Department Of Mathematics NATIONAL INSTITUTE OF TECHNOLOGY .
Department of MathematicsNATIONAL INSTITUTE OF TECHNOLOGYWARANGALSCHEME OF INSTRUCTION AND SYLLABIfor Two-Year M.Sc. (Applied Mathematics) ProgramEffective from 2021-2022DEPARTMENT OF MATHEMATICSScheme and Syllabiw.e.f. 2021-22
Department of MathematicsVision and Mission of the InstituteVISIONTowards a Global Knowledge Hub, striving continuously in pursuit ofexcellence in Education, Research, Entrepreneurship and Technological services tothe societyMISSION Imparting total quality education to develop innovative, entrepreneurial and ethicalfuture professionals fit for globally competitive environment. Allowing stake holders to share our reservoir of experience in education andknowledge for mutual enrichment in the field of technical education. Fostering product-oriented research for establishing a self-sustaining and wealthcreating center to serve the societal needs.Vision and Mission of the DepartmentDepartment of MathematicsVISIONTo be among the best mathematics departments in the country, to build aninternational reputation as a centre of excellence in mathematics and computational research,training, and education, and to inculcate mathematical thinking in order to meet thechallenges and growth of science and technology, as well as the needs of industry andsociety, with moral and ethical responsibility.MISSION To attract motivated and talented students by providing a learning environment where theycan learn and develop the mathematical and computational skills needed to formulate andsolve real-world problems. To foster an environment conducive to quality research and to train principled and highlyskilled researchers with clear thinking and determination capable of meeting the dynamicchallenges of science and engineering. To keep up with the rapid advancements of technology while improving academicstandards through innovative teaching and learning processes. To satisfy the country's human resource and scientific manpower requirements inmathematics through learner-centered contemporary education and research.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsDepartment of Mathematics:Brief about the Department:The Department of Mathematics is one of the highly reputed Departments in theinstitute which functions with excellence as its motto. The Department of Mathematics wasestablished in 1959 along with other engineering departments, expanded in 1984 as Dept. ofMathematics & Humanities and bifurcated in 2009 as Department of Mathematics. TheDepartment is established as a dynamic centre for academic and research activities.The Department offers basic courses in Mathematics for B.Tech. At post-graduatelevel, the Department offers well-designed diverse courses for all programmes of M.Tech.,M.C.A., M.B.A. and M.Sc. Tech (Engg. Physics) and also offers open electives for all UG, PGand Ph.D. Programmes.The Department offers two P.G. Programs, M.Sc. (Applied Mathematics) started in theyear 1970 and M.Sc. (Mathematics and Scientific Computing) started in 2001. The M.Sc.programs for both streams of Mathematics are designed with one laboratory course in eachsemester in addition to the regular rigorous theory courses. They inculcate a spirit of practicalapplication of mathematical concept and also instil enthusiasm for research activity. Specialemphasis is laid on promoting team spirit and improving the oral communication skills of thestudents, which enables all-round development of the students.The Department since its inception in 1959 is known to be an active research centre inMathematics. The frontier areas of research of the department are Fluid Mechanics,Computational Fluid Mechanics, Bio-mechanics, Numerical Analysis, Finite Element Method,Optimization Techniques, Coding Theory, Cryptography, Differential Equations etc., TheDepartment offers Ph.D. program in Mathematics on regular basis, part-time and also underQuality Improvement Program (QIP) and the Department is the only QIP centre forMathematics in India. So far about 115 Ph.Ds. have been awarded and several researchpapers have been published in national and international journals.The Department has a full-fledged computational laboratory to meet the requirementsof the M.Sc. students, research scholars and the faculty. The Department has a well-stockedlibrary for immediate reference of the staff and students.The Department was recognized as a National Resource Centre in Mathematics byMoE, Govt. of India to conduct Online Refresher Courses for all Mathematics Facultymembers (irrespective of their seniority and designation) of all Institutions in the Country.The department organized three international conference (ICCHMT – 2015, NHTFF –2018), two GIAN programs. Several National conferences, Summer/refresher courses andWorkshops.The