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MDU Mathematics -III - Sem III
Section B : Functions of Complex Variable(Definition, Exponential function, Trigonometric and Hyperbolic functions, Logrithmic functions Limit and Continuity of a function, Differentiability and Analyticity Cauchy-Riemann equations, necessary and sufficient conditions for a function to be analytic, polar form of the Cauchy-Riemann equations Harmonic functions, application to flow problems Integration of complex functions Cauchy- Integral theorem and formula)
1. Complex Analysis-I(Mathematics IV) Total View (504)
 
In this and the next chapter we present an elementary treatment of the subject of Complex Analysis. In this chapter, we introduce the concept of a complex function and study some properties of an important class of complex functions, called analytic functions.
Title: Engineering Mathematics Part - IV
Published on: 14/07/14
Author: Chandrasekharaiah D S (DSC)
Publisher: Prism Books Pvt Ltd
Pages: 56
Price: Rs 42

2. Functions of a Complex Variable-I Differentiation(Engineering Mathematics - IV ) Total View (361)
 
Introduction, Review of Relevant Elementary Results, Functions, Limits and Continuity, Analytic Functions, Properties of Analytic Functions, Conformal Mapping
Title: Engineering Mathematics - IV
Published on: 07/06/14
Author: Chandra Mohan M
Publisher: Sanguine Technical Publishers
Pages: 88
Price: Rs 66

3. Analytic Functions, Cauchy-Riemann Equations, Harmonic Functions, Rational Functions(Mathematics) Total View (735)
 
The objective of this unit to show that a function of a complex variable can have a derivative only if the real and imaginary parts satisfy a system of a partial differential equations called the Cauchy-Riemann equations. Further study of the Cauchy-Riemann equations shows a connect ion between complex analysis and harmonic functions.
Title: Math 1.3 Complex Analysis - I
Published on: 07/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 21
Price: Rs 15.75

4. Chapter 3 * Analytic Functions(Mathematics II) Total View (3)
 
Analytic functions - Necessary and sufficient conditions for analyticity in Cartesian and polar coordinates - Properties - Harmonic conjugates - Construction of analytic function - Conformal mapping - Mapping by functions w = z+c, cz, 1/z, z2- Bilinear transformation.
Title: Engineering Mathematics II
Published on: 09/02/19
Author:
Publisher:
Pages: 78
Price: Rs 39

5. Chapter 2 * Analytic Functions(Mathematics) Total View (4)
 
A single valued function f (z) is said to be analytic at a point z0, is it is differentiable at every point in some neighbourhood of z0. Analytic functions are also referred as regular or holomorphic functions.
Title: Vector Calculus and Complex Analysis
Published on: 24/01/20
Author:
Publisher:
Pages: 78
Price: Rs 39

6. Contents(Mathematics II) Total View (26)
 
This comprehensive and assimilable text introduces to the students the Mathematical concepts such as Matrices, Vector Calculus, Analytic Functions, Complex Integration and Laplace Transforms. The simple and systematic presentation will enable the students to grasp the concepts easily.
Title: Engineering Mathematics II
Published on: 09/02/19
Author:
Publisher:
Pages: 10
Price: Rs 0

7. Contents(Mathematics) Total View (14)
 
Mathematics is the queen of all sciences. It is a tool that is used by engineers for expression of ideas and for communication of results. Mathematics plays a major role in Engineering as it is one of the major factors that determine how far engineers advance in their career. This book titled “Vector Calculus and Complex Analysis” written by Dr. P. Anuradha and Mr. V. Sudhakar is a good ......
Title: Vector Calculus and Complex Analysis
Published on: 24/01/20
Author:
Publisher:
Pages: 8
Price: Rs 0

8. Chapter 1 * Functions of a Complex Variable(Mathematics) Total View (0)
 
Introduction, Continuity, Differentiability, Analyticity, properties, Cauchy, Riemann equations in Cartesian and polar coordinates. Harmonic and conjugate harmonic functions-Milne-Thompson method
Title: Mathematics IV
Published on: 27/03/20
Author:
Publisher:
Pages: 50
Price: Rs 25

9. Contents(Mathematics) Total View (0)
 
This book on Mathematics - IV covers the syllabus for the 2nd year 1st Semester course of B.E / B.Tech programmes offered by various major universities and autonomous colleges. It covers the following topics Functions of a Complex Variable, Complex Integration, Evaluation of Integrals, Fourier Series and Transforms and Applications of PDE.
Title: Mathematics IV
Published on: 27/03/20
Author:
Publisher:
Pages: 10
Price: Rs 0

10. Contents(Mathematics) Total View (16)
 
This book on Engineering Mathematics - I covers the syllabus for the 1st Semester course of B.E / B.Tech programmes offered by various major universities and autonomous colleges. It covers the following topics Differential Calculus, Functions of Several Variables, Integral Calculus, Multiple Integrals and Differential Equations.
Title: Engineering Mathematics I
Published on: 26/03/20
Author:
Publisher:
Pages: 10
Price: Rs 0

11. Cauchy's Integral Formula and its Consequences(Mathematics) Total View (739)
 
In this unit, we establish another fundamental result known as Cauchy's integral formula using Cauchy's theorem. As application of Cauchy's integral formula. we also deduce Morera's theorem, Liouville's theorem and Fundamental theorem of Algebra.
Title: Math 1.3 Complex Analysis - I
Published on: 07/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 13
Price: Rs 9.75

