Core Concepts of Differential Calculus

Differential calculus is the essential mathematical tool for understanding how things change. Do you need a clear, rigorous foundation in limits, derivatives, and their practical applications? By the end of this course, you will have mastered the conceptual framework of differentiation, allowing you to confidently calculate derivatives, understand continuity, and apply optimization techniques to model real-world scenarios. What you'll learn: * Understand the rigorous definition of limits and continuity, forming the essential bedrock of calculus. * Master the rules of differentiation, including the chain rule, product rule, and quotient rule. * Apply derivatives to calculate instantaneous rates of change and slopes of tangent lines for various functions. * Practice curve sketching and graphing functions using first and second derivatives to analyze behavior. * Solve applied optimization and related rates problems using calculus techniques to find maximum and minimum values. The course begins with defining limits and continuity before moving systematically through the techniques of differentiation. We conclude by applying these skills to solve practical problems in optimization and mathematical modeling. This course is designed for absolute beginners in calculus, including students, engineers, and self-learners. No prior advanced mathematical knowledge beyond algebra is required. Start building your essential mathematical toolkit today.