Applications in Physics and Geometry

Richard Courant and Fritz John
Additional contact information
Richard Courant: New York University, Courant Institute of Mathematical Sciences
Fritz John: New York University, Courant Institute of Mathematical Sciences

Chapter 4 in Introduction to Calculus and Analysis, 1989, pp 324-439 from Springer

Abstract: Abstract The representation of a curve by an equation y = f(x) imposes a serious geometrical restriction: A curve so represented must not be intersected at more than one point by any parallel to the y-axis. Usually, this restriction can be overcome by decomposing the curve into portions each representable in the form y = f(x). Thus a circle of radius a about the origin is given by the two functions $$y = \sqrt {{a^2} - {x^2}} $$ and $$y = - \sqrt {{a^2} - {x^2}} $$ defined for −a ≤ x ≤ a. However, for as simple a curve as a parallel to the y-axis this device does not work.

Keywords: Closed Curve; Parameter Representation; Direction Cosine; Closed Curf; Plane Curf (search for similar items in EconPapers)
Date: 1989
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-8955-2_4

Ordering information: This item can be ordered from
http://www.springer.com/9781461389552

DOI: 10.1007/978-1-4613-8955-2_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().