Gagan Pratap Advance Maths Complete Class Notes New ^new^

Structured Topic Summary – A chapter-by-chapter breakdown of the key formulas, concepts, and shortcut methods typically covered in Gagan Pratap’s advanced maths notes (Algebra, Trigonometry, Geometry, Mensuration, Number System, etc.).

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1. Official Website: Gagan Pratap’s platform (Gagan Pratap Sir’s app – Gagan Pratap Maths).
2. Amazon / Flipkart: Look for the specific cover: "New Revised Edition 2024-25" with a green stripe at the top.
3. Telegram Channels (Authorized): Only those linked from his YouTube channel.

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Gagan Pratap — Advanced Maths: Complete Class Notes (Concise Text)

1. Real Analysis

• Sequences & Limits: Definitions, convergence, Cauchy sequences, Bolzano–Weierstrass theorem.
• Series: Convergence tests (comparison, ratio, root, alternating series), absolute vs conditional convergence, power series, radius of convergence.
• Continuity: ε–δ definition, uniform continuity, intermediate value theorem, extreme value theorem.
• Differentiation: Definition, mean value theorems (Rolle, Lagrange, Cauchy), Taylor’s theorem with remainder, L’Hôpital’s rule.
• Integration: Riemann and improper integrals, fundamental theorem of calculus, convergence of improper integrals, techniques (substitution, parts).
• Metric Spaces: Open/closed sets, completeness, compactness, continuity, uniform continuity in metric spaces.