Syllabus: Joint Admission Test For
Sequences, Series and Differential Calculus: Sequences of real numbers.
Convergent sequences and series, absolute and conditional convergence. Rolle’s
Theorem, Mean value theorem. Taylor's theorem. Maxima and minima of functions of
a single variable. Functions of two and three variables. Limit, Continuity,
Partial derivatives, differentiability, maxima and minima.
Integral Calculus: Double and triple integrals, Areas, Volumes, and Surface
Differential Equations: Ordinary differential equations of the first order of
the form y'=f(x,y). Linear differential equations of second and higher order
with constant coefficients. Cauchy- Euler equation.
Vector Calculus: Gradient, divergence, curl and Laplacian. Green's, Stokes and
Gauss theorems and their applications.
Group Theory: Groups, subgroups and normal subgroups, Lagrange's Theorem for
finite groups, group homeomorphisms and basic concepts of quotient groups.
Linear Algebra: Vector spaces, Linear dependence of vectors, basis, dimension,
linear transformations and matrix representation with respect to an ordered
basis, rank and inverse of a matrix, determinant, solutions of systems of linear
equations, consistency conditions. Eigen values and eigenvectors.
Real Analysis: Open and closed sets, limit points, completeness of R, Uniform
convergence, Power series.