Calculus Fundamentals: Differentiation and Its Applications

Calculus is the language of change, and differentiation is your key tool for understanding how things vary. Many students struggle with the jump from algebra to calculus. By the end of this course, you will not only memorize the fundamental differentiation rules but also deeply understand the concepts of limits, continuity, and differentiability. You will gain proficiency in applying these principles to model real-world phenomena, paving the way for success in higher-level mathematics, physics, and engineering. What you'll learn: * Understand the foundational concepts of limits, continuity, and the rigorous definition of a derivative. * Master the core rules of differentiation, including the product, quotient, and chain rules. * Apply differentiation techniques to find tangents, normal lines, and instantaneous rates of change. * Analyze differentiability and its connection to complex functions, including implicit and parametric forms. * Practice optimization problems and related rates modeling essential for physical and economic applications. We begin with the theoretical groundwork of limits and continuity before systematically introducing the differentiation rules. The course progresses through complex function analysis and concludes with practical application exercises in modeling. This course is designed for absolute beginners with basic algebra skills. No prior calculus knowledge is required. Start building your foundational calculus skills today.