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B. Tech. I Sem.-I L T P C ASM 101: Eng. Mathematics- I CALCULUS (07 Hours) Reorientation of calculus. Differentiation of Hyperbolic and Inverse Hyperbolic functions. Successive Differentiation,

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B. Tech. I Sem.-I L T P C ASM 101: Eng. Mathematics- I CALCULUS (07 Hours) Reorientation of calculus. Differentiation of Hyperbolic and Inverse Hyperbolic functions. Successive Differentiation, standard forms, Leibnitz s theorem and applications, Power series, Expansion of functions, Taylor s and Maclaurin s series. APPLICATIONS OF DERIVATIVES (08 Hours) Curvature, Radius of curvature, Cartesian, polar parametric curve with application in Engineering problems. Indeterminate forms, L Hospital s rules. ORDINARY DIFFERENTIAL EQUATION (08 Hours) Reorientation of differential equation, Exact differential equation and Integrating factors, First order and higher degree odes, solvable for p, y and x, Modeling of Real world problems particularly Engg. System, spread of epidemic, spread of new technological innovations, RC and RL network. CURVE TRACING (05 Hours) Cartesian, polar and parametric form of standard curves. BETA AND GAMMA FUNCTION (04 Hours) Beta and Gamma function with their properties and duplications formula without proof. APPLICATION OF DEFINITE INTEGRATION (05 Hours) Area, arc length, surface area by revolving curve, volume by revolving area bounded by curve for Cartesian, polar and parametric curves. MATRICES (07 Hours) Elementary row and column transformation, rank of matrix, Linear dependence, consistency of linear system of equations, characteristic equation, Caley Hamilton theorem, Eigen value, Eigen vector. BOOKS RECOMMENDED : (Total Contact Time : 44 Hours) 1. James Steward De Calculas, Thomson Asia, Singapore, Bali and Iyengar. Engg. Mathematics, Laxmi Publications, New Delhi. 3. O Neil Peter., Advanced Engg. Mathematics, Thompson, Singapore, Ind. Ed J. N. Kapur, Mathematical Models in Biology and Medicine. East west Press, New Delhi F. B. Hilderband, Methods of Applied mathematics, PHI, New Delhi, 1968 B. Tech.-I Sem.-II L T P C ASM 102: Eng. Mathematics- II DIFFERENTIAL CALCULUS (07 Hours) Partial differentiation, Euler s theorem for homogeneous function, Modified Euler s theorem, Taylor s and Maclaurins series for two variables. APPLICATIONS OF PARTIAL DIFFRENTATION (08 Hours) Tangent plane and Normal line Error and Approximation, Jacobians with properties, Extreme values of function of two variables, Lagrange s methods of undetermined multipliers. DIFFERENTIAL EQUATION OF HIGHER ORDER (08 Hours) Solution of homogenous equations, complementary functions, Particular Integrals, Linear differential equation with variable coefficient, Cauchy s Euler and Legendre s equation with variable coefficient, Method of variation of parameters. MATHEMATICAL MODELS (07 Hours) Electrical network models, Detection of diabetes model and Bending beam models. SERIES SOLUTION AND SPECIAL FUNCTIONS (07 Hours) Regular point, Singular point, series solution of ODE of 2 nd order with variable coefficient with special emphasis to differential equation of Legendre s and Bessel s for different cases of roots of indicial equations. LAPLACE TRANSFORM (07 Hours) Laplace transform, Existance theorem, Laplace transform of derivatives and integrals, Inverse Laplace transform, Unit step functi ons, Dirac delta functions, Laplace transform of periodic functions, Convolutions theorem, Application to solve simple linear and simultaneous differential equations. BOOKS RECOMMENDED : 1. E. Kreyszig : Advanced Engg. Mathematics. 8th Ed, John Wiley & Sons., New York. 2. Jain and Iyenger, Advanced Engg. Mathematics, Narosa Publications, New Delhi. 3. James Steward, Calculas, Thomson Asia, 5 edition, Singapore, J. N. Kapur, Mathematical Models in Biology and Medicine, Eas t west press. 