Free online courseIntroductory Calculus

Course Description

Calculus becomes much easier when the foundations feel natural. This free online course is designed to help you move from core pre-calculus ideas into the essential toolkit of Calculus I, with clear explanations and plenty of guided practice. You will strengthen the skills that make everything else possible: working confidently with the number system, inequalities, absolute value, and the function mindset needed to model change.

From there, you will develop a solid understanding of limits, including one-sided behavior, infinite limits, and limits at infinity. You will learn how limit laws streamline algebraic evaluation, how the squeeze theorem justifies tricky conclusions, and how continuity connects graphs and formulas through important results like the intermediate value theorem. These concepts are presented to help you reason about what a function is doing, not just manipulate symbols.

Next, you will build fluency with derivatives as rates of change and slopes of tangent lines. Along the way, you will practice the full set of differentiation tools: rules for powers and combinations, product and quotient techniques, chain rule thinking, implicit differentiation, and derivatives involving trigonometric, inverse trig, exponential, logarithmic, and even hyperbolic functions. You will also see how derivatives support real problem-solving, including related rates, approximation ideas, and numerical methods.

As your skills grow, you will connect derivatives to behavior and decision-making: maxima and minima, critical points, concavity, and curve sketching. You will learn when key theorems apply and how they support reliable conclusions, then use these insights in applications such as optimization. When limits produce indeterminate forms, you will gain an additional strategy with L’Hopital’s rule and asymptote analysis to better interpret function behavior.

Finally, you will transition into integration, building intuition for area under curves and the meaning of definite integrals. You will work with integral properties, antiderivatives, and the fundamental theorem of calculus to connect accumulation and rate of change. The course supports steady progress through review points and exam-style questions, making it a strong choice for high school or early college learners who want a structured path to genuine Calculus I confidence.