Page 85 - DMTH402_COMPLEX_ANALYSIS_AND_DIFFERENTIAL_GEOMETRY

Complex Analysis and Differential Geometry

Notes 7. In a bilinear transformation, a circle transforms into a circle and inverse points transform
into ................
8. An ................ which also conserves the sense of rotation is called conformal mapping. Thus
in a conformal transformation, the sense of rotation as well as the magnitude of the angle
is preserved.

7.6 Review Questions

Find the bilinear transformation which maps
(i) 1, i, 2 onto 0, 2, i respectively.

(ii) 1, i, 0 onto 1, i, 1 respectively.
(iii) 0, 1,  onto , i, 1 respectively.
(iv) 1, , i into 0, , 1 respectively.
(v) , i, 0 onto 0, i, respectively.

(vi) 1, 0, 1 onto i, , 1 respectively.
(vii) 1, i, 1 onto i, 0, i respectively.

Answers: Self Assessment

1. w = Az + B 2. reflection
3. one-one transformation 4. bilinear transformation
az b

5. bilinear transformation. 6. w = cz d

7. inverse points. 8. isogonal transformation
7.7 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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