Department has successfully completed several research projects funded byvarious organizations like MHRD, AICTE, UGC, CSIR and DST etc and there are 3 ongoingprojectsList of Programs offered by the Department:ProgramIntegrated M.Sc.M.Sc.MinorPh.D. (Full time, Part-time and QIP)Title of the ProgramIntegrated M.Sc., MathematicsM.Sc., Applied MathematicsM.Sc., Mathematics and Scientific ComputingMathematicsMathematicsNote: Refer to the following weblink for Rules and Regulations of PG tions/PGProgrammes/Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsM.Sc. in Applied MathematicsProgram Educational ObjectivesPEO-1PEO-2PEO-3PEO-4PEO-5Provide sufficient understanding of the fundamentals of mathematics withcomputational techniques, and program core to address challenges faced inmathematics and other related interdisciplinary fields.Facilitate as a deep learner and progressive careers in teaching, academia,research organizations, national/international laboratories and industryDevelop models and simulation tools for real life problems by analysing andapplying mathematical and computational tools and techniques.Demonstrate effective communication and interpersonal, management andleadership skills to fulfil professional responsibilities, retaining scientific fervourin day-to-day affairs.Engage in lifelong learning and adapt to changing professional and societalneedsProgram Articulation MatrixPEOPEO1PEO2PEO3PEO4PEO523232To foster an environment conducive to qualityresearch and to train principled and highly skilledresearchers with clear thinking and determinationcapable of meeting the dynamic challenges ofscience and engineering.33322To keep up with the rapid advancements oftechnology while improving academic standardsthrough innovative teaching and learning processes.23222To satisfy the country's human resource andscientific manpower requirements in mathematicsthrough learner-centered contemporary educationand research.32333Mission StatementsTo attract motivated and talented students byproviding a learning environment where they canlearn and develop the mathematical andcomputational skills needed to formulate and solvereal-world problems.1-Slightly;Scheme and Syllabi2-Moderately;3-Substantiallyw.e.f. 2021-22
Department of MathematicsM.Sc. in Applied MathematicsProgram OutcomesAt the end of the program, the student will be able to:PO1PO2PO3PO4PO5PO6Gain and apply the knowledge of basic scientific and mathematicalfundamentals to understand the Nature and apply it to develop new theoriesand models.Design models for complex mathematics problems and find out solutions thatmeet the specified needs with appropriate consideration for the public health,safety, cultural, societal and environmental considerations.Use of research-based knowledge and research methods including design ofphysical/computational experiments and evolve procedures appropriate to agiven problem.Create, select, and apply appropriate techniques, resources, and modern ITtools including prediction and modelling to complex real-life problems with anunderstanding of the limitations.Function effectively as an individual, and as a member or leader in diverseteams to manage projects in multidisciplinary environmentsUse numerical analysis and simulation modelling and interpretation of data toprovide valid conclusionsScheme and Syllabiw.e.f. 2021-22
Department of MathematicsSCHEME OF INSTRUCTIONM.Sc. (Applied Mathematics) – Course StructureI - Year, I – SemesterS. MA4106MA4107Course NameReal AnalysisOrdinary Differential EquationsAdvanced Modern AlgebraLinear AlgebraComputer Programming in C Numerical AnalysisCPP LabLTPCredits3333330Total otal 33333300Total CPCCPCCI - Year, II – SemesterS. 5MA4159MA4198Course NameProbability & StatisticsPartial Differential EquationsComplex AnalysisTopologyMathematical ProgrammingELECTIVE – INumeric Computing LaboratorySeminar - ICat.CodePCCPCCPCCPCCPCCPECPCCSEMII - Year, I – SemesterS. 3MA5148Scheme and SyllabiCourse NameMechanicsNumerical Solution of DifferentialEquationsFunctional AnalysisDiscrete MathematicsELECTIVE – IIELECTIVE – IIIMathematical Programming LabSeminar - IICat.CodePCCPCCPCCPCCPECPECPCCSEMw.e.f. 2021-22
Department of MathematicsII - Year, II – SemesterS. No.12345CourseCodeMA5161MA5197MA5199Course NameELECTIVE – IVELECTIVE – VNSDE LabComprehensive VivaDissertation 5Cat.CodePECPECPCCCVVDWSCHEME OF INSTRUCTIONCredits in Each SemesterCat. CodePCCPECDWSEMCVVTotalScheme and 0.5Sem-IV1.5610219.5Total5115102280w.e.f. 2021-22
