(Syllabus) Joint Admission Test (JAM) Syllabus for Mathematics (MA) : 2009

Joint Admission Test (JAM) Syllabus for Mathematics (MA) : 2009

Sequences, Series and Differential Calculus:

• Sequences of real numbers.
• Convergent sequences and series, absolute and conditional convergence.
• Mean value theorem.
• Taylor 's theorem.
• Maxima and minima of functions of a single variable.
• Functions of two and three variables.
• Partial derivatives, maxima and minima.

Integral Calculus:

• Integration, Fundamental theorem of calculus.
• Double and Triple, integrals, Surface areas and volumes.

Differential Equations:

• Ordinary differential equations of the first order of the form y'=f(x,y).
• Linear differential equations of second order with constant coefficients.
• Euler-Cauchy equation.
• Method of variation of parameters.

Vector Calculus:

• Gradient, divergence, curl and Laplacian.
• Green's, Stokes' and Gauss' theorems and their applications.

Algebra:

• Groups, subgroups and normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups, rings, ideals, quotient rings and fields.

Linear Algebra:

• Systems of linear equations.
• Matrices, rank, determinant, inverse.
• Eigenvalues and eigenvectors.
• Finite Dimensional Vector Spaces over Real and Complex Numbers, Basis, Dimension, Linear Transformations.

Real Analysis:

• Open and closed sets, limit points, completeness of R, Uniform Continuity, Uniform convergence, Power series.

Get Your Dream Job.Post Your Resume Online.