bsc 2nd year maths, ka all subject sallubus

Hello,

There are 6 subjects in total in B.Sc maths Hons. The list of subjects are as follows:-

3rd Semester:
> Mechanics II- Motion of a particle in two dimensions, Velocities and accelerations in Cartesian, intrinsic coordinates. Equations of motion, Motion of a projectile in a resisting medium, central forces, Motion of a particle in a plane under different laws of resistance, Stability of nearly circular orbits, the universe law, Motion under Kepler's laws. Time of describing an arc and area of any orbit along with Slightly disturbed orbitsz, Motion of satellites, problems of motion of varying mass such as falling raindrops and rocket, tangential and normal accelerations. Motion of a particle on a smooth or rough curve, Motion of a particle in three dimensions and Motion on a smooth sphere on any surface of revolution.

> Differential Equations II- Ordinary Differential Equations, series solutions of differential equations, bessel, legendre, Power series method, and Hyper geometric equations. Hyper geometric functions along with the properties like Convergence, recurrence, generating relations, Orthogonality of functions, Sturra-Liouville problem. Right of eigenvalues. Orthogonality of eigen functions, Orthogonality of Bessel functions and Legendre polynomials, Laplace transforms. Introduction to infinite integrals, existence of theorem, Linearity of Laplace trans-forms. Shifting theorem, Laplace transforms of derivatives and integrals, Convolution theorem, Solution of integral equations.

> Analysis I- order of properties of Q, Countability of Z and its order incompleteness, Construction of R from Q using Dedekind cuts, order complete ness of R: The upper bound least property and equivalent conditions including the Uncountability of R bounds nested interval property, bounded sets, and their properties, sup and inf of sets. Sequence, Bolzano-Weierstrass theorem, cauchy Sequence, Bounded sequences, monotone sequences and their convergence, limsup and liming and convergence criterion using them, subsequence’s, and their convergence criterion. It also includes Interior points and limit points, open, closed, and perfect sets. Compact sets, Limits and continuity, Basic properties of continuous functions, Operations on sequences, Uniform continuity, Bounded functions, Continuous functions defined on a compact set: Discontinuitie, Geometric series. Monotonic. Series of non-negative terms. The condensation tests. Integral test. Ratio and root tests, absolute and conditional convergence, leibnitz theorem, Alternating series.

4th Semester:
> Vector Analysis- Vector Algebra, Operations with vectors, Scalar and vector product of three vectors, Product of four vectors, Reciprocal vectorsz ,Vector Calculus. Also, Scalar-valued functions over the plane and the space and vector function of a scalar variable, Curves and Paths Vector fields, Vector differentiationz, Directional derivatives, the tangent plane, total differential, gradient, divergence, and curl. Vector integration: Path, line, surface, and volume integrals. Conservative fields, integration, Line integrals of linear differential forms. Thera are Serret-Frenet Formulasz theorems of Green, Gauss, Stokes, and problems based on these.

> Differential Equations III- Partial differential equations. Formation of partial differential equations, types of solutions, PDEs of the first order,lagrange's solution. Thera are also Some special types of equations which can be solved easily by methods other than the general methods such as Charpit's and Jacobi's general method of solutionz , Partial differential equations of second and higher orderz, Classification of linear partial differential equations of second order. It also includes Homogeneous and non-homogeneous equations with constant coefficients, Partial differential equations reducible to equations with constant coefficients, Monge's methods. Calculus of variations, Variational problems with fixed boundaries - Euler's equation for functionals containing first-order derivative and one independent variable. There are some other important topicslik Functionals dependent on higher order derivatives, Functionals dependent on more than one independent variable, Variational problems in parametric form, Invariance of Euler's equation under coordinate transformation. Some other from exam perspective are Variational problems with moving boundaries, Functionals dependent on one and two functions, One sided variation, sufficient conditions for an extremum — Jacobi and Legendre conditions, second variation, Variational principle of least action and it's Applications.

> Analysis II- derivation, Differentiation, Rolle's theorem, Mean Value Theorem, darboux's theorem on intermediate value property of derivatives, Taylor's theorem, Indeterminate forms. Integration, The Riemann Integral and its properties. Some other are Integrability of continuous and monotonic functions, functions of bounded variation, their relation with monotonic functions, and integrability, The fundamental theorem of calculus, Mean value theorems of integral calculus, Convergence of improper integrals, Comparison tests, Abel's and Dirichlet's test, Beta and Gamma functions. Some other are Frullani's integral, Integral as a function of a parameter, and its continuity, differentiability, and integrability.

These are the subjects in B.Sc 2nd year.

Thank You.

• Theory of real function
• group theory-1
• Multivariate calculus