Department of MathematicsList of e NameI - Year, II – Semester: Elective-IIntegral Transforms and Integral EquationsDifferential Geometry and Tensor AnalysisFinite Volume MethodII - Year, I – Semester: Elective-IIFluid DynamicsMultivariate Data AnalysisLie group Methods for Differential EquationsDistribution TheoryII - Year, I – Semester: Elective-IIIFinite Element MethodDynamical SystemsIterative MethodsSpectral MethodsII - Year, II – Semester: Elective-IVMeasure and IntegrationNon-Newtonian FluidsComputational Fluid DynamicsDynamo TheorySobolev SpacesII - Year, II – Semester: Elective-VInventory, Queueing Theory and Non-Linear ProgrammingHeat and Mass TransferBio-Fluid MechanicsElectro-kinetic Transport PhenomenaVariational Methods and SplinesNote:1. In addition to the above listed electives, a student may register for electives fromMathematics and Scientific Computing stream on satisfying the minimum prerequisite of the specific course(s).2. An elective may be offered to the students, only if a minimum of 15 students optfor it.3. Students can take maximum of TWO subjects (other than the above listed) fromMOOC in any of the Elective slots with the approval of DAC - PG & R.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsDETAILED SYLLABUS FOR EACH COURSEM.Sc. (Applied Mathematics):: I Year I SemesterCourse Code:MA4101Credits3-0-0: 3Real AnalysisPre-Requisites: NILCourse Outcomes:At the end of the course, the student will be able to:CO1CO2CO3CO4Find whether a given function can be Riemann integrableTest whether a given improper integral can be convergentExamine uniform convergence of given sequence and /or series of functionsExpand a given function into Fourier seriesCourse Articulation 33323223233Syllabus:Basic Topology: IntroductionRiemann Stieltje’s integral: Definition and existence of the integral, Properties of theintegral, Integration and differentiation of integral with variable limits.Improper integrals: Definitions and their convergence, Tests of convergence, and functions.Uniform convergence: Tests for uniform convergence, Theorems on limit and continuity ofsum functions, Term by term differentiation and integration of series of functions.Power series: Convergence and their properties.Fourier series: Dirichlet’s’ conditions, Existence, Problems, Half range sine and cosineseries.Learning Resources:Text Books:1. Principles of Mathematical Analysis, Walter Rudin, McGraw Hill, 2017, Third Edition.2. Real Analysis, Brian S.Thomson, Andrew M.Bruckner, Judith B.Bruner, Prentice HallInternational, 2008.Reference Books:1. Introduction to Real Analysis, William F. Trench, Library of Congress Cataloging-inPublication Data, Free Edition 1.04, April 20102. Real Analysis, N.L. Carothers, Cambridge University Press, 20003. Mathematical Analysis, Tom M. Apostol, Addison Wesley, 1974, Second EditionScheme and Syllabiw.e.f. 2021-22
Department of MathematicsCourse Code:MA4102Ordinary Differential EquationsCredits3-0-0: 3Pre-Requisites: NILCourse Outcomes:At the end of the course, the student will be able to:CO1CO2Determine linearly independent solutions and general solution of a non-homogeneousdifferential equationsFind power series solution to a differential equation containing variable coefficientsCO3Discuss the existence and uniqueness of solution for an initial value problemCO4Use Green's function to solve a non-homogeneous boundary value problemCourse Articulation 33323223233Syllabus:First Order Equations: Picard’s theorem, Non-Local existence theorem.Second Order Equations: Linear dependence and independence, A formula for theWronskian, the non-homogeneous equations, linear equations with variable coefficients,reduction of the order of the homogeneous equation, Sturm comparison theorem, Sturmseparation theorem.Stability: Autonomous Systems. The Phase Plane and Its Phenomena, Types of CriticalPoints. Stability, Critical Points and Stability for Linear Systems.Systems of Differential Equations: Existence theorems, homogeneous linear systems,non-homogeneous linear systems, linear systems with constant coefficients, eigenvalues andeigenvectors, diagonal and Jordan lueproblems,Green'sfunctions, construction of Greens functions, non-homogeneous boundary conditions.Learning Resources:Text Books:1. Differential Equations with Applications and Historical Notes, G.F. Simmons, McGrawHill, 2017, Second Edition.2. An Introduction to Ordinary Differential Equations, E.A. Coddington, PHI Learning, 1999.3. Ordinary Differential Equations, Tyn Myint U, Elesvier, North- Holland, 1978.4. Textbook of Ordinary Differential Equations, V. Raghavendra, Rasmita Kar, S.G. Deo, V.Lakshmikantham, McGraw Hill India, 2015, Third Edition.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsReference Books:1. Differential Equations and Their Applications, M. Braun, Springer-Verlag, 1983, ThirdEdition.2. Differential and Integral Equations, P.J. Collins, Oxford University Press, 2006.3. Elementary Differential Equations and Boundary Value Problems, W.E.Boyce and R.C. DiPrima, John Wiely & Sons, 2001.