Foundational Calculus: Continuity and Differentiation

Calculus is the mathematical language of change, and a strong grasp of continuity and differentiation is the gateway to advanced scientific and engineering disciplines. Many beginners struggle with the theoretical rigor required to truly master these concepts.By the end of this course, you will possess a solid, application-ready understanding of foundational calculus, enabling you to confidently analyze function behavior and rates of change.What you'll learn:<ul><li>Understand the formal definition of limits and master algebraic techniques for their evaluation.</li><li>Learn the rigorous conditions and types of discontinuity for functions across various intervals.</li><li>Master fundamental differentiation rules, including the Chain Rule, Product Rule, and Quotient Rule.</li><li>Apply derivatives to practical real-world scenarios like optimization, related rates, and curve sketching.</li><li>Practice the application of critical theorems, such as Rolle’s Theorem and the Mean Value Theorem, to analyze function properties.</li><li>Configure implicit differentiation techniques for complex equations where variables are intertwined.</li></ul>This course begins with essential terminology and the formal definition of limits before progressing methodically through the rules of differentiation and their practical applications. The material is delivered entirely through written explanations and guided practice exercises.This course is designed for absolute beginners and students seeking a rigorous introduction to calculus. No prior experience with calculus is required—only a basic understanding of algebra and functions.Start building your mathematical expertise today.