Page 27 - DMTH402_COMPLEX_ANALYSIS_AND_DIFFERENTIAL_GEOMETRY

Complex Analysis and Differential Geometry

Notes 13. Find all points at which

x x
f(z)   i
2
2
x  y 2 x  y 2
is differentiable. At what points is f analytic? Explain.
14. Suppose f is analytic on the set D, and suppose Re f is constant on D. Is f necessarily
constant on D? Explain.
15. Suppose f is analytic on the set D, and suppose |f(z)| is constant on D. Is f necessarily
constant on D? Explain.
2.8 Further Readings

Books Ahelfors, D.V. : Complex Analysis
Conway, J.B. : Function of one complex variable
Pati, T. : Functions of complex variable

Shanti Narain : Theory of function of a complex Variable
Tichmarsh, E.C. : The theory of functions
H.S. Kasana : Complex Variables theory and applications
P.K. Banerji : Complex Analysis
Serge Lang : Complex Analysis

H.Lass : Vector & Tensor Analysis
Shanti Narayan : Tensor Analysis
C.E. Weatherburn : Differential Geometry
T.J. Wilemore : Introduction to Differential Geometry

Bansi Lal : Differential Geometry.

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