Calculus: Continuity and Differentiation

Understanding how quantities change is fundamental to many scientific and engineering disciplines, and calculus provides the tools to do just that. This course offers a comprehensive, step-by-step introduction to the core concepts of continuity and differentiation, empowering you to confidently analyze the behavior of functions. By the end of this course, you will be able to: * Understand the formal definitions and properties of continuous functions. * Learn to compute derivatives using fundamental rules and advanced techniques like the Chain Rule. * Master the application of differentiation to find rates of change, slopes of tangents, and critical points. * Practice solving optimization problems and analyzing related rates scenarios. * Grasp the significance of key theorems such as Rolle's Theorem and the Mean Value Theorem. * Apply calculus principles to interpret and solve problems across various fields. The course begins by establishing a solid understanding of limits and continuity, then systematically introduces the rules and applications of differentiation, from basic algebraic functions to transcendental functions. This course is ideal for beginners in calculus, students needing to strengthen their foundational knowledge, or anyone looking to develop robust mathematical analytical skills. Start your journey into calculus and unlock powerful analytical capabilities.