Calculus & Real Analysis
Weightage: 18-22 Marks
- Functions of single and several variables
- Limit, Continuity, Differentiability
- Taylor's Theorem, Maxima and Minima
- Multiple Integrals, Line, Surface, and Volume Integrals
- Green's, Stokes', and Gauss Divergence Theorems
Linear Algebra & Complex Analysis
Weightage: 20-25 Marks
- Finite dimensional vector spaces, Matrix representation
- Eigenvalues, Eigenvectors, Cayley-Hamilton Theorem
- Analytic functions, Contour integration, Residue theorem, Laurent series
Differential Equations & Numerical Analysis
Weightage: 20-25 Marks
- First order ODEs, Higher order linear ODEs with constant coefficients
- Classification of Second Order PDEs, Wave, Heat, Laplace equations
- Numerical solutions of nonlinear equations, Interpolation, Numerical integration
Algebra & Topology
Weightage: 15-18 Marks
- Groups, Subgroups, Homomorphisms, Rings, Ideals
- Basic point set topology, Topological spaces, Compactness, Connectedness