5. F. B. Hilderbrand, Methods of Applied Mathematics, McGraw Hill, New York (Total Contact Time: 44 Hours) English and Communication Skills : ASE- 111 (Common to all branches) Semester -I / II Lecture Tutorial Practical Teaching Hours Exam. Scheme Marks Internal Evaluation 50 End Sem. Exam 50 (A) THEORY: 1. Spoken English : Following Communic ative functions be discussed in meaningful natural dialogue forms: Greetings, Introductions, making request, Suggestions, Invitations, acceptance, refusal, seeking permission, giving a description, stating likes and dislikes, agreeing and disagreeing, stating performances, conversing on telephones, inquires, complains, compliments, encouragements, expressing thanks and apologies etc.( Audio Visual aids could be used for the above) 2. Written English : Business letters, Structures of business letter s, essential of good business letters, letters of enquiries, Complaints, Request etc. Report writing on general as well as scientific topics. Writing formal speeches for occasions like inauguration, introduction of guest speakers farewell etc, recording an d drafting of minutes of meetings. (B) PRACTICALS / DRAWINGS+TUTORIALS ASSIGNMENTS: NILL REFERENCES : 1. Krishna Mohan and Meera Banerji, Developing Communication Skills McMillan Co., N.Krishnaswami and T.Shariram, Creative English Communication, McMillan Co., King and Cree Modern Business Letters Orient Longman, M.I.Joshi, Let s Talk English Gujjar Prakashan, Ahmedabad., 1995 B. Tech II (Computer), Semester III L T P C MH 203 : DISCRETE MATHS GRAPH THEORY (08 Hours) Graphs, Definition & basic concepts of finite & infinite graph, Incidence & Degree, Isomorphism, Subgraph, Walk, Path & circuits, Operations on graphs, c onnected graph, Disconnected graph & components, Complete graph, Regular graph, Bipertite graph, Euler s graph, Hamiltonian paths & circuits, Weighted graphs, Applications, Directed & Undirected graphs, Connectivity of graphs. TREES (08 Hours) Definition & properties of trees, Pendent vertices in a tree, Distance between two vertices Centre, Radius & diameter of a tree, Rooted & binary trees, Representation of Algebraic structure by Binary trees, Binary search trees, Spanning trees & fundamental circuits. RELATION & LATTICES (08 Hours) Definition & Basic properties, Graphs of relation, Matrices of relation, Equivalence relation, Equivalence classes, Partition, Partial ordered relation, Posets, Hasse diagram, Upper bounds, Lower bound, GLB & LUB of sets, Definition & properties of Lattice, Sub lattice, Distributive & modular lattices, complemented & Bounded Lattices, complete lattices & Boolean algebra GROUP THEORY (08 Hours) Basic properties of Group, Groupoid, semigroup & monoid, Abelian group, Subgroup, Cosets, Normal subgroup, Lagrange s theorem, Cyclic group, Permutation group, Homomorphism & Isomorphism of groups, Basic properties, error correction & detection code. MATHEMATICAL LOGIC & PROGRAM VERIFICATION (12 Hours) Propositions, logical operators & propositional algebra, Predi cates & quantifiers, Interaction of quantifiers with logical operators, Logical interference & proof techniques, Formal verification of computer programs (elements of Hoare logic). (Total Contact Time : 44 Hours) 1. Rosen K.H., Discrete Mathematics and Its Applications, McGraw Hill, 6 th Ed., Kolman B., Busby R.C. & Ross S., Discrete Mathematical Structure, Prentice Hall of India Pvt. Ltd, 5th Ed, Tremblay J. P. & Manohar R., Discrete Mathematical structure with applications to computer science, McGraw Hill, Deo Narsingh., Graph theory with applications to Engineering & Computer Science Prentice Hall of India Pvt. Ltd., Liu C.L., Elements of Discrete Mathematics, McGraw Hill, 2000. B. Tech II (Civil), Semester - IV L T P C MH 210 : Engg. Mathematics III CALCULUS, MULTIPLE INTEGRALS (08 Hours) Reorientation of concepts of integrals, Double and Triple integrals, evaluation techniques, change of order of Integration, change of variable, Application of double and triple integrals for evaluation of area, volume and mass. BASIC CONCEPTS OF VECTOR CALCULUS (08 Hours) Line Integrals, scalar and vector point function, differential operator, gradient, directional derivative, physical