Foundational Differential Calculus for Single-Variable Functions

Understanding how functions change is essential for success in science, engineering, and data analysis. This course provides a complete, structured introduction to the core principles of differential calculus. By the end of this program, you will have a deep, working knowledge of derivatives and their applications, allowing you to analyze the behavior of complex functions and tackle optimization challenges with confidence. What you'll learn: * Learn the rigorous definition of limits and continuity, the foundation of all calculus. * Master differentiation rules and techniques for computing the derivative of any single-variable function. * Understand and apply fundamental theorems, including the Mean Value Theorem and L'Hôpital's rule. * Practice analyzing function properties such as monotonicity, concavity, and local extrema for accurate curve sketching. * Apply Taylor's Formula to approximate function values and understand error bounds in numerical analysis. * Configure and solve practical optimization problems using derivatives to find maximum and minimum values. We begin with essential definitions and theoretical frameworks before moving into practical examples and step-by-step problem-solving techniques. The course emphasizes reading comprehension and applying mathematical concepts through written exercises. This course is designed for absolute beginners in calculus who have a working knowledge of algebra and pre-calculus concepts. No prior experience with derivatives or limits is required. Start building your foundational mathematical expertise today.