000 03871nam a22004815i 4500
001 978-1-4614-0195-7
003 DE-He213
005 20180115171512.0
007 cr nn 008mamaa
008 110629s2011 xxu| s |||| 0|eng d
020 _a9781461401957
_9978-1-4614-0195-7
024 7 _a10.1007/978-1-4614-0195-7
_2doi
050 4 _aQA331-355
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.9
_223
100 1 _aAgarwal, Ravi P.
_eauthor.
245 1 3 _aAn Introduction to Complex Analysis
_h[electronic resource] /
_cby Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas.
250 _a1.
264 1 _aBoston, MA :
_bSpringer US,
_c2011.
300 _aXIV, 331 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface.-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.
520 _aThis 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     An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
650 0 _aMathematics.
650 0 _aMathematical analysis.
650 0 _aAnalysis (Mathematics).
650 0 _aFunctions of complex variables.
650 1 4 _aMathematics.
650 2 4 _aFunctions of a Complex Variable.
650 2 4 _aAnalysis.
700 1 _aPerera, Kanishka.
_eauthor.
700 1 _aPinelas, Sandra.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461401940
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-0195-7
912 _aZDB-2-SMA
999 _c370461
_d370461