Advanced calculus I-1
Minimum price
Suggested price

Advanced calculus I-1

Metric spaces, topological spaces and sequences

About the Book

Advanced calculus, or called mathematical analysis in some universities, is fundamental in mathematical training. It is a two-semester four-credit course in the mathematics department of National Tsing Hua University. This book stems from lecture notes for the classes of advanced calculus I that I taught several times. The goal of this book is to provide rigorous but easy to follow mathematical proofs and a book that is convenient to read on portable digital devices. I try to make this book friendly and, hopefully, readers may find those colorful paragraphs and beautiful pictures of the book attractive. Many students find this course difficult as many abstract concepts are introduced at a rather rapid pace. But being able to think abstractly is probably one of the most important abilities in modern sciences and technologies. Learning mathematics is similar to learning language, we need to have enough vocabulary to express our mathematical ideas and we need to spend enough time on it to get connection of different concepts. I try to cut proofs into small pieces so that readers may verify them easier. Based on some knowledge of basic calculus, this book is self-contained and suitable for self-study. Exercises are provided at the end of each section.

Due to the length and size, materials for advanced calculus I is separated into two books: Advanced Calculus I-1 and Advanced Calculus I-2. We had 3 midterm exams and 1 final exam in the course of advanced calculus I. The book Advanced Calculus I-1 contains materials for midterm exam 1 and 2, and the book Advanced Calculus I-2 contains materials for midterm exam 3 and final exam. Practice exams and exam questions are attached to the books.

About the Author

Jyh Haur Teh
Jyh Haur Teh

A professor in the department of mathematics, National Tsing Hua University of Taiwan, Hsinchu, Taiwan.


The Leanpub 60-day 100% Happiness Guarantee

Within 60 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.

See full terms

80% Royalties. Earn $16 on a $20 book.

We pay 80% royalties. That's not a typo: you earn $16 on a $20 sale. If we sell 5000 non-refunded copies of your book or course for $20, you'll earn $80,000.

(Yes, some authors have already earned much more than that on Leanpub.)

In fact, authors have earnedover $12 millionwriting, publishing and selling on Leanpub.

Learn more about writing on Leanpub

Free Updates. DRM Free.

If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).

Most Leanpub books are available in PDF (for computers) and EPUB (for phones, tablets and Kindle). The formats that a book includes are shown at the top right corner of this page.

Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.

Learn more about Leanpub's ebook formats and where to read them

Write and Publish on Leanpub

You can use Leanpub to easily write, publish and sell in-progress and completed ebooks and online courses!

Leanpub is a powerful platform for serious authors, combining a simple, elegant writing and publishing workflow with a store focused on selling in-progress ebooks.

Leanpub is a magical typewriter for authors: just write in plain text, and to publish your ebook, just click a button. (Or, if you are producing your ebook your own way, you can even upload your own PDF and/or EPUB files and then publish with one click!) It really is that easy.

Learn more about writing on Leanpub