MATHEMATICS

1. Albebra- Elements of set Theory ; Algebra of Real and Complex numbers including Demovire's theorem; Polinomials and polinomial equations; Relation between Coefficients and Roots, symmetric functions of roots; Elements of Group Theory ; Sub , Groups, Permutation , Groups and their elementary properties . Rings, Integral Domains and Fields and their elementary properties.
2. Vector Spaces and Matrices- Vector Space, Linear Dependence and Independence . Subspaces. Basis and Dimension, Finite Dimensional Vector Spaces. Linear Transformation of a Finite Dimensional Vector Space, Matrex Representation . Singular and Nonsingular Transformations , Rank and Nullity.
Matrices: Addition , Multiplication . Determinants of a Matrix, Properties of Determinants of order , Inverse of a Matrix . Cramer's rule
3. Geometry and Vectors- Analuytic geometry of straight lines and conics in cartesian and polar coordinates; three dimensional geometory for planes, straight lines, sphere, cone and cylinder. Addition, Subtraction and Products of Vectors and Simple applications to Geometry.
4. Calculus- Function ,Sequences , Series, Limits, Continuity, Derivatives.
Application of Derivatives- Rates of change , Tangents ,Normals , Mixima, Minima, Rolle's Theorem, Mean Value Theorems of Language and Cauchy, Asymptotes, Curvature. Methods of finding indefinite integrals , Definirte Integrals Fundamental Theorem of integrals Calculus. Volume and Surfaces of revolution.
5. Ordinary Differential Equations: Order and Degree of a Differential ; Equation , First order differential Equations , Singular solution . Geometrical interpretation , Second order equations with constant coefficients.
6. Mechanics- Concepts of particles - Lamina; Rigid Body : Displacement; fokrce; Mass; weight; Motion; Velocity; Speed; Acceleration; Parallelogram of force; Parallelogram of velocity , acceleration; resultant; equilibrium of coplanar force; Moments ; Couples ; Friction; Centre of mass, Gravity ; Laws of motion; Motion of particle in a straight line; simple Harmonic Motion; Motion; under covservative forces; Motion under gravity; Projectile; Escape velocity; Motion of aritificial satellites.
7. Elements of Computer Programming- Binary system, Octal and Hexadecimal systems. Conversion to and from Decimal systems. Codes, Bits, Bytes and Works. Memory of a computer. Arithmetic and Logical operators. Algorithms and Flow Charts.