Part 1 Complex Analysis.- Basic Notions.- Holomorphic Functions.- Sequences and Series.- Analytic Functions.- Part 2 Differential Equations.- Ordinary Differential Equations.- Solving Differential Equations.- Fourier Series.- Partial Differential Equations¿.
pThis text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. /ppThe text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty./ppTailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study./p
Emphasis is given to the applications of complex analysis to differential equations
Provides a rigorous approach with the right balance between theory and practice
Includes approximately 200 examples and 200 problems with detailed solutions