← GATE Mathematics guide GATE Mathematics · Section 3
Real Analysis
One of the largest sections — and directly covered.
Books that cover Section 3
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Full syllabus — Section 3
- Metric spaces; Baire category theorem; connectedness, compactness, completeness
- Continuity & uniform continuity; sequences and series of functions; uniform convergence; Ascoli–Arzelà theorem; Weierstrass approximation theorem
- Contraction mapping principle; power series; differentiation of functions of several variables; inverse and implicit function theorems
- Lebesgue measure on the real line; measurable functions; Lebesgue integral; Fatou’s lemma; monotone & dominated convergence theorems; Lp spaces