Mathematics

Algebra

• Elements of Set Theory; Algebra of Real and Complex numbers including Demovire's theorem.
• Polynomials and Polynomial equations, relation between Coefficients and Roots, symmetric functions of roots.
• Elements of Group Theory; Sub-Group, Cyclic groups, Permutation, Groups and their elementary properties.
• Rings, Integral Domains and Fields and their elementary properties.

Vector Spaces and Matrices

• Vector Space, Linear Dependence and Independence.
• Sub-spaces.
• Basis and Dimensions, Finite Dimensional Vector Spaces.
• Linear Transformation of a Finite Dimensional Vector Space, Matrix 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.

Geometry and Vectors

• Analytic Geometry of straight lines and conics in Cartesian and Polar coordinates.
• Three Dimensional geometry for planes, straight lines, sphere, cone and cylinder.
• Addition, Subtraction and Products of Vectors and Simple applications to Geometry.

Calculus

• Functions, Sequences, Series, Limits, Continuity, Derivatives.

Application of Derivatives

• Rates of change, Tangents, Normals, Maxima, Minima, Rolle's Theorem, Mean Value Theorems of Lagrange and Cauchy, Asymptotes, Curvature.
• Methods of finding indefinite integrals, Definite Integrals, Fundamental Theorem of integrals Calculus.
• Application of definite integrals to area, Length of a plane curve, Volume and Surfaces of revolution.

Ordinary Differential Equations

• Order and Degree of a Differential Equation, First order differential Equations, Singular solution, Geometrical interpretation, Second order equations with constant coefficients.

Mechanics

• Concepts of particles-Lamina; Rigid Body; Displacements; force; Mass; weight; Motion; Velocity; Speed; Acceleration; Parallelogram of forces; Parallelogram of velocity, acceleration; resultant; equilibrium of coplanar forces; Moments; Couples; Friction; Centre of mass, Gravity; Laws of motion; Motion of a particle in a straight line; simple Harmonic Motion; Motion under conservative forces; Motion under gravity; Projectile; Escape velocity; Motion of artificial satellites.

Elements of Computer Programming

• Binary system, Octal and Hexadecimal systems.
• Conversion to and from Decimal systems.
• Codes, Bits, Bytes and Words.
• Memory of a computer, Arithmetic and Logical operations on numbers.
• Precisions. AND, OR, XOR, NOT and Shit/Rotate operators, Algorithms and Flow Charts.