Differential Equations and Real Analysis for IIT JAM Preparation

Succeeding in advanced mathematics exams requires a deep, intuitive understanding of both analytical proofs and practical problem-solving. This text-based course is designed to bridge the gap between abstract mathematical theory and the exam-room application needed for the IIT JAM. You will develop a systematic approach to solving ordinary differential equations and constructing rigorous real analysis proofs. By studying clear written explanations, step-by-step derivations, and structured practice problems, you will build the mathematical maturity needed to analyze limits, continuity, differentiability, and convergence with complete confidence. What you'll learn: • Understand foundational concepts of real numbers, sequences, and series convergence. • Solve first-order and higher-order ordinary differential equations using systematic analytical methods. • Apply rigorous proof techniques to limits, continuity, and differentiability of real-valued functions. • Master key theorems such as the Mean Value Theorem, Riemann integration, and the fundamental theorems of calculus. • Practice exam-style problems with detailed, step-by-step written solutions to refine your test-taking strategy. • Explore modern computational verification concepts to cross-check mathematical solutions. The course starts with fundamental definitions of real analysis before progressing to the mechanics of differential equations. You will move from core theory to guided problem-solving exercises designed to mirror competitive exam formats. This course is designed for beginners and university students preparing for the IIT JAM or similar mathematics examinations. A basic background in introductory calculus is helpful, but no advanced prior knowledge of real analysis is required. Start reading today to master the core principles of real analysis and differential equations.