Calculus Fundamentals: Limits, Continuity, and Optimization

Understanding how functions behave is crucial for advanced mathematics, physics, and engineering. This course demystifies the core concepts of calculus—limits, continuity, and differentiation—providing a robust foundation for technical problem-solving. By the end of this course, you will possess a strong theoretical and practical command of the tools necessary to analyze function properties, determine rates of change, and solve complex optimization problems using derivatives. What you'll learn: * Understand the formal definition of a limit and techniques for evaluating indeterminate forms. * Apply the conditions for continuity and differentiability across various types of functions. * Master the rules of differentiation and methods for finding derivatives of complex expressions. * Analyze function behavior, including monotonicity, concavity, and points of inflection using derivative tests. * Configure systematic approaches for solving applied problems involving rates of change and curve sketching. * Practice setting up and solving optimization problems (finding maxima and minima) using calculus techniques. We begin with fundamental definitions and theorems, progressing through detailed written explanations and worked examples. Each section concludes with practice problems designed to solidify your conceptual understanding and application skills. This course is designed for absolute beginners in calculus or those needing a solid refresher on foundational concepts. No prior advanced mathematical knowledge is required. Start building your rigorous foundation in calculus today.