LEADER 02781nam 2200589 450 001 9910153084403321 005 20230803220428.0 010 $a1-292-05339-9 035 $a(CKB)2550000001160304 035 $a(SSID)ssj0001256730 035 $a(PQKBManifestationID)12493303 035 $a(PQKBTitleCode)TC0001256730 035 $a(PQKBWorkID)11272717 035 $a(PQKB)11578288 035 $a(MiAaPQ)EBC5174648 035 $a(MiAaPQ)EBC5187182 035 $a(MiAaPQ)EBC5833104 035 $a(MiAaPQ)EBC5137928 035 $a(MiAaPQ)EBC6399587 035 $a(Au-PeEL)EBL5137928 035 $a(CaONFJC)MIL543509 035 $a(OCoLC)1017000386 035 $a(EXLCZ)992550000001160304 100 $a20210330d2014 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApplied partial differential equations $ewith Fourier series and boundary value problems /$fRichard Haberman 205 $aFifth, Pearson new international edition. 210 1$aHarlow, England :$cPearson,$d[2014] 210 4$d©2014 215 $a1 online resource (644 pages) $cillustrations 225 1 $aPearson custom library 300 $aIncludes index. 311 $a1-292-03985-X 311 $a1-306-12258-9 327 $aCover -- Table of Contents -- 1. Heat Equation -- 2. Method of Separation of Variables -- 3. Fourier Series -- 4. Wave Equation: Vibrating Strings and Membranes -- 5. Sturm-Liouville Eigenvalue Problems -- 6. Finite Difference Numerical Methods for Partial Differential Equations -- 7. Higher-Dimensional Partial Differential Equations -- 8. Nonhomogeneous Problems -- 9. Green's Functions for Time-Independent Problems -- 10. Infinite Domain Problems: Fourier Transform Solutions -- 11. Green's Functions for Wave and Heat Equations -- 12. The Method of Characteristics for Linear and Quasilinear Wave Equations -- 13. Laplace Transform Solution of Partial Differential Equations -- Index. 330 $aThis text emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Green's functions, and transform methods.   This text is ideal for students in science, engineering, and applied mathematics. 410 0$aPearson custom library. 606 $aDifferential equations, Partial 615 0$aDifferential equations, Partial. 676 $a515.353 700 $aHaberman$b Richard$f1945-$042625 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910153084403321 996 $aApplied partial differential equations$9230664 997 $aUNINA LEADER 06004nam 22005655 450 001 9910973853803321 005 20250904131224.0 010 $a1-4612-0817-3 024 7 $a10.1007/978-1-4612-0817-4 035 $a(CKB)3400000000089283 035 $a(SSID)ssj0001296807 035 $a(PQKBManifestationID)11763966 035 $a(PQKBTitleCode)TC0001296807 035 $a(PQKBWorkID)11373577 035 $a(PQKB)10171688 035 $a(DE-He213)978-1-4612-0817-4 035 $a(MiAaPQ)EBC3073894 035 $a(PPN)238026639 035 $a(EXLCZ)993400000000089283 100 $a20121227d1995 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aFunctions of One Complex Variable II /$fby John B. Conway 205 $a1st ed. 1995. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1995. 215 $a1 online resource (XVI, 396 p.) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v159 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a0-387-94460-5 311 08$a1-4612-6911-3 320 $aIncludes bibliographical references and index. 327 $aof Volume II -- 13 Return to Basics -- 1 Regions and Curves -- 2 Derivatives and Other Recollections -- 3 Harmonic Conjugates and Primitives -- 4 Analytic Arcs and the Reflection Principle -- 5 Boundary Values for Bounded Analytic Functions -- 14 Conformal Equivalence for Simply Connected Regions -- 1 Elementary Properties and Examples -- 2 Crosscuts -- 3 Prime Ends -- 4 Impressions of a Prime End -- 5 Boundary Values of Riemann Maps -- 6 The Area Theorem -- 7 Disk Mappings: The Class S -- 15 Conformal Equivalence for Finitely Connected Regions -- 1 Analysis on a Finitely Connected Region -- 2 Conformal Equivalence with an Analytic Jordan Region -- 3 Boundary Values for a Conformal Equivalence Between Finitely Connected Jordan Regions -- 4 Convergence of Univalent Functions -- 5 Conformal Equivalence with a Circularly Slit Annulus -- 6 Conformal Equivalence with a Circularly Slit Disk -- 7 Conformal Equivalence with a Circular Region -- 16 Analytic Covering Maps -- 1 Results for Abstract Covering Spaces -- 2 Analytic Covering Spaces -- 3 The Modular Function -- 4 Applications of the Modular Function -- 5 The Existence of the Universal Analytic Covering Map -- 17 De Branges?s Proof of the Bieberbach Conjecture -- 1 Subordination -- 2 Loewner Chains -- 3 Loewner?s Differential Equation -- 4 The Milin Conjecture -- 5 Some Special Functions -- 6 The Proof of de Branges?s Theorem -- 18 Some Fundamental Concepts from Analysis -- 1 Bergman Spaces of Analytic and Harmonic Functions -- 2 Partitions of Unity -- 3 Convolution in Euclidean Space -- 4 Distributions -- 5 The Cauchy Transform -- 6 An Application: Rational Approximation -- 7 Fourier Series and Cesŕro Sums -- 19 Harmonic Functions Redux -- 1 Harmonic Functions on the Disk -- 2 Fatou?s Theorem -- 3 Semicontinuous Functions -- 4 Subharmonic Functions -- 5 The Logarithmic Potential -- 6 An Application: Approximation by Harmonic Functions -- 7 The Dirichlet Problem -- 8 Harmonic Majorants -- 9 The Green Function -- 10 Regular Points for the Dirichlet Problem -- 11 The Dirichlet Principle and Sobolev Spaces -- 20 Hardy Spaces on the Disk -- 1 Definitions and Elementary Properties -- 2 The Nevanlinna Class -- 3 Factorization of Functions in the Nevanlinna Class -- 4 The Disk Algebra -- 5 The Invariant Subspaces of Hp -- 6 Szegö?s Theorem -- 21 Potential Theory in the Plane -- 1 Harmonic Measure -- 2 The Sweep of a Measure -- 3 The Robin Constant -- 4 The Green Potential -- 5 Polar Sets -- 6 More on Regular Points -- 7 Logarithmic Capacity: Part 1 -- 8 Some Applications and Examples of Logarithmic Capacity -- 9 Removable Singularities for Functions in the Bergman Space -- 10 Logarithmic Capacity: Part 2 -- 11 The Transfinite Diameter and Logarithmic Capacity -- 12 The Refinement of a Subharmonic Function -- 13 The Fine Topology -- 14 Wiener?s criterion for Regular Points -- References -- List of Symbols. 330 $aThis is the sequel to my book Functions of One Complex Variable I, and probably a good opportunity to express my appreciation to the mathemat­ ical community for its reception of that work. In retrospect, writing that book was a crazy venture. As a graduate student I had had one of the worst learning experiences of my career when I took complex analysis; a truly bad teacher. As a non-tenured assistant professor, the department allowed me to teach the graduate course in complex analysis. They thought I knew the material; I wanted to learn it. I adopted a standard text and shortly after beginning to prepare my lectures I became dissatisfied. All the books in print had virtues; but I was educated as a modern analyst, not a classical one, and they failed to satisfy me. This set a pattern for me in learning new mathematics after I had become a mathematician. Some topics I found satisfactorily treated in some sources; some I read in many books and then recast in my own style. There is also the matter of philosophy and point of view. Going from a certain mathematical vantage point to another is thought by many as being independent of the path; certainly true if your only objective is getting there. 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