May 20th, 2017 07:36 PM | ||

Unregistered | Re: Syllabus of PhD entrance exam in Delhi UniversityI WANT TO KNOW HOW COULD I DOWNLOAD THE SYLLABUS OF PUNJABI FOR PHD ENTRANCE TEST OF DELHI UNIVERSITY | |

October 2nd, 2015 12:48 PM | ||

shabnams | Re: Syllabus of PhD entrance exam in Delhi UniversityAs you want I am here giving you syllabus for M.Phil/Ph.D (Mathematics) Entrance Test of Delhi University. Syllabus :Section I – Analysis: Finite, countable and uncountable sets, bounded and unbounded sets, Archimedean property, ordered field, completeness of ℝ, sequence and series of functions, uniform convergence, Riemann integrable functions, improper integrals, their convergence and uniform convergence, Fourier series. Partial and directional derivatives, Taylor’s series, implicit function theorem, line and surface integrals, Green’s theorem, Stoke’s theorem. Elements of metric spaces, convergence, continuity, compactness, connectedness, Weierstrass’s approximation theorem, completeness, Baire’s category theorem, Bolzano- Weirstrass theorem, compact subsets ofℝ , Heine-Borel theorem, Lebesgue outer measure, Lebsegue measure and Lebsegue integration, Riemann and Lebesgue integrals. Complex numbers, analytic functions, Cauchy-Riemann equations, Riemann sphere and stereographic projection, lines, circles, crossratio, Mobius transformations, line integrals, Cauchy’s theorems, Cauchy’s theorem for convex regions, Morera’s theorem, Liouville’s theorem, Cauchy’s integral formula, zero-sets of analytic functions, exponential, sine and cosine functions, power series representation, classification of singularities, conformal mapping, contour integration, fundamental theorem of algebra. Banach spaces, Hahn-Banach theortem, open mapping and closed graph theorem, principle of uniform boundedness, boundedness and continuity of linear transformations, dual spaces, embedding in the second dual, Hilbert spaces, projections, orthonormal bases, Riesz representation theorem, Bessel’s inequality, Parseval’s identity. Elements of Topological spaces, continuity, convergence, homeomorphism, compactness, connectedness, separation axioms, first and second countability, separability, subspaces, product spaces. Section II – Algebra: Space of n-vectors, linear dependence, basis, linear transformations, algebra of matrices, rank of a matrix, determinants, linear equations, characteristic roots and vectors. Vector spaces, subspaces, quotient spaces, linear dependence, basis, dimension, the algebra of linear transformations, kernel, range, isomorphism,linear functional, dual space, matrix representation of a linear transformation, change of bases, reduction of matrices to canonical forms, inner product spaces, orthogonality, eigenvalues and eigenvectors, projections, triangular form, Jordan form, quadratic forms, reduction of quadratic forms. Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, Symmetric groups, alternating groups, simple groups. conjugate elements and class equations of finite groups, Sylow’s theorem, solvable groups, Jordan-Holder theorem, direct products, structure theorem for finite abelian groups. Rings, Ideals, prime and maximal ideals, quotient ring, integral domains, Euclidean domains, principal ideal domains, unique factorization domains,polynomial rings, chain conditions on rings,fields, quotient fields, finite fields, characteristic of field, field extensions, elements of Galois theory, solvability by radicals, ruler and compass construction. Section III- Differential Equations and Mechanics: First order ODE, singular solutions, initial value problems of first order ODE, general theory of homogeneous and non-homogeneous linear ODEs, variation of parameters, Lagrange’s and Charpit’s methods of solving first order PDEs, PDEs of higher order with constant coefficients. Existence and uniqueness of solution ( , ) dy dx f x y = , Green’s function, Sturm-Liouville boundary value problems, Cauchy problems and characteristics, classification of second order PDE, separation of variables for heat equation, wave equation and Laplace equation, Equation of continuity in fluid motion, Euler’s equations of motion for perfect fluids, two dimensional motion, complex potential, motion of sphere in perfect liquid and motion of liquid past a sphere, vorticity, Navier-Stoke’s equations of motion for viscous flows, some exact solutions. Address:University of Delhi New Delhi, Delhi 110021 | |

October 2nd, 2015 12:48 PM | ||

Unregistered | Re: Syllabus of PhD entrance exam in Delhi UniversityCan you please provide here syllabus for M.Phil/Ph.D (Mathematics) Entrance Test of Delhi University ? | |

June 2nd, 2014 05:58 PM | ||

Educhamp | Re: Syllabus of PhD entrance exam in Delhi UniversityAs you want to get the entrance exam syllabus to get admission in PhD in Delhi University so here is the information of the same for you: I want to tell you that please specify the PhD subject for which you want to get the entrance exam syllabusPhD in Delhi University is offered in these subjects: Anthropology Arabic Botany Buddhist Studies Commerce Computer Science Development Communication & Extension Fabric & Apparel Science Food & Nutrition Genetics Geography German Hispanic ome Science Human Development & Childhood Studies Italian Library Information Science Linguistics Microbiology Operational Research Persian Political Science Psychology Punjabi Resource Management & Design Application Russian Sanskrit Social Work Sociology Zoology Adult Continuing Education & Extension Here for your reference I am giving you the entrance exam syllabus of PhD in Computer Science of DU:Programming Fundamentals A Brief History of C C is middle-level Language The Form of a C Program Variables, Data Types, Operator & Expression Data Declaration & Definition Operator & Expression C as a Structured Language Console input and output Formatted Input/ Output Control Statement Nested switch Iteration Statements for loop Pointers Memory Organization Pointer Arithmetic Array & String Complier Vs Interpreters Arguments & local variables Storage Class & Scope Declaration and Initializing Structure Preprocessor Directive Macro Substitution File handling Void Pointer Bitwise Operator Graphics In C Data StructuresIntroduction To Data Structure Implementation of Data Structure Array as Data Structure Polynomial Representation Using Arrays Sparse Matrices Drawback of Sequential Storage Implementation of Linked List Other Operation & Applications Generalized Linked List Operation on Stack Static & Dynamic Implementation of a Stack Operation on a Queue Static & Dynamic Implementation of Queue Tree Terminology Binary Search Tree Traversal Database Management SystemDatabase and Need for DBMS Views of data-schemas and instances Database Design using ER model Relational Model Relational Database design Storage and File Structure Transaction And Concurrency control Crash Recovery and Backup Security and privacy AlgorithmsDivide And Conquer Greedy Method Dynamic Programming Backtracking Branch and Bound Computer NetworksIntroduction to Networking Common Network Architecture The OSI Reference Model Local Area Networks Broad Band Networks IP Addressing & Routing Domain Network Services Network Applications SNMP Network Security Operating SystemsOperating system functions and characteristics Real time systems Methodologies for implementation of O/S service system Functions of the system File access and allocation methods Structured Organizations Storage allocation methods Virtual memory concepts Hardware Management Deadlock detection and recovery Contact Details:University of Delhi University Rd, New Delhi, Delhi 110007 011 2766 7853 India Map Location: | |

June 2nd, 2014 11:45 AM | ||

Unregistered | Syllabus of PhD entrance exam in Delhi UniversityI want to get admission in PhD in Delhi University and for that I need to get the entrance exam syllabus so can you provide me that as it is very urgent for me? |

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