Section 3.2 The Cauchy-Riemann Equations - Maple Application Center
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Section 3.2 The Cauchy-Riemann Equations

: Dr. John Mathews
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We saw in the last section that computing the derivative of complex functions written in a nice form such as f(z) = z^2; is a rather simple task. But life is not so easy, for many times we encounter complex functions written as f(x+i*y) = u(x,y)+i*v(x,y);. For example, suppose we had f(x+i*y) = x^3-3*x*y^2+i*(3*x^2*y-y^3). Is there some criterion---perhaps involving the partial derivatives for u;, and v; - - that we can use to determine whether f; is differentiable, and if so, to find the value of `f '(z)`;?

Application Details

Publish Date: October 01, 2003
Created In: Maple V
Language: English



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