meaning of gradient, divergence, curl and Laplacian with their properties, Surface Integral, Volume integral, Green s,gauss and Stoke s theorem & application. FOURIER SERIES (06 Hours) Definition, Fourier series with arbitrary period, in particular periodic function with period 2. Fourier series of even and odd function, Half range Fourier series. PARTIAL DIFFERENTIAL EQUATION (06 Hours) Second order pde of mathematical physics (Heat, wave and Laplace equation, one dimensional with standard boundary conditions, solution by separation of variable method using Fourier series. STATISTICS (06 Hours) Correlation between two variable, application of correlation, evaluation of coefficients of correlation, Rank correlation, Regression, frequency distribution, Binomial, Poisson s distribution and Normal distribution, application to industrial problem. TESTING OF HYPOTHESIS (05 Hours) 2 Test of significance, Chi-square ( )test, student s t Test, application of the t -test, F-distribution. TIME SERIES ANALYSIS (05 Hours) Short term fluctuation, trend, Decision theory. (Total Contact Time : 44 Hours) 1. Kreyszing E., Advanced Engineering Mathematics, John Wiley & Sons, Singapore, Int. Student Ed Wiley C. R., Advanced Engineering Mathema tics, McGraw Hill Inc., New York Ed O Neil Peter., Advanced Engg. Mathematics, Thompson, Singapore, Ind. Ed Greenbar Michael D., Advanced Engg. Mathematics, Pearson, Singapore, Ind. Ed Ramana D. V., Higher Engg. Mathematics, The MaGraw-Hill Inc., New Delhi, 2007. B. Tech II (Computer), Semester - IV L T P C MH 210 : Engg. Mathematics III BASIC CONCEPTS OF INTEGRALS VECTOR CALCULUS (04 Hours) Reorientation of concepts of integrals, line Integrals, scalar and vector point function, differential operator, gradient, directional derivative, physical meaning of gradient, divergence, curl and Laplacian with their properties. FOURIER SERIES (06 Hours) Definition, Fourier series with arbitrary period, in particular periodic function with period 2. Fourier series of even and odd function, Half range Fourier series. FOURIER TRANSFORM AND FOURIER TRANSFORM OF AN INTEGRAL (06 Hours) Fourier transform and its operational properties, Fourier Integral theorem, Fourier Cosine and solution, transform of derivatives, Inversion formula for Fourier transforms. COMPLEX VARIABLES (06 Hours) Basic mathematical concept, Analytic function, Cauchy Riemann equations, Harmonic functions, its applications, Linear transformation of complex domain, bilinear transformations, conformal mapping and its application, complex integration over closed contour. BASIC OF STATISTICS AND PROBABILITY DISTRIBUTION (06 Hours) Reorientation of random experiments, events, probability and its distributions of Binomial & Poisson s, their properties and Normal distribution, jointly distributed random variables, expected values, function of random variable moments, moment generating functions. SAMPLING THEORY AND ESTIMATION (07 Hours) Some basics of sampling, statistical inference, Random Samples, Sampling distribution, Sample mean, variance and other statistics, point estimate and interval estimate confidence of interval, maximum likehood estimate. TESTING OF HYPOTHESIS (07 Hours) Sampling and Test of significance, Statistical hypothesis and significance, Type I and Type II errors, Test of 2 significance. Level of Significance, single tail and two tail tests hypothesis Chi-square ( )test, student s t Test of significance of the mean of a random sample,t-test for difference of means of two small samples, Snedecor s variance ratio test or F-test and tis applications. (Total Contact Time : 42 Hours) 1. Kreyszing E., Advanced Engineering Mathematics, John Wiley & Sons, Singapore, Int. Student Ed Wiley C. R., Advanced Engineering Mathema tics, McGraw Hill Inc., New York Ed O Neil Peter., Advanced Engg. Mathematics, Thompson, Singapore, Ind. Ed Greenbar Michael D., Advanced Engg. Mathematics, Pearson, Singapore, Ind. Ed Ramana D. V., Higher Engg. Mathematics, The MaGraw-Hill Inc., New Delhi, 2007. B. Tech. II (CIVIL), Semester