Calculus I entire course by Kimberly Brehm

About this course

If you want calculus to feel logical instead of intimidating, this free online course is built to take you from essential algebra and graphing habits to the core ideas that power STEM, economics, and data-driven work. You will strengthen the foundations that typically slow students down, then learn how to read functions, interpret change, and connect equations to real meaning. Along the way, guided practice helps you turn common sticking points into routines you can rely on under exam pressure.

You will start by sharpening the prerequisites that make Calculus I much easier: factoring efficiently, recognizing patterns in graphs, and understanding how linear models describe rates of change. From there, you will develop a clear picture of what it means for a relation to be a function and how trig behavior shows up in graphs. These early skills become your toolkit for the first big calculus theme: limits. You will learn how limits answer questions about behavior near a point, why they sometimes fail to exist, and how the formal epsilon-delta idea supports the intuitive one. That naturally leads into continuity, where you learn to classify discontinuities and use powerful theorems that guarantee certain values must occur.

Next, you will shift to derivatives as a precise language for instantaneous change. You will understand the derivative from its definition, then gain fluency with the main rules used in problem solving, including product, quotient, chain, and implicit differentiation. You will also practice turning derivatives into modeling tools through related rates and optimization, so you can translate a word problem into an equation and make decisions using calculus rather than guessing.

Finally, you will build the bridge to integrals and accumulation. You will connect area ideas to sigma notation and Riemann sums, see how definite integrals are defined, and understand why the Fundamental Theorem of Calculus is the key link between rates of change and total change. You will also gain comfort with substitution and with logarithmic, exponential, and inverse trigonometric tools that commonly appear in later courses. A comprehensive review at the end helps you pull everything together and study with purpose.