Unit 1: Analysis & Linear Algebra
Weightage: 65-75 Marks
- Real Analysis: Sequences, Series, Metric Spaces, Continuity, Uniform Continuity, Riemann Integration, Function of Several Variables
- Linear Algebra: Vector Spaces, Subspaces, Basis, Dimension, Linear Transformations, Matrix Representation, Eigenvalues & Eigenvectors, Cayley-Hamilton, Jordan Canonical Form, Quadratic Forms
Unit 2: Complex Analysis & Modern Algebra
Weightage: 55-65 Marks
- Complex Analysis: Analytic Functions, Cauchy-Riemann Equations, Cauchy's Theorem, Residue Theorem, Conformal Mapping, Maximum Modulus Principle
- Abstract Algebra: Groups, Subgroups, Normal Subgroups, Sylow Theorems, Rings, Ideals, Fields, Galois Theory
Unit 3: Applied Mathematics
Weightage: 50-60 Marks
- Ordinary Differential Equations (ODE)
- Partial Differential Equations (PDE)
- Calculus of Variations (COV)
- Linear Integral Equations (IE)
- Classical Mechanics & Numerical Analysis