4. Real And Complex Numbers :
(I) Real Numbers : Natural Numbers, Integers, Rational, Irrational, Real Numbers, Algebra Of Real Numbers, Order Relation In Real Numbers, Countability, Uncountability, Real Sequences, Series, Their Convergence.
(Ii) Complex Numbers : Algebra Of Complex Numbers, Argument, Modulus, Inverse, Demoivre’s Theorem And Applications.
5. Matrices :
Algebra Of Matrices, Determinant Of Matrices, Inverse Of Matrix, Transpose, Solution Of Linear Equations, Symmetric Matrices, Skew-Symmetric Matrices, Hermitian Matrices, Skew-Hermitian Matrices, Rank Of A Matrix.
6. Combinatrics And Probability :
(I) Counting Principles, Permutations, Different Type Of Permutations, Combinations, Binomial Theorem.
(Ii) Definition, Axioms Of Probability, Independent Events, Baye’s Law.
7. Differential Calculus :
Limit, Continuity, Derivatives, Higher Order Derivatives, Tangent, Normal, Increasing, Decreasing Functions, Maxima, Minima, Rolle’s Theorem, Mean Value Theorems, Taylor’s Theorem, Partial Differentiation, Euler’s Theorem.
8. Integral Calculus :
Integration As Reverse Process Of Differentiation, Definite Integral, Methods Of Integration, Area Under Plane Curves.
9. Differential Equation :
Order, Degree Of O.D.E., First Order Differential Equation, Their Solutions, Higher Order Differential Equation With Constant Coefficients, Their Solutions.
10. 2-Dimensional Geometry :
Preliminaries, Straight Lines, Circles, Pair Of Lines, Parabola, Ellipse, Hyperbola.
11. 3-Dimensional Geometry And Vectors:
(I) Preliminaries, Direction Cosines, Planes, Lines, Sphere, Tangent Plane To Spheres.
(Ii) Algebra Of Vectors, Linear Dependence And Independence, Scalar And Vector Product Of Vectors, Scalar And Vector Triple Products.
12. Mechanics :
(I) Statics : Force, Parallelogram Law Of Forces, Equilibrium Of Forces, Moments, Couples, Friction, Centre Of Mass.
(Ii) Dynamics : Laws Of Motion, Kinematics, D’ Alemberts Principle, Motion Of A Particle In Plane, Projectile, Moment Of Inertia Of Plane Bodies.
13. Group :
Properties Of Groups, Permutation Group, Cyclic Group, Sub-Group, Lagrange’s Theorem, Counting Principles, Normal Sub-Groups, Homomorphism And Isomorphism.
14. Rings And Fields And Vector Spaces :
(I) Definitions, Ring, Division Ring, Integral Domain, Fields, Sub-Ring, Ideals, Homomorphism And Isomorphism.
(Ii) Vector Space, Subspace, Linear Dependence, Independence, Basis, Dimension.
15. Numerical Methods :
Numbers In Binary, Octal And Hexadecimal Systems, Errors, Solution Of Algebraic And Transcendental Equations By Bisection, Secant, Newton-Raphson Method, Interpolation, Lagrange And Newton’s Methods, Quadrature, Trapezoidal And Simpson’s 1/3rd Rule. Numerical Solution Of I.V.P., Euler’s Method, Second Order Runge-Kutta Method.