# Introduction to complex analysis / H.A. Priestley.

Material type: TextPublication details: Oxford : Clarendon Press, New York : Oxford University Press, 1985Description: xi, 197 p. ill. ; 24 cmISBN:- 0198532474 :
- 9780198532460

- 515.9 19 P9494

Item type | Current library | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|

Books | UE-Central Library | 515.9 P9494 (Browse shelf(Opens below)) | Available | T3061 |

Includes index.

Part 1 The complex plane: complex numbers; open and closed sets in the complex plane; limits and continuity. Part 2 Holomorphic function and power series: complex power series; elementary functions. Part 3 Prelude to Cauchy's theorem: paths; integration along paths; connectedness and simple connectedness; properties of paths and contours. Part 4 Cauchy's theorem: Cauchy's theorem, level I and II; logarithms, argument and index; Cauchy's theorem revisited. Part 5 Consequences of Cauchy's theorem: Cauchy's formulae; power series representation; zeros of holomorphic functions; the maximum-modulus theorem. Part 6 Singularities and multifunctions: Laurent's theorem; singularities; meromorphic functions; multifunctions. Part 7 Cauchy's residue theorem: counting zeroes and poles; claculation of residues; estimation of integrals. Part 8 Applications of contour integration: improper and principal-values integrals; integrals involving functions with a finite number of poles and infinitely many poles; deductions from known integrals; integrals involving multifunctions; evaluation of definite integrals. Part 9 Fourier and Laplace tranforms: the Laplace tranform - basic properties and evaluation; the inversion of Laplace tranforms; the Fourier tranform; applications to differential equations; proofs of the Inversion and Convolution theorems. Part 10 Conformal mapping and harmonic functions: circles and lines revisited; conformal mapping; mobius tranformations; other mappings - powers, exponentials, and the Joukowski transformation; examples on building conformal mappings; holomorphic mappings - some theory; harmonic functions.

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