Buch, Englisch, 331 Seiten, Format (B × H): 164 mm x 245 mm, Gewicht: 1470 g
ISBN: 978-1-4614-0194-0
Verlag: Springer Us
This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner.
Key features of this textbook:
-Effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures
- Uses detailed examples to drive the presentation
-Includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section
-covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics
-Provides a concise history of complex numbers
Zielgruppe
Upper undergraduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preface.-Complex Numbers.-Complex Numbers II .- Complex Numbers III.-Set Theory in the Complex Plane.-Complex Functions.-Analytic Functions I.-Analytic Functions II.-Elementary Functions I.- Elementary Functions II.- Mappings by Functions.- Mappings by Functions II.- Curves, Contours, and Simply Connected Domains.- Complex Integration.- Independence of Path.- Cauchy–Goursat Theorem.- Deformation Theorem.- Cauchy’s Integral Formula.- Cauchy’s Integral Formula for Derivatives.- Fundamental Theorem of Algebra.- Maximum Modulus Principle.- Sequences and Series of Numbers.- Sequences and Series of Functions.- Power Series.- Taylor’s Series.- Laurent’s Series.- Zeros of Analytic Functions.- Analytic Continuation.- Symmetry and Reflection.- Singularities and Poles I.- Singularities and Poles II.- Cauchy’s Residue Theorem.- Evaluation of Real Integrals by Contour Integration I.- Evaluation of Real Integrals by Contour Integration II.- Indented Contour Integrals.- Contour Integrals Involving Multi–valued Functions .- Summation of Series. Argument Principle and Rouch´e and Hurwitz Theorems.- Behavior of Analytic Mappings.- Conformal Mappings.- Harmonic Functions.- The Schwarz–Christoffel Transformation.- Infinite Products.- Weierstrass’s Factorization Theorem.- Mittag–Leffler’s Theorem.- Periodic Functions.- The Riemann Zeta Function.- Bieberbach’s Conjecture.- The Riemann Surface.- Julia and Mandelbrot Sets.- History of Complex Numbers.- References for Further Reading.- Index.
