Complex Variables by Francis J Flanigan, , available at Book Depository with free delivery worldwide. A caution to mathematics professors: Complex Variables does not or first-year graduate course is covered, discussion Flanigan, Francis J. Buy Complex Variables (Dover Books on Mathematics) on ✓ FREE Not so here — Dr. Flanigan treats this most important field of contemporary.
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Complex Variables does not follow conventional outlines of course material.
complex variables flanigan One reviewer noting its complex variables flanigan wrote: Derivatives of functions of a complex variable, analytic functions, Cauchy-Riemann equations, conjugate harmonic functions, power series, elementary analytic functions, exponential and trigonometric functions, complex logarithm, general complex power function, branches of multi-valued functions.
Line integrals along curves in the complex plane, Cauchy's theorem, Cauchy's integral formula, derivatives of analytic functions, Morera's theorem, Liouville's theorem on bounded analytic functions, fundamental theorem of algebra, maximum modulus theorem.
Taylor series of a function analytic in a circle, uniqueness theorem, Laurent series of a function analytic in an annulus, uniform convergence, integration of uniformly-convergent series, multiplication and division of power series, isolated singular points of analytic functions, poles complex variables flanigan residues, essential singularities.
Evaluation of Definite Integrals Using Residues: Improper integrals of rational functions, rational complex variables flanigan times a trigonometric function, Jordan's lemma, rational expressions of trigonomeric functions, integrals with indentations, Cauchy principal value, integrands containing general powers, keyhole contours.
Partial Fraction and Infinite Product Expansions: Meromorphic functions, partial fraction expansion via residue theory, expansion of the tangent and cotangent, entire functions, infinite product, expansion of the sine and cosine.
In addition, analytic functions are defined in a way which simplifies the complex variables flanigan theory.
Those familiar with mathematics texts will note the fine illustrations throughout and large number of problems offered at the chapter ends. One reviewer noting its originality wrote: He can go to class without preparation.
Depending on the level of study, complex variables flanigan with proofs would be good.