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- HPSC Maths Optional Syllabus
HPSC Maths Optional Syllabus
1. Linear
Algebra:
Vector space, linear dependence
and independence, subspaces, bases, dimensions. Finite dimensional vector
spaces. Matrices, Cayley Hamilton theorem, Eigen values and Eigenvectors.
Matrix of linear transformation, row and column reduction, Echelon form, equivalence,
congruence and similarity, reduction to canonical form, rank, orthogonal, symmetrical,
skew symmetrical, unitary, Hermitian, skew Hermitian forms their Eigen values. Orthogonal and unitary reduction of quadratic
and Hermitian forms, positive definite quadratic form.
2. Calculus:
Real numbers, limits, continuity, differentiability, mean value theorems, Taylor
1. Vector
Analysis:
Scalar and vector fields, triple
products. Differentiation of vector function of a scalar variable. Gradient, Divergence and curl in cartesian, cylindrical
and spherical coordinates and their physical interpretations. Higher order derivatives, vector identities
and vector equations. Application to
Geometry: Curves in space, Curvature and Torsion. Serret?Frenet's formulae,
Gauss and Stokes' theorems, Green's identities.
2. Real
Analysis:
Real number system, ordered sets,
Bounds, ordered field, real number system as an ordered field with least upper
bound. Cauchy sequence. Completeness.
Continuous Functions. Uniform continuity. Properties of continuous functions on
compact sets. Riemann integral, improper
integrals. Differentiation of functions of several variables, maxima and
minima. absolute and conditional convergence of series of real and complex
terms, rearrangement of series. Uniform convergence. Infinite Products.
Continuity, differentiability and integrability for series. Multiple integrals. Infinite and alternating
series.
3. Numerical
Analysis:
Numerical methods: Solution of
algebraic and transcendental equations of one variable by bisection, Regula?
Falsi and Newton?Raphson methods, solution of system of linear equations by Gaussian
elimination and Gauss?Jordan (direct) methods, Gauss?Seidel(iterative) method.
Interpolations: Newton