| TEST TYPE |
Modules |
DATE |
Syllabus |
| MWT-01 |
Real Analysis: I |
3-Jan-23 |
Sequences and Series of Real Numbers: convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series. : limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule
|
| MWT-02 |
Differential Equations |
6-Jan-23 |
Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.
|
| MWT-03 |
Linear Algebra I |
09-01-23 |
Finite Dimensional Vector Spaces: linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, eigenvectors. |
| MWT-04 |
Integral Calculus |
12-Jan-23 |
fundamental theorem of calculus.double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals. Riemann integration (definite integrals and their properties),
|
| MWT-05 |
Group Theory |
15-Jan-22 |
Groups: cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange's theorem for finite groups, group homomorphisms.
|
| MWT-06 |
Linear Algebra II |
18-Jan-23 |
Matrices: systems of linear equations, rank, nullity, ranknullity theorem, inverse, determinant, eigenvalues, eigenvectors.
|
| MWT-07 |
Real Analysis: II |
21-Jan-23 |
Taylor's theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus. Functions of Two or Three Real Variables: limit, continuity, partial derivatives, total derivative, maxima and minima. radius and interval of convergence, term-wise differentiation and integration of power series. Multivariable Calculus & Differential Equations: Functions of Two or Three Real Variabels: Limit, continuity, partial derivatives, maxima and minma.
|
| MWT-08 |
Group Theory + Linear Algebra |
25-Jan-23 |
Matrices: systems of linear equations, rank, nullity, ranknullity theorem, inverse, determinant, eigenvalues, eigenvectors. Finite Dimensional Vector Spaces: linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. Groups: cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange's theorem for finite groups, group homomorphisms.
|
| MWT-09 |
Integral Calculus + ODE |
28-Jan-23 |
Integral Calculus: double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals. Differential Equations: Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.
|
| MWT-10 |
Real Analysis (Full Syllabus) |
31-Jan-23 |
Sequences and Series of Real Numbers: convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series. Functions of One Real Variable: limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus. Functions of Two or Three Real Variables: limit, continuity, partial derivatives, total derivative, maxima and minima.
|
| FLT-01 |
Full Length Test |
02-Feb-23 |
As per Exam Pattern |
| FLT-02 |
Full Length Test |
04-Feb-23 |
As per Exam Pattern |
| FLT-03 |
Full Length Test |
06-Feb-23 |
As per Exam Pattern |
| FLT-04 |
Full Length Test |
08-Feb-23 |
As per Exam Pattern |
