Buy Complex Analysis Book by Lars Ahlfors - Bookswagon
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Complex analysis, complex variables > Complex Analysis
Complex Analysis

Complex Analysis


     0     
5
4
3
2
1



Out of Stock


Notify me when this book is in stock
X
About the Book

A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.

Table of Contents:
Chapter 1: Complex Numbers1 The Algebra of Complex Numbers1.1Arithmetic Operations1.2Square Roots1.3Justification1.4Conjugation, Absolute Value1.5Inequalities2 The Geometric Representation of Complex Numbers2.1Geometric Addition and Multiplication2.2The Binomial Equation2.3Analytic Geometry2.4The Spherical RepresentationChapter 2: Complex Functions1 Introduction to the Concept of Analytic Function1.1Limits and Continuity1.2Analytic Functions1.3Polynomials1.4Rational Functions2 Elementary Theory of Power Series2.1Sequences2.2Series2.3Uniform Coverages2.4Power Series2.5 Abel's Limit Theorem3 The Exponential and Trigonometric Functions3.1 The Exponential3.2 The Trigonometric Functions3.3 The Periodicity3.4 The LogarithmChapter 3: Analytic Functions as Mappings1 Elementary Point Set Topology1.1Sets and Elements1.2Metric Spaces1.3Connectedness1.4Compactness1.5 Continuous Functions1.6 Topological Spaces2 Conformality2.1Arcs and Closed Curves2.2Analytic Functions in Regions2.3Conformal Mapping2.4Length and Area3 Linear Transformations3.1 The Linear Group3.2 The Cross Ratio3.3 Symmetry3.4 Oriented Circles3.5 Families of Circles4 Elementary Conformal Mappings4.1 The Use of Level Curves4.2 A Survey of Elementary Mappings4.3 Elementary Riemann SurfacesChapter 4: Complex Integration1 Fundamental Theorems1.1Line Integrals1.2Rectifiable Arcs1.3Line Integrals as Functions of Arcs1.4Cauchy's Theorem for a Rectangle1.5 Cauchy's Theorem in a Disk2 Cauchy's Integral Formula2.1The Index of a Point with Respect to a Closed Curve2.2The Integral Formula2.3Higher Derivatives3 Local Properties of Analytical Functions3.1 Removable Singularities. Taylor's Theorem3.2 Zeros and Poles3.3 The Local Mapping3.4 The Maximum Principle4 The General Form of Cauchy's Theorem4.1 Chains and Cycles4.2 Simple Connectivity4.3 Homology4.4 The General Statement of Cauchy's Theorem4.5 Proof of Cauchy's Theorem4.6 Locally Exact Differentials4.7 Multiply Connected Regions5 The Calculus of Residues5.1 The Residue Theorem5.2 The Argument Principle5.3 Evaluation of Definite Integrals6 Harmonic Functions6.1 Definition and Basic Properties6.2 The Mean-value Property6.3 Poisson's Formula6.4 Schwarz's Theorem6.5 The Reflection PrincipleChapter 5: Series and Product Developments1 Power Series Expansions1.1Wierstrass's Theorem1.2The Taylor Series1.3The Laurent Series2 Partial Fractions and Factorization2.1Partial Fractions2.2Infinite Products2.3Canonical Products2.4 The Gamma Function2.5 Stirling's Formula3 Entire Functions3.1 Jensen's Formula3.2 Hadamard's Theorem4 The Riemann Zeta Function4.1 The Product Development4.2 Extension of ζ(s) to the Whole Plane4.3 The Functional Equation4.4 The Zeros of the Zeta Function5 Normal Families5.1 Equicontinuity5.2 Normality and Compactness5.3 Arzela's Theorem5.4 Families of Analytic Functions5.5 The Classical DefinitionChapter 6: Conformal Mapping, Dirichlet's Problem1 The Riemann Mapping Theorem1.1Statement and Proof1.2Boundary Behavior1.3Use of the Reflection Principle1.4 Analytic Arcs2 Conformal Mapping of Polygons2.1The Behavior at an Angle2.2The Schwarz-Christoffel Formula2.3Mapping on a Rectangle2.4 The Triangle Functions of Schwarz3 A Closer Look at Harmonic Functions3.1 Functions with Mean-value Property3.2 Harnack's Principle4 The Dirichlet Problem4.1 Subharmonic Functions4.2 Solution of Dirichlet's Problem5 Canonical Mappings of Multiply Connected Regions5.1 Harmonic Measures5.2 Green's Function5.3 Parallel Slit RegionsChapter 7: Elliptic Functions1 Simply Periodic Functions1.1Representation by Exponentials1.2The Fourier Development1.3Functions of Finite Order2 Doubly Periodic Functions2.1The Period Module2.2Unimodular Transformations2.3The Canonical Basis2.4 General Properties of Elliptic Functions3 The Weierstrass Theory3.1 The Weierstrass p-function3.2 The Functions ζ(z) and σ(z)3.3 The Differential Equation3.4 The Modular Function λ(r)3.5 The Conformal Mapping by λ(r)Chapter 8: Global Analytic Functions1 Analytic Continuation1.1The Weierstrass Theory1.2Germs and Sheaves1.3Sections and Riemann Surfaces1.4 Analytic Continuations along Arcs1.5 Homotopic Curves1.6 The Monodromy Theorem1.7 Branch Points2 Algebraic Functions2.1The Resultant of Two Polynomials2.2Definition and Properties of Algebraic Functions2.3 Behavior at the Critical Points3 Picard's Theorem3.1 Lacunary Values4 Linear Differential Equations4.1 Ordinary Points4.2 Regular Singular Points4.3 Solutions at Infinity4.4 The Hypergeometric Differential Equation4.5 Riemann's Point of ViewIndex

About the Author :
Retired


Best Sellers


Product Details
  • ISBN-13: 9780070006577
  • Publisher: McGraw-Hill Education - Europe
  • Publisher Imprint: McGraw-Hill Professional
  • Height: 231 mm
  • Returnable: N
  • Weight: 590 gr
  • ISBN-10: 0070006571
  • Publisher Date: 16 Dec 1978
  • Binding: Hardback
  • Language: English
  • Spine Width: 25 mm
  • Width: 160 mm


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Complex Analysis
McGraw-Hill Education - Europe -
Complex Analysis
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Complex Analysis

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!