Gagan Pratap Advance Maths Complete Class Notes New ❲TESTED · 2027❳

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.

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.

Phase 2 (Practice - Week 5-12): Solve the "Classroom Assignment" and "Home Assignment" sections strictly with a timer. If a geometry problem takes more than 2 minutes, watch his YouTube solution (linked via QR codes in the new edition).

• Triangle Theorems: Congruence, similarity, and the 50+ properties of triangles (Incenter, Circumcenter, Orthocenter, Centroid).
• Quadrilaterals & Polygons: Cyclic quadrilaterals, trapeziums, and interior/exterior angle formulas.
• Circles: Chords, tangents, secants, and the revolutionary "Direct Common Tangent" tricks.
• Mensuration 3D/2D: Cylinders, cones, spheres, frustums, and prism/pyramid questions asked in Tier 2 exams.