Complex Analysis and Differential Equations

✍ Scribed by Luis Barreira, Claudia Valls (auth.)

• Publisher: Springer-Verlag London
• Year: 2012
• Tongue: English
• Leaves: 425
• Series: Springer Undergraduate Mathematics Series
• Edition: 1
• Category: Library

✦ Synopsis

This 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.

The 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.

Tailored 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.

✦ Table of Contents

Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Basic Notions....Pages 3-35
Holomorphic Functions....Pages 37-108
Sequences and Series....Pages 109-148
Analytic Functions....Pages 149-220
Front Matter....Pages 221-221
Ordinary Differential Equations....Pages 223-279
Solving Differential Equations....Pages 281-332
Fourier Series....Pages 333-372
Partial Differential Equations....Pages 373-411
Back Matter....Pages 413-415

✦ Subjects

Fourier Analysis; Functions of a Complex Variable; Ordinary Differential Equations; Partial Differential Equations; Sequences, Series, Summability