Book:H.A. Priestley/Introduction to Complex Analysis/Revised Edition
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H.A. Priestley: Introduction to Complex Analysis (Revised Edition)
Published $\text {1990}$, Oxford Science Publications
- ISBN 0-19-853428-0
Subject Matter
Contents
- Preface to the revised edition (Oxford, November 1989)
- Preface to the first edition (Oxford, March 1985)
- Notation and terminology
- 1. The complex plane
- Complex numbers
- Open and closed sets in the complex plane
- Limits and continuity
- Exercises
- 2. Holomorphic functions and power series
- Holomorphic functions
- Complex power series
- Elementary functions
- Exercises
- 3. Prelude to Cauchy's theorem
- Paths
- Integration along paths
- Connectedness and simple connectedness
- Properties of paths and contours
- Exercises
- 4. Cauchy's theorem
- Cauchy's theorem, Level I
- Cauchy's theorem, Level II
- Logarithms, argument, and index
- Cauchy's theorem revisited
- Exercises
- 5. Consequences of Cauchy's theorem
- Cauchy's formulae
- Power series representation
- Zeros of homomorphic functions
- The Maximum-modulus theorem
- Exercises
- 6. Singularities and multifunctions
- Laurent's theorem
- Singularities
- Mesomorphic functions
- Multifunctions
- Exercises
- 7. Cauchy's residue theorem
- Cauchy's residue theorem
- Counting zeros and poles
- Calculation of residues
- Estimation of integrals
- Exercises
- 8. Applications of contour integration
- Improper and principal-value integrals
- Integrals involving functions with a finite number of poles
- Integrals involving functions with infinitely many poles
- Deductions from known integrals
- Integrals involving multifunctions
- Evaluation of definite integrals: summary
- Summation of series
- Exercises
- 9. Fourier and Laplace transforms
- The Laplace transform: basic properties and evaluation
- The inversion of Laplace transforms
- The Fourier transform
- Applications to differential equations, etc.
- Appendix: proofs of the Inversion and Convolution theorems
- Convolutions
- Exercises
- 10. Conformal mapping and harmonic functions
- Circles and lines revisited
- Conformal mapping
- Möbius transformations
- Other mappings: powers, exponentials, and the Joukowski transformation
- Examples on building conformal mappings
- Holomorphic mappings: some theory
- Harmonic functions
- Exercises
- Supplementary exercises
- Bibliography
- Notation index
- Subject index
Further Editions
Source work progress
- 1990: H.A. Priestley: Introduction to Complex Analysis (Revised ed.) ... (previous) ... (next): $1$ The complex plane: Complex numbers $\S 1.5$ Subsets of the complex plane