Set theory: Set operations, relations, functions. Propositional logic: Formulation, deduction, evaluation, puzzles. Linear Algebra: Solution of a system of linear equations. Determinant and inverse of a matrix, basic properties of matrices. Co-ordinate Geometry and Conic Sections: Solution of a system of linear equations. Determinant and inverse of a matrix, basic properties of matrices. Trigonometry: Identities, computation of heights and lengths. Differential Calculus: Total and partial differentiation, limit of a function. Integral Calculus: Definite and indefinite integrals, solution of differential equations, computation of areas and volumes. Series and sequences: sum, mean, convergence, limit. Real and complex numbers: surds, solution of equations on complex domain. Polynomials: solution of quadratic equations, properties of roots of polynomials with real coefficients, binomial expansion, Taylor series. Permutations and Combinations. Elementary Probability Theory: Computing probability from combinatorial reasoning, conditional probability. |