12. The Exponential, Logarithmic and Trigonomotric Functions.(Mathematics) Total View (738)
 
The person who approaches calculus exclusively from the point of view of real numbers will not expect any relationship between the exponential function and the trignometric functions cos x and sin x. Indeed, these functions seem to be derived from completely different sources and with different purposes in mind.
Title: Math 1.3 Complex Analysis - I
Published on: 07/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 10
Price: Rs 7.5

13. Complex Trigonometry, Differential Calculus, Integral Calculus, Vector Differentiation, Ordinary Differential Equations(Advanced Mathematics I) Total View (50)
 
Complex Trigonometry, Differential Calculus, Integral Calculus, Vector Differentiation, Ordinary Differential Equation.
Title: Additional Mathematics-I
Published on: 16/12/16
Author: Prasad Lal
Publisher: Sanguine Technical Publishers
Pages: 466
Price: Rs 233

14. Cauchy's Theorem for a Rectangle and a Disc(Mathematics) Total View (739)
 
There are several forms of Cauchy's theorem, but they differ in t heir topological rather than in their analytical content. It is natural to begin with a case in which the topological considerations are trivial. In this unit we determine Cauchy theorem for a rectangle and Cauchy' s theorem for a disc.
Title: Math 1.3 Complex Analysis - I
Published on: 07/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 10
Price: Rs 7.5

15. Local Properties of Analytical Functions(Mathematics) Total View (741)
 
This unit is devoted to a consideration of functions which are analytic at all points in a bounded domain except at a finite number of points. Such exceptional points are known as singular points. In this content, the first portion will naturally consists of classification of singular points in terms of the behavior of the function in their neighborhood.
Title: Math 1.3 Complex Analysis - I
Published on: 07/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 9
Price: Rs 6.75

16. Functions of a Complex Variable-II lntegration(Engineering Mathematics - IV ) Total View (358)
 
Complex Line Integral, Cauchy's Theorem (Cauchy's Integral Theorem), Cauchy's Integral Formula, Power Series, Zeros, Singularities and Residues
Title: Engineering Mathematics - IV
Published on: 28/10/14
Author: Chandra Mohan M
Publisher: Sanguine Technical Publishers
Pages: 65
Price: Rs 48.75

17. Cauchy Problem(Mathematics) Total View (760)
 
In this unit, the reader studies about the Cauchy problem, principle of superposition. They also study the method of characteristics to solve semi-linear, quasilinear and non-linear PDEs.
Title: Math 1.5 Differential Equations
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 14
Price: Rs 10.5

18. Line Integrals, Rectifiable Arcs(Mathematics) Total View (739)
 
The integration of a function of a complex variable is carried out over a curve and leads to results of great importance in pure and applied mathematics. In this unit, we discuss first complex valued functions then curves and finally integration over curves.
Title: Math 1.3 Complex Analysis - I
Published on: 07/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 11
Price: Rs 8.25

19. Contents(Mathematics) Total View (5)
 
This book on Matrices and Calculus covers the syllabus for the 1st Semester course of B.E / B.Tech programmes offered by various Universities and Engineering Colleges (Autonomous). It covers the following topics: Matrices, Functions of Several Variables, Applications of Differential Calculus, Applications of Integral Calculus, and Ordinary Differential Equations.
Title: Matrices and Calculus
Published on: 09/01/20
Author:
Publisher:
Pages: 10
Price: Rs 0

20. Hadamard's Theorem(Mathematics) Total View (428)
 
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.
Title: Math 2.3 Complex Analysis - II
Published on: 28/10/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 10
Price: Rs 7.5

21. Chapter 4 * Complex Integration(Mathematics II) Total View (0)
 
Line integral - Cauchy's integral theorem - Cauchy's integral formula - Taylor's and Laurent's series - Singularities - Residues - Residue theorem - Application of residue theorem for evaluation of real integrals - Use of circular contour and semicircular contour.
Title: Engineering Mathematics II
Published on: 09/02/19
Author:
Publisher:
Pages: 110
Price: Rs 55

22. Jensen's Formula(Mathematics) Total View (425)
 
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.
Title: Math 2.3 Complex Analysis - II
Published on: 28/10/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 5
Price: Rs 3.75

23. Difference Equations and Generating Functions(Mathematics) Total View (738)
 
After going through this unit we can define and construct generating functions for sequences arising in various types of combination problems. Also we use generating functions to find the number of integer solution to linear equations. We solve recurrence relation using generating functions.
Title: Math 1.4 Discrete Mathematics
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 16
Price: Rs 12

24. Integral Test and Kummer's Test(Mathematics) Total View (738)
 
In this unit we shall discuss Cauchy-Maclaurin's integral test and Cauchy's condensation test. Further Kummer's test and its consequences will also be discussed.
Title: Math 1.2 Real Analysis - I
Published on: 28/10/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 12
Price: Rs 9

25. Chapter 1 * Differential Calculus(Mathematics) Total View (0)
 
Representation of functions - Limit of a function - Continuity - Derivatives - Differentiation rules - Maxima and Minima of functions of one variable.
Title: Engineering Mathematics I
Published on: 26/03/20
Author:
Publisher:
Pages: 136
Price: Rs 68



 
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