Differential Calculus, Graphs, and Functions for Competitive Exams

Succeeding in competitive mathematics exams requires a deep, intuitive understanding of how functions behave and how to analyze them. This text-based course guides you from the fundamental definitions of functions and graphs to the core principles of differential calculus. Through clear, step-by-step written explanations and structured mathematical exercises, you will develop the analytical skills needed to dissect complex equations, sketch functions accurately, and apply calculus theorems with precision. What you'll learn: - Understand the fundamental properties of functions, domains, ranges, and types of mappings - Master graphical transformations to quickly sketch and analyze complex mathematical equations - Apply the concepts of limits, continuity, and differentiability to evaluate function behavior - Calculate derivatives using core rules, implicit differentiation, and successive differentiation techniques - Analyze function extrema, monotonicity, and curvature using first and second derivative tests - Solve practical optimization and rate-of-change problems step-by-step The course begins with foundational definitions of functions and graphing techniques before advancing to limits, continuity, and the core mechanics of differential calculus. You will progress through structured text-based lessons designed to build your problem-solving speed and accuracy. This course is designed for beginners starting their exam preparation journey and college students looking to build a rock-solid foundation in calculus, with no prior advanced mathematics required. Start reading today to master the mathematical principles that will elevate your exam performance.