Abstract
Classical vector analysis is rife with geometric and physical ideas, but appears precarious from a modern viewpoint of pure mathematics. Modern vector analysis with differential forms is surely up to the contemporary standard of mathematical rigor, but geometric ideas are completely lost in the bulk of dull calculations. The main goal in this paper is to show that synthetic differential geometry, which has replenished differential geometry with nilpotent infinitesimals, can mathematically sanitize classical vector analysis by eradicating its total confusion between approximate calculations and infinitesimal calculations, thereby helping it retrieve mathematical rigor.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
