Calculus 1
Master differential and integral calculus concepts
Calculus is the study of change and accumulation. Instead of working with fixed quantities, calculus focuses on how quantities vary and how small changes build into larger effects. Calculus I introduces the core ideas of limits, derivatives, and integrals. These concepts are closely connected: limits explain how quantities behave near a point, derivatives measure rates of change, and integrals measure total accumulation. Together, they form a unified way of thinking about motion, growth, and area.
Not sure where to start? Take the Diagnostic for Calculus 1.
Topics
Explore mathematical concepts at your own pace
Limits
Limits describe how a function behaves as the input gets close to a certain value. They allow us to reason about behavior near a point, even when the function is not defined there. This section focuses on building intuition for limits and understanding why they are the foundation of calculus.
Derivatives
A derivative measures how fast a quantity is changing. It connects algebraic formulas to ideas like slope, velocity, and sensitivity to change. This section introduces derivatives as rates of change and explains how differentiation rules come from this basic idea.
Applications of Derivatives
Derivatives are useful because they describe real behavior. They tell us when quantities increase or decrease, reach maximum or minimum values, or change direction. This section applies derivatives to motion, optimization, and analyzing the shape of graphs.
Integrals
An integral measures accumulation. It answers questions about total change, area, and how small pieces add up to a whole. This section introduces integrals as the inverse of derivatives and explains their connection through the Fundamental Theorem of Calculus.
Limits
IntermediateLimits describe how a function behaves as the input gets close to a certain value. They allow us to reason about behavior near a point, even when the function is not defined there. This section focuses on building intuition for limits and understanding why they are the foundation of calculus.