Syllabus of Zoology Optional Subject

Agriculture

Animal Husbandry and Veterinary Science

Anthropology

Botany

Chemistry

Civil Engineering

Commerce and Accountancy

Economics

Electrical Engineering

Geography

Geology

History

Law

Management

Mathematics

Mechanical Engineering

Medical Science

Philosophy

Physics

Political Science and International Relations(PSIR)

Psychology

Public Administration

Sociology

Statistics

Zoology

Literature of Assamese

Literature of Bengali

Literature of Bodo

Literature of Dogri

Literature of Gujarati

Literature of Hindi

Literature of Kannada

Literature of Kashmiri

Literature of Konkani

Literature of Maithili

Literature of Malayalam

Literature of Manipuri

Literature of Marathi

Literature of Nepali

Literature of Oriya

Literature of Punjabi

Literature of Sanskrit

Literature of Santhali

Literature of Sindhi

Literature of Tamil

Literature of Telugu

Literature of Urdu

Literature of English

# Syllabus of Mathematics Optional Subject

01-01-1970

05:30:AM

304 Views

__PAPER-I__

**1. Linear Algebra :**

- Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimensions, Linear transformations, rank and nullity, matrix of a linear transformation.
- Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rankof a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors,

**2. Calculus :**

- Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem,
- Riemann’s definition of definite integrals; Indefinite integrals; Infinite and improper integral; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.

**3. Analytic Geometry :**

- Cartesian and polar coordinates in three dimensions, second degree equations in three variables,

**4. Ordinary Differential Equations :**

- Formulation of differential equations; Equations of first order and first degree, integrating factor;
- Second and higher order liner equations with constant coefficients, complementary function, particular integral and general solution.
- Section order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters.
- Laplace and Inverse Laplace transforms and their properties, Laplace transforms of elementary functions.
- Application to initial value problems for 2nd order linear equations with constant coefficients.

**5. Dynamics and Statics :**

- Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; Constrained motion; Work and
- Equilibrium of a system of particles; Work and potential energy, friction, Common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions.

**6. Vector Analysis :**

- Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in
- Application to geometry : Curves in space, curvature and torsion; Serret-Furenet's formulae.
- Gauss and Stokes’ theorems, Green's indentities.

__ ____PAPER-II__

**1. Algebra :**

- Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups,
- Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains,

**2. Real Analysis :**

- Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence,
- Riemann integral, improper integrals; Fundamental theorems of integral calculus.
- Uniform convergence, continuity, differentiability and integrability for sequences and series of functions;

**3. Complex Analysis :**

- Analytic function, Cauchy-Riemann equations, Cauchy's theorem, Cauchy's integral formula, power

**4. Linear Programming :**

- Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical
- Transportation and assignment problems.

**5. Partial Differential Equations :**

- Family of surfaces in three dimensions and formulation of partial differential equations; Solution of

**6. Numerical Analysis and Computer Programming :**

- Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection,
- Numerical integration: Trapezoidal rule, Simpson’s rule, Gaussian quadrature formula.
- Numerical solution of ordinary differential equations : Eular and Runga Kutta methods.
- Computer Programming : Binary system; Arithmetic and logical operations on numbers; Octal and
- Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms.
- Representation of unsigned integers, signed integers and reals, double precision reals and long integers.
- Algorithms and flow charts for solving numerical analysis problems.

**7. Mechanics and Fluid Dynamics :**

- Generalised coordinates; D’Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions.
- Equation of continuity; Euler’s equation of motion for inviscid flow; Stream-lines, path of a particle;

## Comments

Login To Comment

## Recent Comments