III L T P C MH 207: ENGINEERING ECONOMICS & MANAGEMENT ECONOMICS: (12 Hours) Introduction To Economics, Micro & Macro Economics, Applications & Scopes Of Economics, Demand Analysis, Demand Forecasting, Factors Of Production, Types Of Cost, Market Structures, Break Even Analysis, Concept Of Supply, National Income MANAGEMENT: (16 Hours) Introduction To Management, Features Of Management, Nature Of Management, Development Of Management Thoughts Scientific Management By Taylor & Contribution Of Henry Fayol, Coordination & Functions Of Management, Centralization & Decentralization, Decision Making Fundamentals Of Planning Objectives & MBO Types Of Business Organizations: Private Sector, Public Sector & Joint Sector Organizational Behavior: Theories Of Motivation, Individual & Group Behavior, Perception, Value, Attitude, Leadership FUNCTIONAL MANAGEMENT: (12 Hours) Marketing Management: Core Concepts Of Marketing, Marketing Mix (4p), Segmentation Targeting Positioning, Marketing Research, Marketing Information System, Concept Of International Marketing, Difference Between Domestic Marketing & International Marketing Personnel Management: Roles & Functions Of Personnel Manager, Recruitment, Selection, Training Financial Management: Goal Of Financial Management, Key Activities In Financial Management, Organization Of Financial Management, Financial Institutions, Financial Instruments, Sources Of Finance MODERN MANAGEMENT ASPECTS: (05 Hours) Introduction To ERP, e CRM, SCM, RE Engineering, WTO, IPR Etc. Books Recommended: (Total Contact Hours: 45 Hours) 1. Prasad L.M., Principles & Practice Of Management, Sultan Chand & Sons, Banga T. R. & Shrama S.C., Industrial Organisation & Engineering Economics, Khanna Publishers, Robbins S., Organizational Behavior, Phi (Pearson), Kotler P., Keller, Koshi & Jha, Marketing Management A South Asian Perspective, Pearson, Aswathapa K, Human Resource and Personnel Management, Tata McGraw Hill, 2001 B. Tech II (Chemical), Semester - III L T P C MH 210 : Engg. Mathematics III CALCULUS, MULTIPLE INTEGRALS (08 Hours) Reorientation of concepts of integrals, Double and Triple integrals, evaluation techniques, change of order of Integration, change of variabl e, Application of double and triple integrals for evaluation of area, volume and mass. BASIC CONCEPTS OF VECTOR CALCULUS (08 Hours) Line Integrals, scalar and vector point function, differential operator, gradient, directional derivative, physical meaning of gradient, divergence, curl and Laplacian with their properties, Surface Integral, Volume integral, Green s,gauss and Stoke s theorem & application. FOURIER SERIES (06 Hours) Definition, Fourier series with arbitrary period, in particular periodic function with period 2. Fourier series of even and odd function, Half range Fourier series. PARTIAL DIFFERENTIAL EQUATION (06 Hours) Second order pde of mathematical physics (Heat, wave and Laplace equation, one dimensional with standard boundary conditions, solution by separation of vari able method using Fourier series. FOURIER INTEGRAL & TRANSFORM (06 Hours) Fourier Integral theorem, Fourier sine and cosine integral complex form of integral, Inversion formula for Fourier transforms, Fourier t ransforms of the derivative of a function, Application of Fourier transforms to boundary value problems. COMPLEX VARIABLES (08 Hours) Basic mathematical concept, Analytic function, C R equations, Harmonic functions, its applications, Linear transformation of complex domain, some special transformation, bilinear transformations, conformal mapping and its ap plication, complex integration including contour integration. ELEMENTS OF STATISTICS & PROBABILITY (08 Hours) Correlation between two variable, application of correlati on, evaluation of coefficients of correlation, Rank correlation, Regression, frequency distribution, Binomial, Poisson s distribution and Normal distribution, 2 application to industrial problem, Test of significance, Chi -square test, student s t Test, application of the t- test, F-distribution. (Total Contact Time : 50 Hours) 1. Kreyszing E., Advanced Engineering Mathematics, John Wiley & Sons, Singapore, Int. Student Ed Wiley C. R., Advanced Engineering Mathematics, McGraw Hill Inc., New York Ed O Neil Peter., Advanced Engg. Mathematics, Thompson, Singapore, Ind. Ed Greenbar Michael D., Advanced Engg. Mathematics, Pearson, Singapore, Ind. Ed Ramana D. V., Higher Engg. Mathematics, The MaGraw -Hill Inc., New Delhi, 2007. B. Tech II, (Electrical), Semester III L T P C MH 210 : Engg. Mathematics III CALCULUS, MULTIPLE INTEGRALS (08 Hours) Reorientation of concepts of integrals, Double and Triple integrals, evaluation techniques, change of order of Integration, change of variable, Application of double and triple integrals for evaluation of area, volume and mass. BASIC CONCEPTS OF VECTOR CALCULUS (08 Hours) Line Integrals, scalar and vector point function, differential operator, gradient, directional derivative, physical meaning of gradient, divergence, curl and Laplacian with their properties, Surface Integral, Volume integral, Green s,gauss and Stoke s theorem & application. FOURIER SERIES (06 Hours) Definition, Fourier series with arbitrary period, in particular periodic function with period 2. Fourier series of even and odd function, Half range Fourier series. FOURIER INTEGRAL & TRANSFORM (06 Hours) Fourier Integral theorem, Fourier sine and cosine integral complex form of integral, Inversion formula for Fourier transforms, Fourier transforms of the derivative of a function. PARTIAL DIFFERENTIAL EQUATION (06 Hours) Second order pde of mathematical physics (Heat, wave and Laplace equation, one dimensional with standard boundary conditions, solution by separation of variable method using Fourier series, Solution by Separation of variables & transformation techniques. COMPLEX VARIABLES (10 Hours) Basic mathematical concept, Analytic function, C R equations, Harmonic functions, its applications, Linear transformation of complex domain, some special transformation, bilinear transformations, conformal mapping and its application, complex integration including contour integration. 1. Kreyszing E., Advanced Engineering Mathematics, John Wiley, Int. Student Ed Wiley C. R., Advanced Engineering Mathematics, McGraw Hill, Int. Student Ed O Neil Peter., Advanced Engg. Mathematics, Thompson, Singapore, Ind. Ed Greenbar Michael D., Advanced Engg. Mathematics, Pearson, Singapore, Ind. Ed Ramana D. V., Higher Engg. Mathematics, The MaGraw -Hill Inc., New Delhi, (Total Contact Time : 44 Hours) B. Tech.II (Mechanical & Production), Semester IV L T P C MH 210: ENGG. MATHEMATICS III CALCULUS, MULTIPLE INTELRALS (08 Hours) Reorientation of concepts of integrals, Double and Triple integrals evaluation techniques, Change of order of Integration, Change of variable, Application of double and triple integrals for evaluation of area, volume and mass. BASIC CONCEPTS OF VECTOR CALCULU S (08 Hours) Line Integrals, Scalar and vector point function, Differential operator, Gradient, Directional derivative, Physical meaning of gradient, Divergence, Curl and Laplacian with their properties, Surface Integral, Volume integral, Green s,gauss and Stoke s theorem & application. FOURIER SERIES (06 Hours) Definition, Fourier series with arbitrary period, in particular periodic function with period 2π. Fourier series of even and odd function, Half range, Fourier series. PARTIAL DIFFERENTIAL EQUATION (08 Hours) Second order PDE of mathematical physics (Heat, wave one dimensional equation and Laplace equation with standard boundary conditions), Solution by separation of variable method using Fourier series. INTRODUCTION TO ENGINEERING ANALYSIS (06 Hours) Types of problems encountered in Mechanical Engineering, Classification of problems based on methods of solution. SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS (12 Hours) Euler s method, Runge-Kutta method, Boundary value and eigen value problems, Application to mechanical engineering problems, Taylor s series and Predictor-Corrector meth

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