Akademik Dersler - İçerik

Comprehend complex integrals and their properties.
Defines integrals along parametric curves and over contours.
Expresses Cauchy–Goursat and Cauchy integral theorems.
Calculates higher-order derivatives using Cauchy derivative formulas.
Express fundamental properties of analytic functions.
Explains Morera’s Theorem.
Expresses the Maximum Modulus Theorem.
Explains Liouville’s Theorem and the Fundamental Theorem of Algebra.
Explain the concepts of sequences and series of complex functions.
Expresses the concept of convergence in sequences and series of complex functions.
Defines uniform and absolute convergence.
Applies the Cauchy criterion and the Weierstrass test.
Calculates power series and their radius of convergence.
Define the concepts of Taylor and Laurent series.
Finds Taylor series expansions of functions.
Defines Laurent series and classifies singular points.
Comprehend the zeros, poles, and the residue concept of a complex function.
Classifies singular points.
Explains the Residue Theorem.
Perform applications of the Residue Theorem.
Calculates complex integrals using the Residue Theorem.
Calculates real integrals using the Residue Theorem.
Expresses the logarithmic derivative and Rouche’s Theorem.