Complex VariablesComplex numbers; Point sets in the complex plane; Infinite series tests for convergence; Functions of a complex variable; Elementary functions; Straight line and circle; Integration. |
Contents
Point Sets in the Complex Plane Sequences Limits | 30 |
Infinite Series Tests for Convergence | 51 |
Functions of a Complex Variable | 78 |
Copyright | |
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Common terms and phrases
a+ib absolutely convergent angle approaches infinity approaches zero bilinear transformation Cauchy Cauchy sequence Cauchy-Riemann equations Cauchy's theorem circle with centre complex numbers complex plane consider constant cosh curve deduce defined definition denote Determine df/dz differentiable divergent domain easily evaluate example Exercise exists expression finite formula function ƒ ƒ is regular geometrical given gives Hence imaginary axis infinite number integral round interior interval limit point mapping method modulus multiplication neighbourhood non-zero number of points obtain origin p-numbers power series principal amplitude proof Prove r₁ radius of convergence rational real axis real line real numbers real variable regular function representing residue result S₁ semicircle sequence Show simple pole singularities sinh straight line triangle u+iv unit circle upper half-plane values write x+iy y)+iv(x z-plane z-zo z₁