Syllabus of Mathematics for B.A. and B.Sc.I year

Click to download PDF of Proposed Syllabus for B. Sc. Semester program implemented from Session 2016-17 of Kumaun University for Mathematics


Paper-1  Matrices, Trigonometry and Vector Analysis
M.M.: 50

Note:  There   shall   be   three   sections   A,B  and   C   in   this   paper.   Questions   within   all   the   three sections shall carry equal marks. Section A will be compulsory and objective in nature having
ten   questions.   Marks   allotted   to   this   section   will   be   10.   Questions   in   section   B   will   be   short answer type of 20 marks. Candidates will have to attempt four out of eight questions selecting at
least one question  from all the three parts (viz.Matrices,Trigonometry and Vector Analysis). Question in section C will be of descriptive nature of 20 marks. Candidates will have to attempt any two out of four questions. The number of questions for framing of question paper shall  be  30%from  Matrices, 30% from   Trigonometry  and 40% from Vector Analysis. The question paper be framed proportionately from the whole syllabus.


Matrices
Symmetric, Skew-Symmetric, Hermitian and skew-Hermitian matrices, Orthogonal  and Unitary matrices, Elementary operations on matrices, Inverse of a matrix, Linear dependence of rows and columns of a matrix, Row rank, column rank and their equivalence, Rank of a matrix, Eigen     vectors,   Eigen   values   and   the  characteristics    equation    of  a  matrix,   Cayley-Hamilton theorem and its use in finding inverse of a matrix, Applications of matrices in solving system of linear(both   homogeneous   and   non-homogeneous)   equations,   Conditions   of   consistency   for   a system of linear equations.

Trigonometry
Exponential,  Logarithmic,     Circular    and   hyperbolic    functions     together   with   their
inverses,   Gregory’s   series,   Summation   of   Trigonometric   series,   Trigonometric   expansions   of
sine and cosine as infinite products(without proof).

Vector Analysis
Vector Algebra: Triple products, Reciprocal vectors, products of four vectors.
Vector  Differentiation:  Ordinary  Differentiation  of  vectors, Applications   to  mechanics  and geometry,      Differential  operators,del,  Definitions of  del,  Gradient,  Divergence,  Curl, Vector identities.
Vector integration: Line, Surface and Volume  Integrals, Simple  applications of  Gauss’s divergence theorem, Green’s theorem and Stroke’s theorem (without proof).




Paper-II  :   Calculus
M.M.: 50

Note:  There   shall   be   three   sections   A,   B   and   C   in   this   paper.   Questions   within   all   the   three sections shall carry equal marks. Section A will be compulsory and objective in nature having ten questions.   Marks   allotted   to   this   section   will   be   10.   Questions   in   section   B   will   be  short answer type of 20 marks. Candidates will have to attempt four out of eight questions selecting at least one question from two parts (viz. Differential Calculus and Integral Calculus).Question in section C will be of descriptive nature of 20 marks. Candidates will have to attempt any two out of   four   questions.   The   number of questions for framing  of   question   paper   shall   be   60% from Differential   Calculus  and  40% from Integral    Calculus. The  question  paper  be framed proportionately from the whole syllabus.


Differential Calculus
A   brief   review   of   limit,   Continuity   and   differentiability,   Rolle’s   theorem,  Mean   value theorem and their applications, intermediate value theorem, successive differentiation, Taylor’s and Maclaurin’s series expansions, Indeterminate forms, Tangents and normals of polar curves, Derivatives of arc,  Asymptotes, Curvature, Double Points, Curve tracing, Functions of  two variables,  Partial    differentiation  and change     of    independent   variables(two  variables), jacobians(simple applications-function   of  a   function   case),   Maxima   and  Minima   of  two independent variables.



Integral Calculus

Integral as limit of a sum, Fundamental theorem of  integral calculus(statement only), Beta  and Gamma  Functions, Change of order of   integration   in   double   integrals,   Drichlet’s theorem and its Liovelle’s extension, Multiple integrals, Area(quadrature), Rectification(length of curves), Volumes and Surfaces, Differentiation and integration under the integral sign.




Paper-III : Geometry of Two and Three Dimensions
M.M. 50


Two Dimensions

A   briefreview   of    general   equation   of   second   degree,   Confocal   conics        and   Points   of
contact, Polar equation of a conic, Equation of a Chord, Tangent, Normal and polar to a conic.


Three Dimensions

System of coordinates in three dimensions, change of origin, Projections, dc’s and dr’s, Change   of   axes,   Plane,   straight   Line,   intersection   of   three   panes,   Volume   of   a   tetrahedron, Sphere,     Cylinder,    Cone     central   conicoids    with   basic   fundamental      properties,    paraboloids, General equation of second degree in three dimensions. Cylindrical,   Spherical   coordinate   systems,   their   transformations  and   their   relation   to   Cartesian coordinate systems.



PDF of Mathematics Syllabus of B.Sc. I of Kumaun University


Source : Kumaun University