{"product_id":"9783032139955-lectures-on-complex-analysis","title":"Lectures on Complex Analysis","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003ean introduction to the theory of ordinary differential equations in the complex domain, culminating in a proof of the Cauchy–Kovalevskaya theorem;\u003cbr\u003e\u003cp\u003eThis elegant textbook offers a comprehensive course on one-dimensional complex analysis. It includes many topics that, in this scope, are not covered in most other textbooks, such as a detailed investigation of the Schwarzian derivative and its associated differential equation, with applications to conformal mappings of circular polygons; various proofs of the uniformisation theorem for planar domains; an introduction to the theory of ordinary differential equations in the complex domain, culminating in a proof of the Cauchy–Kovalevskaya theorem; an introduction to the theory of normal families, including Zalcman's lemma; a proof of the Paley–Wiener theorem; a complete discussion of the Laguerre–Pólya class; solution of the Dirichlet problem, with special emphasis on harmonic measure and Green's function, and applications to conformal mappings of multiply connected domains; a detailed description of the dynamics of polynomials; and the consistent use of the theory of proper mappings whenever possible.\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":58095094432118,"sku":"9783032139955","price":62.66,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_41642967_45a956b6-bb26-45eb-8e63-560e09d3523f.jpg?v=1781773858","url":"https:\/\/www.rarewaves.com\/products\/9783032139955-lectures-on-complex-analysis","provider":"Rarewaves.com","version":"1.0","type":"link"}