- The student is familiar with the concept of holomorphic function.
- The student is familiar with the Cauchy Integral Theorem and the Cauchy integral formulas.
- The student is familiar with the concept of Taylor series and Laurent series for holomorphic functions.
- The student is able to apply the theory to concrete examples, in particular, to computing integrals using the Residue Theorem.
- The student is familiar with the theory of analytic continuation.
- The student is familiar with conformal mappings.
- The student is familiar with general results about the product expansion of entire and meromorphic functions, and is able to apply them to elementary functions.
- The student is familiar with analytic properties of new classes of special mathematical functions, in particular, of the gamma function and hypergeometric function.
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In this course a systematic introduction to complex analysis and the theory of complex-valued functions is performed. The theory studies complex differentiable functions defined on a domain in the complex plane. Contour integrals play an important role, with main results around the Cauchy integral theorem. Numerous applications of the residue sum theorem, analytic continuation, conformal mappings are discussed, and certain particular instances of special functions, including the gamma and hypergeometric functions, are highlighted. This classical subject ought to be viewed as basic in the bachelor program.
Instructional Modes
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| Lineaire Algebra en Calculus; bij voorkeur ook Analyse 2 |
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