Introduction to Complex Variables and Applications |
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Page 199
... sheet Ro to the sheet R1 , where 0 grows from 2 to 4π . As the point moves still farther , it passes back to the sheet Ro where the values of 0 vary either from 4 to 6π or from zero to 2π , a choice that does not effect the value of the ...
... sheet Ro to the sheet R1 , where 0 grows from 2 to 4π . As the point moves still farther , it passes back to the sheet Ro where the values of 0 vary either from 4 to 6π or from zero to 2π , a choice that does not effect the value of the ...
Page 200
... sheets of the continuous surface so formed cross each other along the segment L , so that a point can move continuously from one sheet to the other by crossing that segment , and only in that way . Let the sheet Ro be the one on which ...
... sheets of the continuous surface so formed cross each other along the segment L , so that a point can move continuously from one sheet to the other by crossing that segment , and only in that way . Let the sheet Ro be the one on which ...
Page 201
... sheet Ro we specify that each of the three angles 0 , 41 , and 42 may range from zero to 2π , and on R1 from 2 to 4π ; but we add the specifica- tion that the angles corresponding to a point on either sheet may be increased or ...
... sheet Ro we specify that each of the three angles 0 , 41 , and 42 may range from zero to 2π , and on R1 from 2 to 4π ; but we add the specifica- tion that the angles corresponding to a point on either sheet may be increased or ...
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Common terms and phrases
absolute value According to equation analytic continuation analytic function angle Appendix approaches zero arctan boundary branch cut C₁ C₂ Cauchy-Goursat theorem Cauchy-Riemann conditions Cauchy's integral formula closed curve coefficients complex number complex potential complex variable conformal mapping conjugate continuous function corresponding cosh defined definition denote example EXERCISES exists Find finite number flow fluid follows formula function f(z function is analytic half plane harmonic function Hence inequality infinite integrand interior inverse Laurent series limit line integral linear fractional transformation Maclaurin series maps MICHIGAN neighborhood partial derivatives path pole polygon positive number power series quadrant R₁ real axis real numbers represents residue Riemann surface satisfied single-valued and analytic single-valued function sinh steady temperatures strip tends to infinity unit circle upper half vanishes vector velocity w₁ write xy plane z₁ πί ди дх მყ