Interactive Real Analysis

• Real Analysis
• About
• Site Overview
• Guest Book
• 1. Sets and Relations
• 2. Infinity and Induction
• 3. Sequences of Numbers
• 4. Series of Numbers
• 5. Topology
• 6. Limits, Continuity, and Differentiation
• 7. The Integral
• 8. Sequences of Functions
• 9. Historical Tidbits
• Java Tools

Interactive Real Analysis

Real Analysis

Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, power series, and more. The text is changing constantly, and your comments are very welcome: please sign our guest book.

IRA News: 30 Years of IRA: hard to believe, but version 1.0 of IRA was published as one of the earliest web applications more than 30 years ago, and has been available for free to students ever since. Here is to the next 30 years.

Version 3 is in the works. It will finally include new working vesions of the interactive tools. They will be re-created using HTML 5.0, the current standard for such program. Of coure there's a number of correctons and typos, as usual.It will take until the end of this year (2026) to get the new version ready - until then, enjoy what there is.

IRA has been free of any form of advertisements for many years. However, I've got to live, so version 3.0 will include a limited number of ads, as unobtrousive as possible. Sorry. The alternative is to charge money outright for using this project, and that would not be in anyone's interest. So, ads it is. Please click on them plenty! I also want to ecourage you to sign the guest book I have nearly 2,000 signatures and comments collected over the years, and the more people are using IRA, the easier it is to obtain funding to continue the project.

Now Mobile-friendly: IRA is now mobile-friendly. the site has been reformatted to work as usual on 'large screens' (laptops, desktops, tablets) and switch automatically to a different layout appropriate for small screens (mobile phones). Check it out on your smart phone and let me know any comments.

New material: I expanded the section on measures (still more coming soon), the glossary has been expanded, I added the Leaning Tower of Lire and Hilbert's Hotel. A new chapter on Fourier Series, FFT, and applications to MP3 sound files is in the works. Keep your comments coming!