- Home
- -
- BPSC Maths Optional Syllabus
BPSC Maths Optional Syllabus
Linear Algebra, Calculus, Analytic Geometry of two and three dimensions and Differential Equations
Linear Algebra:
Vector space bases, dimension of finitely generated space. Linear transformations, Rank and nullity of a linear transformation, Cayley Hamilton theorem. Eigenvalues and Eigenvectors. Matrix of a linear transformation. Row and Column reduction. Echelon form. Equivalence. Congruence and similarity. Reduction to canonical forms. Orthogonal, symmetrical, skew-symmetrical, unitary, Hermitian and Skew-Hermitian matrices
Algebra, Real Analysis, Complex Analysis, Partial
Differential equations. Mechanics,
Hydrodynamics, Numerical Analysis. Statistics including probability operational
research.
Algebra:
Groups, sub-groups, normal sub-groups, homomorphism of groups,
quotient groups. Basic isomorphism theorems. Sylow theorems. Permutation
Groups, Cayley's theorem. Rings and Ideals, Principal Ideal domains, Unique factorization
domains and Euclidean domains. Field Extensions. Finite fields.
Real Analysis:
Metric spaces, their topology with special reference to Rn sequence in a metric space, Cauchy sequence, Completeness, Completion Continuous
functions, Uniform Continuity, Properties of Continuous function on Compact
sets. Riemann-Stieltjes integral, Improper integrals and their conditions of
existence. Differentiation of functions of several variable, Implicit function
theorem, maxima and minima, Absolute and conditional convergence series of real
and complex terms, Re-arrangement of series. Uniform convergence, Infinite
products, Continuity, differentiability and integrability for series, Multiple integrals.
Complex Analysis:
Analytic functions, Cauchy's theorem, Cauchy's integral
formula, Power series, Taylor's, Singularities, Cauchy's Residue theorem and
Contour integration.
Partial Differential Equations:
Formations of partial differential equations. Types of integrals of partial differential Equations of first order Charpit