Free online courseCalculus 1

Course Description

Calculus often feels like a sudden leap from familiar algebra into a world of symbols and new rules. This free online course is designed to make that leap manageable by building intuition first and then turning it into reliable problem-solving skills. You will start from the geometry of lines and slopes, connect that foundation to functions and graphs, and quickly move into the big ideas that power calculus: limits, continuity, derivatives, and integrals.

As you progress, you will learn how calculus explains change in a precise way. Limits provide the language for describing behavior near a point, and continuity clarifies when a function behaves smoothly enough to work with confidently. From there, the derivative becomes a practical tool for understanding instantaneous rate of change, slope of a curve, motion, and sensitivity in real situations. Step by step, you will strengthen your fluency with essential differentiation techniques, including product and quotient rules, the chain rule, and implicit differentiation, so that common expressions stop feeling intimidating and start feeling routine.

Beyond computation, the course emphasizes interpretation. You will see how derivatives reveal where a function increases or decreases, how concavity shapes a graph, and how the first and second derivative tests support clear conclusions. You will also practice the kind of thinking used in optimization, where calculus helps choose the best outcome under constraints, a skill that appears across science, engineering, and economics.

The second half of the journey focuses on integration as the natural partner of differentiation. You will build an understanding of area and accumulation from Riemann sums and limits, then learn to evaluate definite integrals efficiently and connect everything through the Fundamental Theorem of Calculus. With this perspective, topics like substitution, area between curves, and volumes of solids of revolution become logical extensions rather than disconnected tricks. By the end, you will be prepared to approach typical Calculus I assignments and exams with more confidence, accuracy, and insight.