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DU M. Phil Entrance Exam Syllabus 2017, Admit Card


DU M. Phil Entrance Exam Syllabus 2017, Admit Card:

University of Delhi is likely to release the official communication in respect of MPHIL Entrance Test Syllabus at the quickest possible through the official website. All the students who apply for the admission after that all are willingly desperate to download the entrance test syllabus through the official website.  

DU M. Phil Entrance Examination Syllabus 2017 Download

The University of Delhi (DU), issued the entrance exam syllabus of M.Phil for all those candidates who want to take admission in M.Phil programme 2017-19 academic session under the Delhi University. After publishing the entrance test syllabus, candidate needs to do hard preparation of entrance test if they want to score highest score in the entrance test. Hereby we are also provide you entrance test syllabus.

Syllabus of M. Phil Entrance 2017

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 and 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
  • Weierstrass’s approximation theorem
  • Completeness
  • Baire’s category theorem
  • BolzanoWeirstrass theorem
  • Compact subsets of ℝn
  • Heine-Borel theorem
  • 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
  • Lowville’s theorem
  • Elements of Topological spaces
  • Continuity
  • Convergence
  • Homeomorphism
  • Compactness
  • Connectedness
  • Separation axioms
  • First and second count ability
  • Subspaces
  • Product spaces

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
  • Rings
  • Ideals
  • Prime and maximal ideals
  • Quotient ring
  • Integral domains
  • Euclidean domains
  • Principal ideal domains
  • Unique factorization domains
  • Polynomial rings
  • Chain conditions on ring
  • Fields, quotient fields, finite fields, characteristic of field, field extensions
  • Elements of Galois Theory
  • Solvability by radicals
  • Ruler and compass construction

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
  • Navier-Stoke’s equations of motion for viscous flows

DU MPHIL Entrance Admit Card 2017

We would like to inform you as soon as possible display the MPHIL course 2017 entrance test Admit Card at the website of Delhi University. When the university upload at the website then you can download it through the website of the official.

Interview

The admission to the programme is through a written test, which results in the shortlisting of the candidates for the interview process. It may be noted that certain departments may have mode of evaluation other than Interview. The list of shortlisted candidates and dates of the interview shall be notified on the M. Phil. admission portal.

Results of the Written Examination and Interviews shall be declared on the M. Phil. admission portal.  Selected candidates are required to furnish the necessary documents at the time of admission.

Wishing Here for the Best of Luck for the Students!

Official DU PORTAL Website: http://www.du.ac.in/

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