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Title      : Math 2.3 Complex Analysis - II
Subject      : Mathematics
copyright ©  2018     : Karnataka State Open University
Author      : KSOU
Publisher      : Karnataka State Open University
Chapters/Pages      : 12/143
Total Price      : Rs.      : 99
 
 
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Chapters
     
The Residue Theorem, the Argument Principle Total views (954)  
This unit deals with Residue Theorem, Argument Theorem and Rouche's Theorem and related problems.
Pages: 14
Price: Rs 0   
 
The Calculus of Residues and Harmonic Functions Total views (949)  
The residue theorem in complex analysis has a vast application in particular for evaluating the integrals including many integrals from the ordinary calculus. This unit demonstrates this application with a series of examples.
Pages: 22
Price: Rs 16.5   
 
Definition and Basic Properties of Harmonic Functions Total views (958)  
Harmonic functions are tremendously important for the role they play in physics and engineering where they turn out naturally in a variety of context including electronics fluid dynamics and heat transfer. This unit deals with harmonic functions and mean value property for harmonic functions.
Pages: 12
Price: Rs 9   
 
Poisson's Formula, Schwarz's Theorem, the reflection principle Total views (971)  
This unit describes theorems on harmonic functions such as Poisson's integral formula, Schwarz's theorem, Hermite's inequality, Reflection principle.
Pages: 10
Price: Rs 7.5   
 
The Weierstrass Theorem, the Taylor Series Total views (426)  
Sequence and series representation of a fun ct ion play very important role in many branches of Mathematics. In this unit, we discuss how an analytic function in an open disk can be represented as a Taylor series.
Pages: 15
Price: Rs 11.25   
 
The Laurent Series, Partial Fractions,Mittag-Leffler's Theorem Total views (424)  
In this unit, we discuss the infinite product and their relations with infinite series. Further, we study Weierstrass Factorization theorem which deals with representation of meromorphic function as an infinite product. We also study canonical product.
Pages: 14
Price: Rs 10.5   
 
Infinite Products,Canonical Products Total views (424)  
In this unit, we discuss the infinite product and their relations with infinite series. Further, we study Weierstrass factorization theorem which deals with representation of meromorphic function as an infinite product. We also study Canonical product.
Pages: 12
Price: Rs 9   
 
The Gamma and Beta Functions, Sterling's Formula Total views (423)  
The function s such as polynomials, exponential functions, trigonometric functions, inverse trigonometric functions, hyperbolic functions, inverse hyperbolic functions and logarithmic functions are called elementary functions. The functions which can be expressed as the combinations of elementary functions are also called as elementary functions. The functions which cannot be expressed as element ......
Pages: 15
Price: Rs 11.25   
 
Jensen's Formula Total views (424)  
Jensen's formula relates the modulus of f(z) on the circle to the modulus of the zeroes. It has many important applications in the theory of entire functions.
Pages: 5
Price: Rs 3.75   
 
Hadamard's Theorem Total views (425)  
In the previous blocks, we have considered the representation of entire functions as infinite products. In this unit we study the connection between product representation and the rate of growth of the function.
Pages: 10
Price: Rs 7.5   
 
Definition and the Properties of the Riemann-Zeta Function Total views (425)  
Riemann-zeta function was defined by Riemann in 1859 and he established a relation between its zeros and the distribution of prime numbers in his famous paper entitled 'On the number of primes less than given magnitude'. The values of Riemann zeta function at even positive integers were completed by Euler.
Pages: 4
Price: Rs 3   
 
Extension of Zeta-Function to the Whole Plane, the Functional Equation, the Zeros of the Zeta-function Total views (426)  
In his paper entitled ' On number of primes less than the given magnitude', Riemann deduced certain functional equations satisfied by Riemann-zeta functions which involves Gamma function. He also relates Riemann-zeta function with Dedekind eta functions. In this unit, we study these types of functional relations.
Pages: 10
Price: Rs 7.5   
 


 
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