Calculus 1 by Dr Trefor Bazett

About this course

This free online course helps you move from memorizing formulas to actually understanding calculus. Instead of treating ideas like limits, derivatives, and integrals as separate chapters, you learn how they connect and why they work. You will build intuition from the kinds of questions that show up in real problems: how velocity changes in time, what a function is doing near a point, and how a small change in x affects the output. That big-picture understanding makes later techniques feel natural rather than mysterious.

You start by exploring change through average and instantaneous velocity, then develop the language of limits using numerical and graphical thinking. As the course progresses, you get comfortable with key tools that make challenging limits manageable, including limit laws, algebraic strategies, and methods for tricky behaviors like oscillation, infinite limits, and limits at infinity. Along the way, you strengthen your reasoning with important ideas about continuity and guaranteed values, giving you a solid foundation for everything that follows.

From there, the course builds the derivative from the ground up using the definition, so the rules are not just facts to memorize. You learn to compute derivatives efficiently and interpret them as slopes, rates of change, and local behavior. Techniques such as product and quotient rules, chain rule, implicit differentiation, and logarithmic differentiation become practical tools for modeling and solving problems. Applications are emphasized so the mathematics feels useful, including tangent-line approximation, related rates, and optimization that trains you to translate a situation into equations and make decisions with calculus.

The final arc ties the story together through antiderivatives and definite integrals, connecting area and accumulation to derivatives via the Fundamental Theorem of Calculus. You gain confidence with Riemann-sum definitions, evaluating integrals, and substitution as the reverse of the chain rule, including both indefinite and definite cases. With practice questions and exam-style walkthroughs, you will be prepared for coursework, placement tests, and future STEM classes, with clearer intuition and stronger problem-solving habits.