Analysis with Ultrasmall Numbers

¡ ¡
¡ Textbooks in Mathematics āĻŦāχ 17 ¡ CRC Press
āχ-āĻŦ⧁āĻ•
316
āĻĒ⧃āĻˇā§āĻ āĻž
āωāĻĒāϝ⧁āĻ•ā§āϤ
āϰ⧇āϟāĻŋāĻ‚ āĻ“ āϰāĻŋāĻ­āĻŋāω āϝāĻžāϚāĻžāχ āĻ•āϰāĻž āĻšā§ŸāύāĻŋ  āφāϰāĻ“ āϜāĻžāύ⧁āύ

āĻāχ āχ-āĻŦ⧁āϕ⧇āϰ āĻŦāĻŋāĻˇā§Ÿā§‡

Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon-delta methods. Students can fully prove fundamental results, such as the

āϞ⧇āĻ–āĻ• āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇

Karel Hrbacek, Olivier Lessmann, Richard O'Donovan

āχ-āĻŦ⧁āϕ⧇ āϰ⧇āϟāĻŋāĻ‚ āĻĻāĻŋāύ

āφāĻĒāύāĻžāϰ āĻŽāϤāĻžāĻŽāϤ āϜāĻžāύāĻžāύāĨ¤

āĻĒāĻ āύ āϤāĻĨā§āϝ

āĻ¸ā§āĻŽāĻžāĻ°ā§āϟāĻĢā§‹āύ āĻāĻŦāĻ‚ āĻŸā§āϝāĻžāĻŦāϞ⧇āϟ
Android āĻāĻŦāĻ‚ iPad/iPhone āĻāϰ āϜāĻ¨ā§āϝ Google Play āĻŦāχ āĻ…ā§āϝāĻžāĻĒ āχāύāĻ¸ā§āϟāϞ āĻ•āϰ⧁āύāĨ¤ āĻāϟāĻŋ āφāĻĒāύāĻžāϰ āĻ…ā§āϝāĻžāĻ•āĻžāωāĻ¨ā§āĻŸā§‡āϰ āϏāĻžāĻĨ⧇ āĻ…āĻŸā§‹āĻŽā§‡āϟāĻŋāĻ• āϏāĻŋāĻ™ā§āĻ• āĻšā§Ÿ āĻ“ āφāĻĒāύāĻŋ āĻ…āύāϞāĻžāχāύ āĻŦāĻž āĻ…āĻĢāϞāĻžāχāύ āϝāĻžāχ āĻĨāĻžāϕ⧁āύ āύāĻž āϕ⧇āύ āφāĻĒāύāĻžāϕ⧇ āĻĒ⧜āϤ⧇ āĻĻā§‡ā§ŸāĨ¤
āĻ˛ā§āϝāĻžāĻĒāϟāĻĒ āĻ“ āĻ•āĻŽā§āĻĒāĻŋāωāϟāĻžāϰ
Google Play āĻĨ⧇āϕ⧇ āϕ⧇āύāĻž āĻ…āĻĄāĻŋāĻ“āĻŦ⧁āĻ• āφāĻĒāύāĻŋ āĻ•āĻŽā§āĻĒāĻŋāωāϟāĻžāϰ⧇āϰ āĻ“ā§Ÿā§‡āĻŦ āĻŦā§āϰāĻžāωāϜāĻžāϰ⧇ āĻļ⧁āύāϤ⧇ āĻĒāĻžāϰ⧇āύāĨ¤
eReader āĻāĻŦāĻ‚ āĻ…āĻ¨ā§āϝāĻžāĻ¨ā§āϝ āĻĄāĻŋāĻ­āĻžāχāϏ
Kobo eReaders-āĻāϰ āĻŽāϤ⧋ e-ink āĻĄāĻŋāĻ­āĻžāχāϏ⧇ āĻĒāĻĄāĻŧāϤ⧇, āφāĻĒāύāĻžāϕ⧇ āĻāĻ•āϟāĻŋ āĻĢāĻžāχāϞ āĻĄāĻžāωāύāϞ⧋āĻĄ āĻ“ āφāĻĒāύāĻžāϰ āĻĄāĻŋāĻ­āĻžāχāϏ⧇ āĻŸā§āϰāĻžāĻ¨ā§āϏāĻĢāĻžāϰ āĻ•āϰāϤ⧇ āĻšāĻŦ⧇āĨ¤ āĻŦā§āϝāĻŦāĻšāĻžāϰāĻ•āĻžāϰ⧀āϰ āωāĻĻā§āĻĻ⧇āĻļā§āϝ⧇ āϤ⧈āϰāĻŋ āϏāĻšāĻžā§ŸāϤāĻž āϕ⧇āĻ¨ā§āĻĻā§āϰāϤ⧇ āĻĻ⧇āĻ“ā§ŸāĻž āύāĻŋāĻ°ā§āĻĻ⧇āĻļāĻžāĻŦāϞ⧀ āĻ…āύ⧁āϏāϰāĻŖ āĻ•āϰ⧇ āϝ⧇āϏāĻŦ eReader-āĻ āĻĢāĻžāχāϞ āĻĒāĻĄāĻŧāĻž āϝāĻžāĻŦ⧇ āϏ⧇āĻ–āĻžāύ⧇ āĻŸā§āϰāĻžāĻ¨ā§āϏāĻĢāĻžāϰ āĻ•āϰ⧁āύāĨ¤

āϏāĻŋāϰāĻŋāϜ āĻĒāĻĄāĻŧāĻž āϚāĻžāϞāĻŋā§Ÿā§‡ āϝāĻžāύ

Karel Hrbacek āĻāϰ āĻĨ⧇āϕ⧇ āφāϰ⧋

āĻāĻ•āχ āϧāϰāύ⧇āϰ āχ-āĻŦ⧁āĻ•