Delhi University M.SC Entrance Exam syllabus

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Here I am giving you syllabus for M.SC Entrance Examination organized by Delhi university below ./

Syllabus M. Sc. Entrance Exam Delhi University:

SECTION 1
Elementary set theory, Finite, countable and uncountable sets, Real number
system as a complete ordered field, Archimedean property, supremum,
infimum.
Sequence and series, Convergence, limsup, liminf.
Bolzano Weierstrass theorem, Heine Borel theorem.

Continuity, Uniform continuity, Intermediate value theorem, Differentiability,
Mean value theorem, Maclaurin’s theorem and series, Taylor’s series.
Sequences and series of functions, Uniform convergence.

Riemann sums and Riemann integral, Improper integrals.
Monotonic functions, Types of discontinuity.
Functions of several variables, Directional derivative, Partial derivative.
Metric spaces, Completeness, Total boundedness, Separability, Compactness,
Connectedness.

SECTION 2
Eigenvalues and eigenvectors of matrices, Cayley-Hamilton theorem.
Divisibility in Z, congruences, Chinese remainder theorem, Euler’s -
function.
Groups, Subgroups, Normal subgroups, Quotient groups, Homomorphisms,
Cyclic groups, Permutation groups, Cayley’s theorem, Class equations, Sylow
theorems.

Rings, Fields, Ideals, Prime and Maximal ideals, Quotient rings, Unique
factorization domain, Principal ideal domain, Euclidean domain, Polynomial
rings and irreducibility criteria.

Vector spaces, Subspaces, Linear dependence, Basis, Dimension, Algebra of
linear transformations, Matrix representation of linear transformations,
Change of basis, Inner product spaces, Orthonormal basis.

SECTION 3

Existence and Uniqueness of solutions of initial value problems for first order
ordinary differential equations, Singular solutions of first order ordinary
differential equations, System of first order ordinary differential equations,
General theory of homogeneous and non-homogeneous linear ordinary
differential equations, Variation of parameters, Sturm Liouville boundary
value problem, Green’s function.

Lagrange and Charpit methods for solving first order PDEs, Cauchy problem
for first order PDEs, Classification of second order PDEs, General solution of
higher order PDEs with constant coefficients, Method of separation of
variables for Laplace, Heat and Wave equations.

Numerical solutions of algebraic equations, Method of iteration and Newton-
Raphson method, Rate of convergence, Solution of systems of linear
algebraic equations using Guass elimination and Guass-Seidel methods, Finite
differences, Lagrange, Hermite and Spline interpolation, Numerical
integration, Numerical solutions of ODEs using Picard, Euler, modified Euler
and second order Runge-Kutta methods.

Velocity, acceleration, motion with constant and variable acceleration,
Newton’s Laws of Motion, Simple Harmonic motion, motion of particle
attached to elastic string, motion on inclined plane, motion of a projectile,
angular velocity and acceleration, motion along a smooth vertical circle, work,
energy and impulse, Collision of elastic bodies, Bodies falling in resisting
medium, motion under action of central forces, central orbits, planetary
motion, moment of inertia and couple, D’Alembart’s principle.

Equilibrium of particle and a system of particles, Mass centre and centres of
gravity, Frictions, Equilibrium of rigid body, work and potential energy.