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsCourse Code:MA4103Advanced Modern AlgebraCredits3-0-0: 3Pre-Requisites: NILCourse Outcomes:At the end of the course, the student will be able to:CO1CO2CO3CO4CO5Analyse the structure of groupsDistinguish the properties among ring structuresUnderstand extension of fields and their constructionsApply the concepts and results to solve problems of Modern AlgebraConstruct proofs that arise in various algebraic structuresCourse Articulation 22222222332222222222Syllabus:Groups: Group actions; Cayley’s theorem; Class equation, Automorphisms; Sylow theoremsand applications;Rings: Ring homomorphisms and quotient rings; Quadratic integer rings; Properties of ideals;Rings of fractions; The Chinese Remainder Theorem;Classes of Rings: Euclidean domains – norm, division algorithm, field norm on quadraticinteger rings, results; Principal ideal domains – properties and results, Dedekind-Hasse norm;Unique factorization domains – irreducible elements, prime elements, associates, propertiesand results; Polynomial rings over fields, polynomial rings that are UFDs, irreducibility criteria;Fields: Brief introduction to fields, field extensions, finite fields;Learning Resources:Text Books:1. Abstract Algebra, David S. Dummit and Richard M. Foote, John Wiley & Sons, 2004,Third Edition2. Topics in Algebra, I. N. Herstein, John Wiley & Sons, 1975, Second EditionReference Books:1. Algebra, Michael Artin, Pearson, 2016, Second Edition2. Contemporary Abstract Algebra, Joseph A. Gallian, Cengage Learning, 2013, EighthEdition3. Algebra, Serge Lang, Springer, 2002, Revised Third Edition.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsCourse Code:MA4104Credits3-0-0: 3Linear AlgebraPre-Requisites: NILCourse Outcomes:At the end of the course, the student will be able to:CO1CO2CO3CO4CO5Test the consistency of system of linear algebraic equationsVerify rank nullity theorem for a given linear transformationFind eigenvalues and canonical forms of a linear operatorIdentify the importance of orthogonal property in the spectral theoryDemonstrate the knowledge of bilinear form and its natureCourse Articulation Syllabus:System of Linear Equations: Matrices and elementary row operations, Uniqueness ofechelon forms, Moore-Penrose Generalized inverse, Solutions of homogeneous and nonhomogeneous linear system of equations.Vector Spaces and Linear Transformations: Vector spaces, Subspaces, Bases anddimension, Coordinates, Linear transformations and its algebra and representation bymatrices, Algebra of polynomials.Diagonalization of Matrices: Elementary canonical forms, Characteristic values andcharacteristic vectors, Cayley-Hamilton theorem, Annihilating polynomial, Invariantsubspaces. Simultaneous triangularization, Simultaneous diagonalization, Jordan form.Inner Product Spaces: Inner product spaces, Unitary and normal operators, Bilinear forms.Learning Resources:Text Books:1. Linear Algebra, K.Hoffman and R.Kunze, Prentice Hall of India, New Delhi, 2003.2. Linear Algebra Done Right, Sheldon Axler, Springer nature, 2015, Third Edition.Reference Books:1. First Course in Linear Algebra, P.G. Bhattacharya, S.K. Jain and S.R. Nagpaul, WileyEastern Ltd., New Delhi, 1991.2. Matrix and Linear Algebra, K.B.Datta, Prentice Hall of India, New Delhi, 2006.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsCourse Code:MA4105Credits3-0-0: 3Computer Programming in C Pre-Requisites: NILCourse Outcomes:At the end of the course, the student will be able to:CO1CO2CO3CO4Develop algorithms for mathematical and scientific problemsUnderstand the components of computing systemsChoose data types and structures to solve mathematical and scientific problemsDevelop modular programs using control structuresCourse Articulation 32112211Syllabus:Introduction: History of C , Overview of Procedural Programming and Object-OrientationProgramming, Using main () function, Compiling and Executing Simple Programs.Expressions and operators: Tokens, Expressions and Operators, loops and controlling theloop execution, logic, bitwise and arithmetic operators.Functions: Function Declarations, different methods of passing parameters and theirpurpose, Default Arguments, Structures and unions.Pointers: Arrays Pointers into Arrays, Constants, Pointer to Function, References Pointers tovoid Structures.Strings: converting values of different types, strings:assignments, functions and strings, pointers and strings.declarations,initializations,Learning Resources:Text Books:1. C : The Complete Reference, H. Schildt, McGraw Hill, 2003, Fourth Edition.2. Programming with C , John R. Hubbard, McGraw-Hill, 2006, Second edition.Reference Books:1. C Primer, Stanley B. Lippman, Josee Lajoie, and Barbara E. Moo, PearsonEducation, 2013, Fifth Edition.2. Problem solving with C , Walter Savitch, Pearson Education, 2014, 9th edition.3. Let Us C , Yashavant Kanetkar, BPB Publications, 2020.