Free online courseCalculus 1 lectures

Course Description

Strengthen your foundation in Calculus 1 with a free online course designed to turn intimidating concepts into tools you can use with confidence. If limits, derivatives, and integrals have felt like a collection of rules to memorize, this course helps you connect ideas, understand why procedures work, and recognize which technique fits a problem. It is ideal for high school and college students, self-learners preparing for exams, or anyone who needs calculus for STEM pathways.

You will begin by developing real intuition for limits using graphical and numerical reasoning, then refine that understanding with formal definitions, continuity, one-sided limits, and infinite limits. From there, the focus shifts to derivatives: interpreting them as slopes, instantaneous rates of change, and tangible answers to real questions about motion, change, and sensitivity. As you progress, you will learn to differentiate efficiently and accurately, including product, quotient, and chain rules, as well as implicit differentiation for relationships that cannot be solved neatly for one variable.

To move beyond computation, you will apply derivatives to decision-making. You will analyze increasing and decreasing behavior, extrema on intervals, and concavity, using key theorems that power curve sketching and justify results. You will also practice optimization and numerical approximation with Newton’s method, gaining problem-solving habits that transfer to physics, economics, engineering, and data-driven fields.

The course continues with exponential and logarithmic functions, building comfort with common forms seen in applications. You will also see how calculus models change over time through introductory differential equation ideas like growth and decay. Reviews placed throughout help you consolidate what you learned and prepare strategically for major exams. With lecture support and targeted exercises, you can study at your own pace and leave with a clearer, more reliable grasp of Calculus 1.