Which should be taught first: differential or integral calculus?

In nearly every modern math curriculum, differential calculus is taught before integral calculus. While the two topics were developed more concurrently by historical figures like Newton and Leibniz, the standard educational approach has a clear pedagogical reason for this order.

The primary reason is that the core concept of differential calculus—the rate of change—is more intuitive and easier to grasp initially.

• An Intuitive Start: We all have a real-world understanding of speed, which is a rate of change. Differential calculus begins by formalizing this idea, using limits to define the derivative, which represents an instantaneous rate of change. This provides a logical and relatable starting point.
• Building a Foundation: The tools and concepts you learn in differential calculus, especially limits and derivatives, are the essential building blocks needed to properly define and understand integrals.

The two branches are fundamentally linked by the Fundamental Theorem of Calculus, which reveals that differentiation and integration are inverse operations (much like multiplication and division). By learning about derivatives first, you gain the necessary framework to fully appreciate this powerful theorem and understand how integrals work as a method of "anti-differentiation" or accumulation.

In short, starting with differential calculus creates a more logical and comprehensible learning path, allowing each concept to build naturally on the last.