Introduction to Calculus and Analysis Volume II1 by Fritz John & Richard Courant

Author:Fritz John & Richard Courant
Language: eng
Format: epub
Publisher: Springer-Verlag Wien 2012
Published: 2014-06-18T16:00:00+00:00

6. A transformation of the plane

is conformal if the functions φ and ψ satisfy the identities

7. Prove that if all the normals of a surface z = u(x, y) meet the z-axis, then the surface is a surface of revolution.

8. The equation

determines two values of t, depending on x and y:

(a) Prove that the curves t1 = constant and t2 = constant are ellipses and hyperbolas all having the same foci (confocal conics).

(b) Prove that the curves t1 = constant and t2 = constant are orthogonal.

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