"From one of its keenest observers, a brilliant, witty journey through the "special relationship" between England and America which has done so much to shape the world, from World War 2 to Brexit, through the lens of the fateful bonds between President and Prime Minister"--

This text, and accompanying disk, provides coverage of complex variables. It uses examples and exercise sets, with clear explanations of problem-solving techniqes and material on the further theory of functions.

“Stimulating and highly readable. . . . The Churchill Complex is a rich and rewarding book.” —Wall Street Journal From one of its keenest observers, a brilliant, witty journey through the "Special Relationship" between Britain and America that has done so much to shape the world, from World War II to Brexit. It is impossible to understand the last seventy-five years of American history, through to Trump and Brexit, without understanding the Anglo-American relationship, particularly the bonds between presidents and prime ministers. FDR of course had Winston Churchill; JFK had Harold Macmillan, his consigliere during the Cuban Missile Crisis. Ronald Reagan found his ideological soul mate in Margaret Thatcher; and George W. Bush found his fellow believer, in religion and in war, in Tony Blair. Today, the bond between Donald Trump and Boris Johnson illuminates the populist uprisings in both countries, as well as a new kind of Special Relationship that goes against everything it once stood for. Remembering the past, even its most glorious moments, can be as misleading as forgetting it. Over and over, in the name of freedom and democracy, British and especially American leaders have evoked Winston Churchill as a model for brave leadership (and Nevillle Chamberlain to represent craven weakness). As Ian Buruma shows, in his dazzling, short tour de force of storytelling and analysis, the myths of World War II too often resulted in bad policies and foolish wars. But The Churchill Complex is much more than a reflection on the weight of Churchill's legacy and its misuses. At its heart are shrewd and absorbing character studies of the president-prime minster dyads, which in Ian Buruma's gifted hands serve as a master class in politics, diplomacy, and the personal quirks of our leaders. It has never been a relationship of equals: from Churchill's desperate cajoling and conniving to keep FDR on his side in World War II, British prime ministers have put much more stock in the relationship than their US counterparts. After the loss of its once-great empire, Britain clung to the world's greatest superpower as a path to continued relevance and leverage. As Buruma shows, this was almost always fool's gold, and now, the alliance has floundered on the rocks of isolationism. The Churchill Complex may not have a happy ending, but as with Ian Buruma's other works, piercing lucidity is its own lasting comfort.

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"The story of Winston Churchill's lifelong engagement with Ireland and the irish, now told for the first time. A long overdue book which at last addresses the most neglected part of Churchill's legacy on both sides of the Irish Sea." --back cover.

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recom mend to anyone to look through them. More recent texts have empha sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts.