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Old 1st November 2016, 05:21 PM
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Default B.Sc Syllabus Of Lucknow University

I want the syllabus of B.Sc. I Mathematics of Lucknow University so can you please provide me?
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Old 1st November 2016, 06:05 PM
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Default Re: B.Sc Syllabus Of Lucknow University

Ok, here I am providing you the syllabus of B.Sc. I Mathematics of Lucknow University

Lucknow University B.Sc I Mathematics syllabus

Paper I Algebra

Paper I-

Unit I
Symmetric, Skew symmetric, Hermitian and Skew Hermitian matrices, Elementary operation on
matrices. Inverse of a matrix. Linear Independence of row and column matrices. Row rank
column rank and rank of a matrix. Equivalence of a column and row ranks. Eigenvalues,
eigenvectors and characteristic equation of a matrix: Cayley Hamilton theorem and its use in
finding inverse of a matrix.
Unit II
Application of matrices to a system of linear (both homogenous and nonhomogeneous)
equations. Theorems on consistency of a system of linear equations.
Relations between the roots and coefficients of general polynomial equation in one variable,
transformation of equations, Descarte’s rule of signs. Solution of cubic equations (Cardon’s
method). Biquadratic equations.
Unit III
Mappings. Equivalence relations and partitions. Congruence modulo n. Definition of a group
with examples and simple properties. Subgroup. Generation of groups. Cyclic groups. Coset
decomposition. Lagrange’s theorem and its consequences. Fermat’s and Euler’s theorem.
Homomorphism and isomorphism. Normal subgroups. Quotient groups.
Unit IV
The fundamental theorem of Homomorphism and Isomorphism. Permutations groups. Even and
odd permutations. The alternating groups An . Cayley’s theorem. Introductions to rings.
Subrings, Integral domains and fields. Characteristic of a ring.

Paper II-

Differential Calculus & Vector Calculus

Unit I
Definition of the limit of a function, Basic properties of a limit. Continuous functions and
classification of discontinuities. Differentiability. Successive differentiation. Leibnitz theorem.
Unit II
Maclaurin’s and Taylor’s series expansions. Tangents and Normals, Asymptotes.
Unit III
Curvature. Tests for Concavity and Convexity. Points of Inflexion. Multiple points. Tracing for
curves in Cartesian and polar coordinates.
Unit IV
Vector Differentiation. Gradient, Divergence and Curl. Vector Integration. Theorems of Gauss,
Green, Stokes and problems based on these.

Paper III

Integral Calculus & Trignometry
Unit I
Integration of irrational algebraic functions and transcendental functions. Reductions formulae.
Definite integrals. Quadrature. Rectification. Volumes and Surfaces of solid of revolution.
Unit II
Ordinary Differential Equations
Degree and order of a differential equation. Equation of first order and first degree. Equations in
which the variables are separable. Homogenous equation. Linear equations and equations
reducible to the linear form. Exact differential equations. First order higher degree equations
solvable for x, y, p. Clairaut’s form and singular solutions. Geometric meaning of a differential
equation. Orthogonal trajectories.
Unit III
Linear differential equation with constant coefficients. Homogenous linear ordinary differential
equations.
Linear differential equations of second order. Transformation of the equation by changing the
dependent variable/the independent variable. Method of variation of parameters.
Ordinary simultaneous differential equations.
Unit IV
Trignometry
DeMoivre’s theorem and its applications. Direct and Inverse circular and hyperbolic functions.
Logarithm of a complex quantity. Expansion of trignometrical functions. Gregory’s series.
Summation of series.

Paper IV

Vector Analysis & Geometry
Unit I
Scalar and vector product of vectors. Product of four vectors. Reciprocal vectors.
Unit II
Geometry
General equation of second degree. Tracing of Conics. Systems of Conics. Confocal Conics.
Polar equation of conics.
Unit III
Plane, The straight line, Sphere, Cone, Cylinder.
Unit IV
Central Conicoids. Parabolids. Plane section of Conicoids. Generating lines. Confocal Conicoids.
Reduction of second degree equations.

Contact-

University of Lucknow
Lucknow University Main Building, University Road, Babuganj, Hasanganj, Lucknow, Uttar Pradesh 226007
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