Foundations of Differential Calculus: Functions and Graphs

Differential calculus is a fundamental branch of mathematics essential for understanding change, motion, and optimization across various fields. If you're looking to build a strong, clear foundation in this critical subject, this course is designed for you. By engaging with this course, you will transform your understanding of calculus from abstract concepts into practical problem-solving skills, enabling you to confidently approach complex mathematical challenges. What you'll learn: Understand the foundational concepts of functions, domains, ranges, and graphical representation. Learn to evaluate limits and analyze continuity, essential for understanding calculus. Master the rules of differentiation, including power, product, quotient, and chain rules. Apply derivatives to determine rates of change, slopes of tangents, and critical points for optimization. Explore implicit differentiation and related rates problems to model dynamic situations. Practice solving diverse problems to solidify your conceptual understanding and application skills. The course begins with a thorough review of functions and their graphical properties, then systematically introduces limits and continuity before diving into the core principles and techniques of differentiation. You will progress through clear explanations and practical examples, building your knowledge step-by-step. This course is specifically designed for absolute beginners with no prior calculus experience, providing all the necessary foundational knowledge from the ground up. Start your journey into the powerful world of differential calculus today.