MA8251 Notes Engineering Mathematics 2 Unit 3

MA8251 Notes Engineering Mathematics 2 Unit 3 ANALYTIC FUNCTIONS Regulation 2017 For Anna University Free download. ENGINEERING MATHEMATICS 2 MA8251 Unit 3 ANALYTIC FUNCTIONS Notes Pdf Free download.

Content Engineering Mathematics 2 ma8251 Unit 3 ANALYTIC FUNCTIONS

ANALYTIC FUNCTIONS

1. Introduction –Function of A Complex Variable

1.1 Function of Complex Variable Many complicated integrals of real functions are solved with the help of complex variable. They are very useful in solving large number of engineering and science problems

1.2 Complex Variable:

1.3 Function of Complex Variable:

z=x+ i y and w=u+ iv are two complex variable. If for each value of z in a given region R of the complex plane there corresponds one or more values of w, then w is called a function of z and it is denoted by w=f(z)=u(x, y)+iv(x, y)where u(x, y) ,v(x ,y) are real functions of the real variable x and y. (ma8251 notes engineering mathematics 2 unit 3)

1.4 Single Valued Function

If for each value of z in R, there is correspondingly only one value of w, the w is called a single valued function of z.

2. Analytic Functions(C-R Equations)

2.1 Limit of The Function:

2.2 Continuity:

3. Harmonic and Orthogonal Properties Of Analytic Functions

3.1 Laplace Equation: (ma8251 notes engineering mathematics 2 unit 3)

3.2 Properties Of Analytic Functions And Harmonic Conjugate

3.3 Problems Based On Harmonic Conjugate

4. Construction of Analytic Functions

5. Conformal Mapping

5.1 Definition:

The transformation w=f(z) is called as conformal mapping if it preserves angle between every pair of curves through a point, both in magnitude and sense The transformation w=f(z) is called as Isogonal mapping if it preserves angle between every pair of curves through a point in magnitude but altered in sense (ma8251 notes engineering mathematics 2 unit 3)

5.2 Standard Transformations

5.3 Problems Based on Transformation

6. Bilinear Transformation (ma8251 notes engineering mathematics 2 unit 3)

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