Real Analysis & Sequences of Real Numbers
Weightage: 35-40 Marks
- Sequences and Series of Real Numbers
- Convergence, Bolzano-Weierstrass Theorem
- Functions of One Real Variable: Limit, Continuity, Intermediate Value Property
- Differentiation, Mean Value Theorems, L'Hospital's Rule, Taylor's Theorem
- Riemann Integration, Fundamental Theorem of Calculus
Multivariable Calculus & Differential Equations
Weightage: 25-30 Marks
- Functions of Two or Three Variables: Limit, Continuity, Directional Derivatives, Gradient, Maxima and Minima
- Double and Triple Integrals, Change of Variables, Surface Area, Volume
- First order ODEs, Integrating Factors, Orthogonal Trajectories, Second Order Linear ODEs
Linear Algebra & Abstract Algebra
Weightage: 30-35 Marks
- Vector Spaces, Subspaces, Linear Dependence, Basis, Dimension, Linear Transformations, Matrix Representation
- Eigenvalues, Eigenvectors, Cayley-Hamilton Theorem
- Groups, Subgroups, Cyclic Groups, Permutation Groups, Lagrange's Theorem, Group Homomorphisms