Mathematics honours part -2

MATHEMATICS PAPER-III(Honours)

                    
                   

B.sc part-I math honours patern

Honspaper       Sub paper      Eng/Hind

                                                    💯/marks

200/marks        200/marks     

Paper-I-100       Phy           Chem

Paper-II-100    75-theory   75-theory

                         25-practical  25-practical

B.sc part-II math honours patern

Honspaper       Sub paper      Eng/Hind

                                                    💯/marks

200/marks        200/marks     

Paper-I-100       Phy           Chem

Paper-II-100    75-theory   75-theory

                         25-practical  25-practical

B.Sc part-III honours patern

Paper      paper      paper      paper       GK&GS

  (V)        (VI)         (VII)        (VIII)   

             100 marks all papers

             

MATHEMATICS PAPER-III(Honours)

 Total number of questions 13

Answer any six question selecting at least one from each group.Q.No.1 will be objective and compulsory.

                   GROUP-A

Advanced calculus:

Continuity, sequential continuity, properties of continuous functions,uniform continuity, differentiability 

 Mean value theorems and their geometrical interpretations, Darboux's intermediate value theorem for derivatives, Taylor's theorem with various  forms of remainderes:

 Limit and continuity of functions of two variables, Partial differentiation, change of variables, Euler's theorem on homogeneous functions . 

Taylor's theorem for functions of two variables, Maxima, Minima and saddle points of functions of two variables, Lagrange's multiplier method.

GROUP-B 

Beta and Gamma functions, Double and triple integraals, Dirichlet's integrals, Change of order of integration in double integrals: 

 Definition of a sequence, Theorems on limits of sequences, Bounded and monotonic sequences. Cauchy's Convergence Criterion 

 Series of non negative terms, Comparison tests, Cauchy's root test, Ratio tests, Raabe's Test, Logarithmic Test, De Morgan and Bertrand's test, Cauchy's Condensation test .

Alternativn series, Leibnitz's theorem. Absolute and conditional convergence : 

GROUP-C 

Statics :

Analytical conditions of equilibrum of coplanar forces: 

 Virtual work, Stable and unstable equilibrium : 

 Catenary 

 Foreces in three dimensions Poinset' central axes, Wrenches, Null lines and planes: 

MATHEMATICS PAPER-IV(Honours)

Total number of questions 13

Answer any six question selecting at least one from each group.Q.No.1 will be objective and compulsory.

                   GROUP-A

Differential Equations

Series solution of differential equation: power series method, based legendre and hypergeometrick equation, bessel legendary and hypergeometric functions and their properties, convergence, recurrence and generating relation, orthogonality of functions,strum-loluville problem, Orthogonality of eigen-functions, Reality of eigenvalues, orthogonality of Bessel functions and Legendary polynomials:.                                   

      Laplace Transformation; Linearity of the Laplace transformation, Existence theorem for Laplace transformation, Laplace transforms of derivatives and integrals,Shiffing theorem, Differentiation and integration of transforms, Convolution theorem, Solution of integral equations and systems of differential equations using the Laplace transformation.                 

GROUP-B

Partial differential equations of the first order. Lagrange's solution. Some special type of equations which can be solved easily by methods other than the general method. Charpits's general method of solution :

 Partial differential equations of second order and higher orders, Classification of linear partial differential equations of second order, Homogeneous and non-homogeneous equations with constant coefficients, Partial differential equations reducible to equations with constant coefficients, Monges method

GROUP-C

DYNAMICS:  Velocities and accelarations along radial and tranvers directions and along tangential, normal directions, Simple harmonic motion, Elsatic string : 

Motion on smooth and rough plane curve, Motion in a resisting medium, Motion of particle of varying mass : 

Central orbits, Kepler's law of motion :

  Motion of a particle in three dimensions, Acceleration in terms of different conrdinate systems