DIPS ACADEMY has truly been one of the most profound learning experience where I gained the confidence to move ahead in my carrer with the opportunity to put myself on the forefront in dealing mathematics. DIPS programme is very well designed with very helpful test series. Dubey Sir and other faculty are superb. The lectures of Dubey Sir are the most intersting and inspiring.
I am very contented with the dips family specially dubey sir, he's an excellent mentor with amazing teaching skills.The mathematical atmosphere along with one to one interaction, dips material and doubt clearing sessions provided by DIPS ACADEMY were very helpful throughout the journey.
" The guidance of Dubey Sir, a teacher with immense knowledge and wonderful teaching skills, was of great help for me. His approach towards tackling problems, in particular, is pecular and worth emulating I thank him for his invaluable guidance and continuous motivation. "
I'm Mamta Kumari and I secured AIR 47 in IIT - JAM Mathematics. I am very thankful to Dubey Sir, Amit Sir and all the other faculty members for their teachings and guidance. The classes used to be very interactive and environment was very positive for learning. I have learned a lot from Dips academy and I'm very thankful to all the faculties for teaching us the actual meaning of Mathematics in the best possible way.
Algebra:
Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation
groups; Normal subgroups, Lagrange's Theorem for finite groups, group homomorphism and
quotient groups, Rings, Subrings, Ideal, Prime ideal; Maximal ideals; Fields, quotient field.
Vector spaces, Linear dependence and Independence of vectors, basis, dimension, linear
transformations, matrix representation with respect to an ordered basis, Range space and null
space, rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of
linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley-Hamilton
theorem. Symmetric, Skew symmetric, Hermitian, Skew-Hermitian, Orthogonal and Unitary
matrices.
Real Analysis:
Sequences and series of real numbers. Convergent and divergent sequences, bounded
and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences,
absolute and conditional convergence; Tests of convergence for series of positive terms-comparison
test, ratio test, root test, Leibnitz test for convergence of alternating series.
Functions of one variable: limit, continuity, differentiation, Rolle's Theorem, Cauchy’s Taylor's
theorem. Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact
sets; completeness of R, Power series (of real variable) including Taylor's and Maclaurin's, domain
of convergence, term-wise differentiation and integration of power series.
Functions of two real variable: limit, continuity, partial derivatives, differentiability, maxima
and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's
theorem.
Complex Analysis: Functions of a complex Variable, Differentiability and analyticity, Cauchy Riemann Equations, Power series as an analytic function, properties of line integrals, Goursat Theorem, Cauchy theorem, consequence of simply connectivity, index of a closed curves. Cauchy’s integral formula, Morera’s theorem, Liouville’s theorem, Fundamental theorem of Algebra, Harmonic functions.
Integral Calculus: Integration as the inverse process of differentiation, definite integrals and their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications.
Differential Equations: Ordinary differential equations of the first order of the form y'=f(x,y). Bernoulli's equation, exact differential equations, integrating factor, Orthogonal trajectories, Homogeneous differential equations-separable solutions, Linear differential equations of second and higher order with constant coefficients, method of variation of parameters. Cauchy-Euler equation.
Vector Calculus: Scalar and vector fields, gradient, divergence, curl and Laplacian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their applications.
Linear Programing: Convex sets, extreme points, convex hull, hyper plane & polyhedral Sets, convex function and concave functions, Concept of basis, basic feasible solutions, Formulation of Linear Programming Problem (LPP), Graphical Method of LPP, Simplex Method.
DIPS ACADEMY has truly been one of the most profound learning experience where I gained the confidence to move ahead in my carrer with the opportunity to put myself on the forefront in dealing mathematics. DIPS programme is very well designed with very helpful test series. Dubey Sir and other faculty are superb. The lectures of Dubey Sir are the most intersting and inspiring.
I am very contented with the dips family specially dubey sir, he's an excellent mentor with amazing teaching skills.The mathematical atmosphere along with one to one interaction, dips material and doubt clearing sessions provided by DIPS ACADEMY were very helpful throughout the journey.
" The guidance of Dubey Sir, a teacher with immense knowledge and wonderful teaching skills, was of great help for me. His approach towards tackling problems, in particular, is pecular and worth emulating I thank him for his invaluable guidance and continuous motivation. "
I'm Mamta Kumari and I secured AIR 47 in IIT - JAM Mathematics. I am very thankful to Dubey Sir, Amit Sir and all the other faculty members for their teachings and guidance. The classes used to be very interactive and environment was very positive for learning. I have learned a lot from Dips academy and I'm very thankful to all the faculties for teaching us the actual meaning of Mathematics in the best possible way.