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsCourse Code:MA4106Credits3-0-0: 3Numerical AnalysisPre-Requisites: NILCourse Outcomes:At the end of the course, the student will be able toCO1CO2CO3CO4CO5Construct the Polynomial to the given dataEvaluate the integrals numericallyFind the roots of nonlinear equationsApproximate the function by a polynomialSolve Initial value problems numericallyCourse Articulation 11PO5PO623123Syllabus:Interpolation: Existence, Uniqueness of interpolating polynomial, Error of interpolation,Unequally spaced data - Lagrange’s and Newton’s divided difference formulae, Equallyspaced data - finite difference operators and their properties, Inverse interpolation,Hermite interpolation.Differentiation: Finite difference approximations for first and second order derivatives.Integration: Newton-cotes closed type methods - particular cases and error terms;Newton cotes open type methods - Romberg integration, Gaussian quadrature,Legendre, Chebyshev formulae.Solution of nonlinear and transcendental equations: Regula-Falsi method, NewtonRaphson method, Muller’s method, System of nonlinear equations.Approximation: Norms, Least square (using monomials and orthogonal polynomials),Uniform and Chebyshev approximations.Solution of linear algebraic system of equations: Gauss-Seidal methods, Solution oftridiagonal system, Ill conditioned equations, Eigen values and eigen vectors using Powermethod.Solution of ordinary differential equations - Initial value problems: Single stepmethods; Taylor’s, Euler’s, Runge-Kutta methods, Error analysis; Multi-step methods:Milne’s predictor-corrector methods; System of IVP’s and higher orders IVP’s.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsLearning Resources:Text Books:1. Numerical Methods for Engineers and Scientists, MK Jain, SRK Iyengar and RK Jain,New Age International, 2008.2. Applied Numerical Analysis, C.F.Gerald and P.O.Wheatley, Addison-Wesley, 1984.Reference Books:1. An Introduction to Numerical Analysis, K. Atkinson, Numerical Analysis, JohnWiley,19892. Introduction to Numerical Analysis, F.B. Hildebrandt, Courier Coporation,1987.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsCourse Code:MA4107Credits0-0-3: 1.5CPP LabPre-Requisites: MA4105Course Outcomes:At the end of the course, the student will be able to:CO1CO2CO3CO4Design and test programs to solve mathematical and scientific problems.Develop and test programs using control structures.Implement modular programs using functions.Develop program using pointers and structures.Course Articulation 53221PO63211Syllabus:Programs using1. conditional control constructs.2. loops (while, do-while, for).3. user defined functions and library functions.4. arrays, matrices (single and multi-dimensional arrays).5. pointers (int pointers, char pointers).6. Programs on structures.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsM.Sc. (Applied Mathematics):: I Year II SemesterCourse Code:MA4151Pre-Requisites: NILCourse Outcomes:Credits3-0-0: 3Probability & StatisticsAt the end of the course, the student will be able to:CO1CO2CO3CO4CO5Determine the mean, standard deviation and mth moment of a probabilitydistributionApply theoretical model to fit the empirical dataDifferentiate between Large and small sample testsUse the method of testing of hypothesis for examining the validity of a hypothesisEstimate the parameters of a population from knowledge of statistics of a sampleCourse Articulation 33323111122212Syllabus:Random variables:Review of probability; Probability distributions with discrete andcontinuous random variables - Joint probability mass function, Marginal distribution function,Joint density function – Independent random variables - Mathematical Expectation - Momentgenerating function - Chebyshev’s inequality - Weak law of large numbers - Bernoulli trialsTheoretical Probability Distributions: Binomial, Negative Binomial, Geometric, Poisson,Normal, Rectangular, Exponential, Gaussian, Beta and Gamma distributions and theirmoment generating functions; Fit of a given theoretical model to an empirical data.Sampling and Testing of Hypothesis: Introduction to testing of hypothesis - Tests ofsignificance for large samples – t, F and Chi-square tests; ANOVA - one-way and two-wayclassifications.Theory of estimation: Characteristics of estimation - Minimum variance unbiased estimator Method of maximum likelihood estimation.Correlation and Regression: Scatter diagram - Linear and polynomial fitting by the methodof least squares - Linear correlation and linear regression - Rank correlation - Correlation ofbivariate frequency distribution.Learning Resources:Text Books:1. Fundamentals of Mathematical Statistics, S.C. Gupta and V.K. Kapur, S.Chand & Sons,New Delhi, 20082. An Introduction to Probability theory and Mathematical Sciences, V.K. Rohatgi and A.K.Md. Ehsanes Saleh, Wiley, 2001References1.Miller & Freund’s Probability and Statistics for Engineers, Richard A. Johnson,Pearson, 2018, Ninth EditionScheme and Syllabiw.e.f. 2021-22
