Functions of One Variable for IIT JAM and MSc Mathematics

Rigorous calculus is the backbone of advanced mathematics and competitive entrance exams. Understanding the deep analytical theory behind functions of a single variable is essential for solving complex mathematical problems. This text-based course guides you from foundational definitions to advanced problem-solving techniques, helping you build the mathematical intuition needed to excel in exams like the IIT JAM. You will learn to approach proofs systematically and tackle challenging calculus problems with confidence. What you'll learn: - Understand the fundamental properties of real numbers, intervals, bounds, and function mappings. - Master limits and continuity using both intuitive concepts and rigorous epsilon-delta definitions. - Apply differentiability rules and key mean value theorems to analyze complex function behavior. - Solve optimization, monotonicity, and curvature problems using first and second derivatives. - Practice step-by-step mathematical proofs and analyze common counterexamples in real analysis. The course begins with essential terminology and the foundational properties of real numbers. You will then progress systematically through limits, continuity, and differentiability, culminating in the application of advanced theorems to exam-style problems. This course is designed for undergraduate mathematics students and exam aspirants; no advanced prerequisites beyond high school algebra are required. Start building your mathematical rigor today.