← 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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Real Analysis cover
Real Analysis
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
Covers: The whole section — metric spaces, compactness & completeness, uniform convergence, the Weierstrass and Ascoli–Arzelà theorems, and Lebesgue measure & integration up to the Lp spaces.
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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