Complex Analysis with Applications in Science and by Harold Cohen

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By Harold Cohen

Complex research with functions in technology and Engineering weaves jointly concept and wide applications in arithmetic, physics and engineering. during this version there are lots of new difficulties, revised sections, and a completely new bankruptcy on analytic continuation. This paintings will function a textbook for undergraduate and graduate scholars within the components famous above.

Key gains of this moment Edition:

Excellent insurance of issues reminiscent of sequence, residues and the overview of integrals, multivalued features, conformal mapping, dispersion kinfolk and analytic continuation

Systematic and transparent presentation with many diagrams to explain dialogue of the material

Numerous labored examples and a good number of assigned problems

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Additional resources for Complex Analysis with Applications in Science and Engineering

Sample text

3a) When we set ∆x = 0 first, then take the limit ∆y → 0, as indicated in the third line of eq. 4 is referred to as the Cauchy–Riemann (abbreviated CR) condition expressed in terms of F(x, y). It is also convenient to express this CR condition in terms of the real and imaginary parts of F(z). 1 Derivatives, Cauchy–Riemann Conditions, and Analyticity 39 Substituting this into eq. 6) From the equality of the real and imaginary parts of eq. 7b) and These are the CR conditions expressed in terms of the real and imaginary parts of F(z).

92b) Chapter 2 Complex Numbers 30 Problems 1. Let z = 3 + 2i . Construct an Argand diagram of each of the following complex numbers. (a) - z (b) 2 z (d) - z * (c) iz (e) z 2 ( ) 2 (f) - z * (g) zz * 2. Prove that (a) arg( z1 z2 ) = arg( z1 ) + arg( z2 ) (b) arg( z1 z2 ) = arg( z1 ) - arg( z2 ) Determine (c) arg( z1 z2* ) (d) arg( z1* z2 ) (e) arg( z1* z2* ) in terms of arg(z1) and arg(z2). 3. Express each of the following complex numbers in its Cartesian, trigonometric, and polar representations.

It is also convenient to express this CR condition in terms of the real and imaginary parts of F(z). 1 Derivatives, Cauchy–Riemann Conditions, and Analyticity 39 Substituting this into eq. 6) From the equality of the real and imaginary parts of eq. 7b) and These are the CR conditions expressed in terms of the real and imaginary parts of F(z). Both of these equations must be satisfied in a region R containing z in order for dF/dz to be defined at the point z. If either one of these conditions is not satisfied, then dF/dz is not defined at z.

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