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Cauchy’s integral theorems and the theory of holomorphic functions including the homological version of the residue theorem are derived as an application of the theory of line integrals
In addition to the calculation of important definite integrals which appear in Mathematics and in Physics, theoretic properties of the Gamma function and Riemann’s Zeta function are explored
Numerous examples with varying degrees of difficulty and many informative figures
Continues the modern and clear development that started in Volume I
The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and clear development that started in Volume I is continued. In this way a sustainable basis will be created which allows the reader to deal with interesting applications that sometimes go considerably beyond the material that is represented in traditional textbooks. This applies, for instance, to the exploration of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations.
The book contains numerous examples with varying degrees of difficulty and many informative figures.
This volume will interest advanced undergraduate and graduate students, advisors and teachers.
Content Level »Lower undergraduate
Keywords »Calculation - Complex analysis - Derivation - Derivative - Fourier series - Manifold - Meromorphic function - Real analysis - Variable - calculus - differential equation - equation - function - gamma function