Differential Calculus Fundamentals

Overview

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.

Syllabus

Introduction to derivatives

This module introduces you to the concept of derivatives, helping you understand how rates of change are represented graphically and calculated from first principles. Through readings and hands-on examples, you will begin applying derivatives to simple functions and real-world scenarios.

Rules of differentiation

This week you will explore the product, quotient, and chain rules to differentiate more complex functions. Applying these rules through guided examples and by solving increasingly challenging problems you will gradually build your confidence.

Implicit Differentiation

The focus this week will shift to implicit differentiation, where you will learn to handle equations with interdependent variables. Activities include solving higher-order derivatives and applying the technique to practical problems.

Maxima and Minima

This module covers maxima, minima, and inflection points, showing you how to identify and interpret them using derivatives. You will apply these concepts to optimization problems and explore their relevance in data-driven decision-making.