| 1st November 2016 06:05 PM | |
| shikha | 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 |
| 1st November 2016 05:21 PM | |
| Unregistered | B.Sc Syllabus Of Lucknow University I want the syllabus of B.Sc. I Mathematics of Lucknow University so can you please provide me? |
