IIT JAM Mathematics

Rigorous notes on derivatives, Rolle's theorem, Lagrange and Cauchy mean value theorems, Taylor expansion, maxima, minima, and approximation.

IIT JAM-style checkpoint covering sequences, limits, continuity, differentiability, and convergence of series.

Substitution, integration by parts, partial fractions, trigonometric substitutions, and standard integrals.

Detailed notes on Riemann integration, properties of definite integrals, fundamental theorem, symmetry, area, and improper integrals.

Limits and continuity of multivariable functions, partial derivatives, differentiability, directional derivatives, and gradient.

Double and triple integrals, polar coordinates, Jacobians, transformations, and geometric applications.

IIT JAM-style practice on integration and multivariable calculus, including optimization and multiple integrals.

Matrix operations, determinants, rank, inverse, Gaussian elimination, consistency, and systems of linear equations.

Comprehensive notes on vector spaces, linear combinations, span, linear independence, basis, dimension, and fundamental dimension formulas.

Kernel, image, rank, nullity, matrix representation, composition, and invertibility of linear transformations.

Characteristic polynomial, eigenvalues, eigenspaces, algebraic and geometric multiplicity, diagonalization, and important matrix properties.

Practice on groups, subgroups, basic algebraic structures, matrices, vector spaces, transformations, and eigenvalue problems.

Separable, homogeneous, exact, linear, Bernoulli, and special first-order differential equations.

Complementary functions, particular integrals, constant coefficient equations, Cauchy-Euler equations, and variation of parameters.

First-order systems, matrix formulation, equilibrium points, and solution structure.

Detailed treatment of vector fields, directional derivatives, gradient, divergence, curl, line integrals, and major integral theorems.

Mixed IIT JAM-style questions covering differential equations and vector calculus.

Sample spaces, events, conditional probability, Bayes theorem, random variables, PMF, PDF, CDF, expectation, and variance.

Detailed notes on Bernoulli, Binomial, Poisson, Normal distributions, expectation, variance, covariance, and standard statistical identities.

Bisection, Newton-Raphson, interpolation, numerical integration, error analysis, and convergence concepts.

Structured problem-solving session using representative IIT JAM-style questions across the complete syllabus.

Comprehensive full-length checkpoint simulating IIT JAM Mathematics with mixed conceptual, computational, and application-based questions.