory Methods of NumericalAnalysis‖, Prentice Hall of India4. Jain M. K., Iyenger S. R. K. and Jain R. K.―Numerical Methods for Scientific and Engg.Computations‖, Wiley EasternME-101ENGINEERING MECHANICSL T P Cr5 1 0 4OBJECTIVEEngineering Mechanics is one of the core subjects thatintroduces the student to analysis of forces and motionand prepares the student for studying strength ofmaterials and theory of machines.2 FORCE SYSTEMS: Basic concepts of space,time, mass, force, particle and rigid body; scalarsand vectors; conventions for equations anddiagrams; external and internal effects of a force;principle of transmissibility; force classification;rectangular components of two and threedimensional force systems; resultant of two andthree dimensional and concurrent force systems;moment about a point and about an axis;Varignon‘s theorem; resultant of non-concurrentforce systems; couple; equivalent couples; forcecouple systems.3 EQUILIBRIUM: Equilibrium in two and threedimensions; system isolation and the free-bodydiagram;modeling the action of forces; equilibriumconditions; applications including plane trusses;frames and machines.4 PROPERTIES OF SURFACES/CROSSSECTIONS: Centre of mass; determining thecentre of gravity; centre of mass versus centre ofgravity; centroids of lines, areas and volumesincluding composite sections; moments of inertia;MI of plane figures; MI with respect to axis in itsplane and with respect to an axis perpendicular tothe plane of figure; parallel axis theorem; momentof inertia of a rigid body – of a lamina and of threedimensional body; MI of composite figures.35
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