Foundations of Calculus: Continuity and Differentiability

Are you looking to grasp the fundamental concepts of calculus that underpin many areas of mathematics and science? This course provides a clear and accessible introduction to continuity and differentiability, essential building blocks for further mathematical study. You will gain a solid understanding of how functions behave and how to analyze their rates of change. This knowledge is crucial for problem-solving in various quantitative fields. What you'll learn: * Understand the formal definition of continuity for functions. * Apply limit properties to determine function continuity. * Define differentiability and its relationship to continuity. * Calculate derivatives using fundamental rules and definitions. * Analyze function behavior using derivative concepts. * Practice applying continuity and differentiability in problem-solving scenarios. This course begins with the foundational definitions and progresses through practical applications, ensuring you build a robust understanding from the ground up. It is designed for beginners with no prior calculus knowledge and requires no specific prerequisites. Start your journey into calculus with these essential concepts.