A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject
Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem.
Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features:
- Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects
- Numerous figures to illustrate geometric concepts and constructions used in proofs
- Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes
- Appendices on the basics of sets and functions and a handful of useful results from advanced calculus
Mathematics, mathematical analysis, complex analysis, complex numbers, analytic functions, conformal mapping, linear fractional transformations, Cauchy&rsquo, s integral formula, Cauchy's theorem, residue theorem, harmonic functions, Fourier series, Riemann mapping theorem