DU M.Phil Entrance Exam Syllabus 2016

DU M.Phil Entrance Exam Syllabus 2016:

The Delhi University (DU) has notify the release of the syllabus for the Master of Philosophy (M.Phil) Entrance Examination-2016.

DU M.Phil Entrance Examination Syllabus 2016

DU M.Phil Entrance Exam Syllabus 2015

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 under the Delhi University.

This syllabus will definitely helps our visitors to qualify the entrance examination of M.Phil program.

Syllabus of M.Phil Entrance 2016


  • 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


  • 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

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