Developments and Applications of the Differential Calculus

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

Chapter Chapter 3 in Introduction to Calculus and Analysis, 1989, pp 218-366 from Springer

Abstract: Abstract Frequently in analytical geometry the equation of a curve is given not in the form y = f(x) but in the form F(x, y) = 0. A straight line may be represented in this way by the equation ax + by + c = 0, and an ellipse, by the equation x2/a2 + y2/b2= 1. To obtain the equation of the curve in the form y = f(x) we must “solve” the equation F(x, y) = 0 for y. In Volume I we considered the special problem of finding the inverse of a function y = f(x), that is, the problem of solving the equation F(x, y) = y − f(x)= 0 for the variable x.

Keywords: Differential Form; Tangent Plane; Parametric Representation; Differential Calculus; Subsidiary Condition (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-1-4613-8958-3_3

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