Differential Calculus Fundamentals

Master the essential concepts of differential calculus and develop expertise in analyzing rates of change and solving optimization problems. In this comprehensive course, you'll learn to calculate derivatives from first principles, apply advanced differentiation rules including product, quotient, and chain rules, and use implicit differentiation to handle complex equations with interdependent variables. You'll explore higher-order derivatives to understand function behavior including concavity and acceleration, and analyze critical points to identify maxima, minima, and inflection points. The course culminates with optimization techniques essential for data-driven decision-making across multiple disciplines. By completing this course, you'll gain competency in identifying appropriate differentiation techniques, executing calculations accurately, and applying derivative analysis to real-world problems. Whether you're pursuing data science, engineering, economics, or advanced analytics, these foundational calculus skills are essential for modeling change, optimizing outcomes, and solving quantitative challenges. You'll develop the analytical thinking and mathematical precision needed to tackle sophisticated problems in technical and scientific fields, preparing you for advanced studies in integral calculus and mathematical modeling

• Calculate derivatives from first principles and apply differentiation rules to complex functions
• Use implicit differentiation to handle equations with interdependent variables and compute higher-order derivatives
• Identify and analyze maxima, minima, and inflection points using derivative tests
• Apply differential calculus to analyze rates of change and model real-world phenomena

• Basic familiarity with topic and common terminology
• Readiness to practice through applied exercises or case studies