Department of MathematicsCourse Code:MA4152Partial Differential EquationsCredits3-0-0: 3Pre-Requisites: MA4102Course Outcomes:At the end of the course, the student will be able to:CO1CO2CO3CO4CO5Solve linear and nonlinear first order partial differential equationsDemonstrate the concept of characteristic curves and characteristic ationsdifferentialwithequationsof coefficientsboth first andSolvehigherorderdifferentialconstantsecondorder withFindcanonicalforms of second order partial differential erentialequations ofUtilize theknowledgeof linearPDESandin solvingvariousphysicalproblemsboth first and second order withCourse Articulationdifferent Matrix:methodsorder withPO1different methodsorderwithCO13CO23different llabus:Equations of the First Order: Formulation; Classification of first order partial differentialequations (PDEs); Lagrange’s method, Cauchy problem, and method of characteristics forlinear and quasilinear PDEs; Paffian equation, Condition for integrability; First order non-linearequations, Complete integrals, Envelopes and singular solutions, Method of Charpit andMethod of characteristics.Equations of higher order: Method of solution for the case of constant coefficients;Classification of second order equations; Reduction to canonical forms; Method of solution byseparation of variables.Wave equation: Derivation of the wave equation; D'Alembert solution of wave equation,Domain of dependence and range of influence; Method of separation of variables;Inhomogeneous wave equation, Duhamel’s principle.Diffusion equation: Derivation of the heat equation, Method of separation of variables,Solutions of heat equation with homogeneous and non-homogeneous boundary conditions;Inhomogeneous heat equation, Duhamel’s principle.Laplace’s equation: Basic concepts; Types of boundary value problems; The maximum andminimum principles; Boundary value problems; Method of separation of variables.Learning Resources:Text Books:1. Elements of Partial Differential Equations, I. Sneddon, Dover Publications, 2013.2. Linear Partial Differential Equations for Scientists and Engineers, Tyn Myint-U andLokenath Debnath, Birkhauser, Bostan, 2007, Fourth Edition.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsReference Books:1. Partial Differential Equations, P. Prasad and R. Ravindran, New Age International (P)Ltd., New Delhi, 20102. An Elementary Course in Partial Differential Equations, T. Amaranath, Narosa PublishingHouse, New Delhi, 2003, Second Edition.Scheme and Syllabiw.e.f. 2021-22
Department of MathematicsCourse Code:Credits3-0-0: 3Complex AnalysisMA4153Pre-Requisites: MA4101Course Outcomes:At the end of the course, the student will be able to:CO1CO2CO3CO4CO5Introduce the analyticity of complex functions and study their applicationsEvaluate complex integrals and expand complex functionsDetermine and classify the zeros and singularities of the complex functionsEvaluate improper integrals by residue theoremLearn the uniqueness of conformal transformationCourse Articulation O5PO621212Syllabus:Functions of Complex Variables: Complex variable - Functions of a complex variable Continuity - Differentiability – Analytic functions.Complex Integration: Cauchy’s theorem - Cauchy’s integral formula - Morera’s theorem Cauchy’s inequality - Liouville’s theorem.Series Expansions: Taylor’s theorem - Laurent’s theorem - Zeros of an analytic function SingularitiesContour Integration: Residue - Cauchy’s residue theorem – contour integration - thefundamental theorem of algebra - Poisson’s integral formula. Analytic continuation - branchesof a many-valued function - Riemann surface.Conformal Mapping: The maximum modulus theorem - mean values of f(z) - Conformalrepresentation – Bilinear transformation - Transformation by elementary functions uniqueness of conformal transformation - representation of any region on a circle.Learning Resources:Text Books:1. Complex Variables and Applications, R.V. Churchill and J.W. Brown, McGraw Hill,Tokyo, 2009, Eighth Edition.2. Theory of Complex Variables, E.T. Copson, Oxford University Press, New Delhi, 1974.ReferencesScheme and Syllabiw.e.f. 2021-22
Department of Mathematics1. Complex Variables with Applications, S. Ponnusamy & Herb Silverman, Birkhauser,Boston, 2006, First Edition2. Compl
The Department of Mathematics was established in 1959 along with other engineering departments, expanded in 1984 as Dept. of Mathematics & Humanities and bifurcated in 2009 as Department of Mathematics. The Department is established as a dynamic centre for academic and research activities. The Department offers basic courses in Mathematics for .
