Foundations of Calculus: Derivatives and Continuity

Grasp the fundamental concepts of calculus that underpin much of modern science and engineering. This course will equip you with a robust understanding of continuity, differentiability, and higher-order derivatives, enabling you to confidently approach complex mathematical problems. What you'll learn: * Understand the precise definitions of limits, continuity, and differentiability for functions. * Master techniques for calculating first and higher-order derivatives of various function types. * Apply essential differentiation rules, including the chain rule and implicit differentiation. * Analyze the behavior of functions using derivatives to determine increasing/decreasing intervals and concavity. * Practice solving a diverse range of problems involving these core calculus concepts. The course begins with foundational definitions and gradually progresses through differentiation techniques, culminating in the application of these concepts to understand the characteristics of functions. This course is designed for absolute beginners in calculus with no prior experience required. Embark on your journey to master the essentials of calculus through clear, written explanations and practice.