Free online courseCalculus 2

Course Description

Build real confidence in second-semester calculus with a course designed to connect concepts to problem solving. You will move beyond memorizing rules and learn to recognize patterns: when a logarithm simplifies an expression, when a substitution makes an integral manageable, and how inverse functions reshape the way you think about derivatives and graphs.

The course strengthens your command of exponential and logarithmic behavior, inverse trigonometric functions, and hyperbolic functions, giving you tools that show up constantly in STEM homework and exams. You will also learn how to evaluate tricky limits, including indeterminate forms, by using ideas that clarify why common techniques work instead of treating them like magic steps.

Integration becomes a practical toolkit as you work through methods such as integration by parts, trigonometric integrals and substitutions, partial fractions, improper integrals, and numerical approximation strategies like the trapezoidal rule and Simpson’s rule. These methods help you tackle integrals that appear in physics, engineering, economics, and data-heavy applications where exact antiderivatives are not always the easiest path.

You will then expand into differential equations with separation of variables, building intuition for how equations describe change over time. From there, you will develop a solid foundation in sequences and series: convergence tests, alternating and absolute convergence, power series, and Taylor and Maclaurin expansions for approximation. The final portion broadens geometric intuition with parametric and polar viewpoints, including calculating areas bounded by curves.

As a free online course with guided lectures and targeted exercises, it is a strong fit for students preparing for exams, learners reviewing prerequisites for advanced math, or anyone aiming to sharpen quantitative reasoning through consistent practice.