المصدر: كتاب : Basic Complex Analysis: Jerrold E. Marsden, Michael J. Hoffman في منتدى : قسم الرياضيات Basic Complex Analysis: Jerrold E. Marsden, Michael J. Hoffman Basic Complex Analysis: Jerrold E. Marsden, Michael J. Hoffman W. H. Freeman | ISBN: 071672877X | 1998-12-15 | PDF (OCR) | 600 pages | 53.7 Mb The book reveals complex analysis as a very elegant and lovely branch of mathematics. The level of rigour is not that of Marsden's other book, Elementary Classical Analysis. Instead, Basic Complex Analysis can be usefully read by non-maths majors, especially those in physics and engineering. Key ideas are well covered. Starting with the Laurant series, which generalises the Taylor series. Then, from this, the idea of contour integration is examined. Giving rise to the Residue Theorem and the winding number. All because the only term that does not integrate to 0 is 1/z, which gives the complex log and its imaginary argument is the only thing left. So simple and powerful. Amazing that an essentially arbitrarily intricate contour integral can be given by the residues at the enclosed poles! Yet the text's derivation should get straightforward to follow for most readers. If you are going onto advanced physics, like quantum electrodynamics, then this theorem is used extensively. The book also covers important subsequent ideas. Especially conformal mapping and the Schwartz-Christoffel transformation. The treatment of conformal mapping, though, is only a hint of the richness of analysis available here. The numerous problems are also good for the student to tackle.
