05312oam 22005293 450 991079581600332120220831094644.09781118705278(electronic bk.)9781118705223(MiAaPQ)EBC1895551(Au-PeEL)EBL1895551(CaPaEBR)ebr11078102(CaONFJC)MIL785546(OCoLC)890377891(EXLCZ)991769304720004120220831d2015 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierComplex Analysis A Modern First Course in Function Theory1st ed.New York :John Wiley & Sons, Incorporated,2015.©2015.1 online resource (277 pages)Print version: Muir, Jerry R. Complex Analysis New York : John Wiley & Sons, Incorporated,c2015 9781118705223 Intro -- Title Page -- Copyright -- Table of Contents -- Dedication -- Preface -- Chapter 1: The Complex Numbers -- 1.1 Why? -- 1.2 The Algebra of Complex Numbers -- 1.3 The Geometry of the Complex Plane -- 1.4 The Topology of the Complex Plane -- 1.5 The Extended Complex Plane -- 1.6 Complex Sequences -- 1.7 Complex Series -- Chapter 2: Complex Functions and Mappings -- 2.1 Continuous Functions -- 2.2 Uniform Convergence -- 2.3 Power Series -- 2.4 Elementary Functions and Euler's Formula -- 2.5 Continuous Functions as Mappings -- 2.6 Linear Fractional Transformations -- 2.7 Derivatives -- 2.8 The Calculus of Real-Variable Functions -- 2.9 Contour Integrals -- Chapter 3: Analytic Functions -- 3.1 The Principle of Analyticity -- 3.2 Differentiable Functions are Analytic -- 3.3 Consequences of Goursat's Theorem -- 3.4 The Zeros of Analytic Functions -- 3.5 The Open Mapping Theorem and Maximum Principle -- 3.6 The Cauchy-Riemann Equations -- 3.7 Conformal Mapping and Local Univalence -- Chapter 4: Cauchy's Integral Theory -- 4.1 The Index of a Closed Contour -- 4.2 The Cauchy Integral Formula -- 4.3 Cauchy's Theorem -- Chapter 5: The Residue Theorem -- 5.1 Laurent Series -- 5.2 Classification of Singularities -- 5.3 Residues -- 5.4 Evaluation of Real Integrals -- 5.5 The Laplace Transform -- Chapter 6: Harmonic Functions and Fourier Series -- 6.1 Harmonic Functions -- 6.2 The Poisson Integral Formula -- 6.3 Further Connections to Analytic Functions -- 6.4 Fourier Series -- Epilogue -- Local Uniform Convergence -- Harnack's Theorem -- Results for Simply Connected Domains -- The Riemann Mapping Theorem -- Appendix A: Sets and Functions -- Sets and Elements -- Functions -- Appendix B: Topics from Advanced Calculus -- The Supremum and Infimum -- Uniform Continuity -- The Cauchy Product -- Leibniz's Rule -- References -- Index.End User License Agreement.A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing thebeautiful subject of complex analysis.Geometric function theoryGeometryNumbers, ComplexElectronic books.Geometric function theory.Geometry.Numbers, Complex.515Muir Jerry R1541537Muir Jerry R., Jr1541538MiAaPQMiAaPQMiAaPQ9910795816003321Complex Analysis3793791UNINA03817nam 2200529 450 991080616210332120230617033751.00-19-977490-0(CKB)2550000001204603(StDuBDS)AH24087948(MiAaPQ)EBC5746866(MiAaPQ)EBC728680(Au-PeEL)EBL728680(OCoLC)958583174(EXLCZ)99255000000120460320190704d2005 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierLiberty and freedom /David Hackett FischerOxford ;New York :Oxford University Press,[2005]©20051 online resource (851 pages) illustrationsAmerica, a cultural history ;30-19-516253-6 Includes bibliographical references (pages 739-818) and index.Liberty and freedom: Americans agree that these values are fundamental to our nation, but what do they mean? How have their meanings changed through time? In this new volume of cultural history, David Hackett Fischer shows how these varying ideas form an intertwined strand that runs through the core of American life. Fischer examines liberty and freedom not as philosophical or political abstractions, but as folkways and popular beliefs deeply embedded in American culture. Tocqueville called them "habits of the heart." From the earliest colonies, Americans have shared ideals of liberty and freedom, but with very different meanings. Like DNA these ideas have transformed and recombined in each generation. The book arose from Fischer's discovery that the words themselves had differing origins: the Latinate "liberty" implied separation and independence. The root meaning of "freedom" (akin to "friend") connoted attachment: the rights of belonging in a community of freepeople. The tension between the two senses has been a source of conflict and creativity throughout American history. Liberty & Freedom studies the folk history of those ideas through more than 400 visions, images, and symbols. It begins with the American Revolution, and explores the meaning of New England's Liberty Tree, Pennsylvania's Liberty Bells, Carolina's Liberty Crescent, and "Don't Tread on Me" rattlesnakes. In the new republic, the search for a common American symbol gave new meaning to Yankee Doodle, Uncle Sam, Miss Liberty, and many other icons. In the Civil War, Americans divided over liberty and freedom. Afterward, new universal visions were invented by people who had formerly been excluded from a free society--African Americans, American Indians, and immigrants. The twentieth century saw liberty and freedom tested by enemies and contested at home, yet it brought the greatestoutpouring of new visions, from Franklin Roosevelt's Four Freedoms to Martin Luther King's "dream" to Janis Joplin's "nothin' left to lose." Illustrated in full color with a rich variety of images, Liberty and Freedom is, literally, an eye-opening work of history--stimulating, large-spirited, and ultimately, inspiring.America: a cultural history, Volume IIINational characteristics, AmericanLibertyHistoryUnited StatesHistoryUnited StatesPolitics and governmentUnited StatesHistoryPictorial worksNational characteristics, American.LibertyHistory.323.44/0973Fischer David Hackett1935-889326MiAaPQMiAaPQMiAaPQBOOK9910806162103321Liberty and freedom4038268UNINA