Complex Analysis: Springer Undergraduate Mathematics Series
Autor John M. Howieen Limba Engleză Paperback – 28 mai 2003
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Specificații
ISBN-13: 9781852337339
ISBN-10: 1852337338
Pagini: 272
Ilustrații: XI, 260 p.
Dimensiuni: 178 x 254 x 14 mm
Greutate: 0.48 kg
Ediția:2003
Editura: SPRINGER LONDON
Colecția Springer
Seria Springer Undergraduate Mathematics Series
Locul publicării:London, United Kingdom
ISBN-10: 1852337338
Pagini: 272
Ilustrații: XI, 260 p.
Dimensiuni: 178 x 254 x 14 mm
Greutate: 0.48 kg
Ediția:2003
Editura: SPRINGER LONDON
Colecția Springer
Seria Springer Undergraduate Mathematics Series
Locul publicării:London, United Kingdom
Public țintă
Lower undergraduateCuprins
1. What Do I Need to Know?.- 1.1 Set Theory.- 1.2 Numbers.- 1.3 Sequences and Series.- 1.4 Functions and Continuity.- 1.5 Differentiation.- 1.6 Integration.- 1.7 Infinite Integrals.- 1.8 Calculus of Two Variables.- 2. Complex Numbers.- 2.1 Are Complex Numbers Necessary?.- 2.2 Basic Properties of Complex Numbers.- 3. Prelude to Complex Analysis.- 3.1 Why is Complex Analysis Possible?.- 3.2 Some Useful Terminology.- 3.3 Functions and Continuity.- 3.4 The O and o Notations.- 4. Differentiation.- 4.1 Differentiability.- 4.2 Power Series.- 4.3 Logarithms.- 4.4 Cuts and Branch Points.- 4.5 Singularities.- 5. Complex Integration.- 5.1 The Heine-Borel Theorem.- 5.2 Parametric Representation.- 5.3 Integration.- 5.4 Estimation.- 5.5 Uniform Convergence.- 6. Cauchy’s Theorem.- 6.1 Cauchy’s Theorem: A First Approach.- 6.2 Cauchy’s Theorem: A More General Version.- 6.3 Deformation.- 7. Some Consequences of Cauchy’s Theorem.- 7.1 Cauchy’s Integral Formula.- 7.2 The Fundamental Theorem of Algebra.- 7.3 Logarithms.- 7.4 Taylor Series.- 8. Laurent Series and the Residue Theorem.- 8.1 Laurent Series.- 8.2 Classification of Singularities.- 8.3 The Residue Theorem.- 9. Applications of Contour Integration.- 9.1 Real Integrals: Semicircular Contours.- 9.2 Integrals Involving Circular Functions.- 9.3 Real Integrals: Jordan’s Lemma.- 9.4 Real Integrals: Some Special Contours.- 9.5 Infinite Series.- 10. Further Topics.- 10.1 Integration of f?/f; Rouché’s Theorem.- 10.2 The Open Mapping Theorem.- 10.3 Winding Numbers.- 11. Conformai Mappings.- 11.1 Preservation of Angles.- 11.2 Harmonic Functions.- 11.3 Möbius Transformations.- 11.4 Other Transformations.- 12. Final Remarks.- 12.1 Riemann’s Zeta function.- 12.2 Complex Iteration.- 13. Solutions to Exercises.- SubjectIndexBibliography.- Subject IndexIndex.
Recenzii
From the reviews:
Howie's book is a gem. I want to use it the next time I teach complex analysis. Not only do Howie's selection of topics and their sequence correspond perfectly to what I believe to be the ideal approach to this gorgeous subject, the writing style is (again) wonderful...I think this is a terrific book. I'm going to use it the first chance I get. And I recommend it very, very highly.
MAA Online
Howie has written an outstanding book on complex variables...The readability of the book is improved by more than 80 figures and numerous examples. Also included are 140 exercises with complete solutions in an appendix. All this makes the book ideal for self-study. Summing up: Highly recommended.
CHOICE
"This book provides a self-study text for students in mathematics, science and engineering. It covers all the topics likely to feature in a first course in complex analysis up to Laurent series, the residue theorem and conformal mappings. … Many carefully worked examples and more than 100 exercises with solutions make the book a valuable contribution to the extensive literature on complex analysis." (F.Haslinger, Monatshefte für Mathematik, Vol. 143 (2), 2004)
"This is a superbly well-written, balanced introduction to complex analysis that will meet the needs of a wide range of undergraduates. … Here, page after page, I found myself nodding in agreement with the choices that the author has made ... . ‘Of all the many introductions to complex analysis, Howie’s is arguably the most attractive’." (Nick Lord, The Mathematical Gazette, Vol. 88 (512), 2004)
"This book takes account of the varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. ... Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4),2003)
"Howie … has written an outstanding book on complex variables. … The readability of the book is improved by more than 80 figures and numerous examples. Also included are 140 exercises with complete solutions in an appendix. All this make the book ideal for self-study. Summing Up: Highly recommended." (D.P.Turner, CHOICE, December, 2003)
Howie's book is a gem. I want to use it the next time I teach complex analysis. Not only do Howie's selection of topics and their sequence correspond perfectly to what I believe to be the ideal approach to this gorgeous subject, the writing style is (again) wonderful...I think this is a terrific book. I'm going to use it the first chance I get. And I recommend it very, very highly.
MAA Online
Howie has written an outstanding book on complex variables...The readability of the book is improved by more than 80 figures and numerous examples. Also included are 140 exercises with complete solutions in an appendix. All this makes the book ideal for self-study. Summing up: Highly recommended.
CHOICE
"This book provides a self-study text for students in mathematics, science and engineering. It covers all the topics likely to feature in a first course in complex analysis up to Laurent series, the residue theorem and conformal mappings. … Many carefully worked examples and more than 100 exercises with solutions make the book a valuable contribution to the extensive literature on complex analysis." (F.Haslinger, Monatshefte für Mathematik, Vol. 143 (2), 2004)
"This is a superbly well-written, balanced introduction to complex analysis that will meet the needs of a wide range of undergraduates. … Here, page after page, I found myself nodding in agreement with the choices that the author has made ... . ‘Of all the many introductions to complex analysis, Howie’s is arguably the most attractive’." (Nick Lord, The Mathematical Gazette, Vol. 88 (512), 2004)
"This book takes account of the varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. ... Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4),2003)
"Howie … has written an outstanding book on complex variables. … The readability of the book is improved by more than 80 figures and numerous examples. Also included are 140 exercises with complete solutions in an appendix. All this make the book ideal for self-study. Summing Up: Highly recommended." (D.P.Turner, CHOICE, December, 2003)
Caracteristici
Suitable for both pure and applied mathematicians Takes account of readers' varying needs and backgrounds by presenting ideas through worked examples and informal explanations rather than through "dry" theory Concentrates on the key ideas without getting bogged down in technical details Features a wealth of exercises (with solutions) and numerous worked examples making it ideal for self-study Includes supplementary material: sn.pub/extras