IIT MATHS - Santhosh

Module 1: IIT Mathematics Fundamentals

• Sets, relations, functions

• Trigonometry & inverse trigonometry

• Quadratic equations & inequalities

• Permutations & combinations

• Probability & statistics

• Complex numbers

• Coordinate geometry basics

📌 Module 2: IIT JEE Advanced Mathematics

• Vectors & 3D geometry

• Matrices & determinants

• Binomial theorem & sequences

• Limits, continuity & differentiability

• Application of derivatives

• Definite & indefinite integrals

• Differential equations basics

• Advanced problem-solving for JEE patterns

📌 Module 3: AB Calculus

• Limits and continuity

• Differentiation rules

• Applications of derivatives (optimization, motion, rates)

• Riemann sums & integrals

• Fundamental Theorem of Calculus

• Techniques of integration

• AP/AB Calculus exam-style practice

📌 Module 4: Differential Equations (ODE & PDE)

Ordinary Differential Equations (ODE):

• First-order equations (linear, exact, Bernoulli)

• Second-order equations (homogeneous, non-homogeneous)

• Systems of ODEs

• Applications in physics & engineering

Partial Differential Equations (PDE):

• Formation & classification of PDEs

• Heat equation

• Wave equation

• Laplace equation

• Boundary value problems

• Fourier series for PDEs

📌 Module 5: Advanced Calculus & Analysis

• Sequence convergence

• Series tests

• Multivariable calculus

• Gradient, divergence, curl

• Double & triple integrals

• Line & surface integrals

📌 Module 6: Problem-Solving & Exam Strategy

• JEE mains & advanced pattern questions

• Time-bound mock tests

• Concept revision worksheets

• Doubt-clearing sessions

• Formula revision & shortcuts