Syllabi

Semester 3 Paper Code: C5T (Credit: 6, Full Marks: 75) Paper Name: Theory of Real Functions & Introduction to Metric Space Unit 1 Limits of functions (ε – δ approach), sequential criterion for limits, divergence criteria. Limit theorems, one sided limits. Infinite limits and limits at infinity. Continuous functions, sequential criterion for continuity and discontinuity.

Semester 2 Paper Code: C3T (Credit: 6, Full Marks: 75) Paper Name: Real Analysis Unit 1 Review of algebraic and order properties of \( \mathbb{R} \), ε-neighborhood of a point in \( \mathbb{R} \). Idea of countable sets, uncountable sets and uncountability of \( \mathbb{R} \). Bounded above sets, bounded below sets, bounded sets, unbounded

Syllabus – Calculus, Geometry and Differential Equation Unit 1 Hyperbolic functions Higher order derivatives Leibnitz rule and its applications to problems of type: \(\pmb{e^{ax} + b \sin x}\) \(\pmb{e^{ax} + b \cos x}\) \(\pmb{(ax + b)^n \sin x}\) \(\pmb{(ax + b)^n \cos x}\) Concavity and inflection points Envelopes Asymptotes Curve tracing in Cartesian coordinates Tracing