IBDP MATHEMATICS: ANALYSIS AND APPROACHES SYLLABUS SL 1.1 11 General SL 1.2 11 Mathematics SL 1.3 11 Mathematics SL 1.4 11 General 11 Mathematics 12 General SL 1.5 11 Mathematics SL 1.6 11 Mathematic12 Specialist SL 1.7 11 Mathematic* Not change of base SL 1.8 11 Mathematics SL 1.9 11 Mathematics AHL 1.10 11 Mathematic* only partially AHL 1.11 Not covered AHL 1.12 11 Mathematics AHL 1.13 12 .
as HSC Year courses: (in increasing order of difficulty) Mathematics General 1 (CEC), Mathematics General 2, Mathematics (‘2 Unit’), Mathematics Extension 1, and Mathematics Extension 2. Students of the two Mathematics General pathways study the preliminary course, Preliminary Mathematics General, followed by either the HSC Mathematics .
2. 3-4 Philosophy of Mathematics 1. Ontology of mathematics 2. Epistemology of mathematics 3. Axiology of mathematics 3. 5-6 The Foundation of Mathematics 1. Ontological foundation of mathematics 2. Epistemological foundation of mathematics 4. 7-8 Ideology of Mathematics Education 1. Industrial Trainer 2. Technological Pragmatics 3.
1.1 The Single National Curriculum Mathematics (I -V) 2020: 1.2. Aims of Mathematics Curriculum 1.3. Mathematics Curriculum Content Strands and Standards 1.4 The Mathematics Curriculum Standards and Benchmarks Chapter 02: Progression Grid Chapter 03: Curriculum for Mathematics Grade I Chapter 04: Curriculum for Mathematics Grade II
Department of Mathematics Florida State University 208 Love Building 1017 Academic Way Tallahassee, FL 32306-4510 Phone: 850-644-2202 Fax: 850-644-4053 Web: www.math.fsu.edu DEPARTMENT OF MATHEMATICS AT FLORIDA STATE UNIVERSITY Mark Sussman. 4 May 2020 Faculty . mathematics. Mathematics. math. mathematics.".
DEPARTMENT OF MATHEMATICS Fall 2019 Undergraduate Handbook. Department of Mathematics Page 1 OVERVIEW OF UNDERGRADUATE PROGRAM The Undergraduate Programs in the Department of Mathematics seek to provide a high quality education to our students, focusing both on depth and breadth in all fields of Mathematics. This may include but is not
Mathematics Department office, Kidder 368, open Monday through Friday from 9am to 5pm 2 INTRODUCTION The Department of Mathematics at OSU offers a Bachelor of Science degree in Mathematics, a minor in Mathematics, and a minor in Actuarial Science. The department also offers MA, MS, and PhD degrees at the graduate level.
ANSI A300 Part 9: A nce 28 2012. Reality Bites Puget Sound Energy, 1998 – 2007 34,000 tree-caused outages Trees were primary cause of unplanned service interruptions 95% due to tree failure From Arboriculture & Urban Forestry July 2011. 37(4): 147 - 151 . Key Points What is ANSI A300 (Part 9)? How does it relate to IVM? How does it apply to utilities? ANSI Standard A300 Tree Risk Assessment .
