'Contour integral' diaporamas de présentation

11. Complex Variable Theory

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11. Complex Variable Theory

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October 21 Residue theorem 7.1 Calculus of residues

Chapter 7 Functions of a Complex Variable II. October 21 Residue theorem 7.1 Calculus of residues. Suppose an analytic function f ( z ) has an isolated singularity at z 0 . Consider a contour integral enclosing z 0. z 0.

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Complex number : Complex algebra: Complex conjugation:

Chapter 6 Functions of a Complex Variable I. October 3 Cauchy-Riemann conditions 6.1 Complex algebra. Complex number : Complex algebra: Complex conjugation:. Polar representation:. Modulus (magnitude):. Argument (phase):. Functions of a complex variable:

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Maximum Modulus Principle:

Maximum Modulus Principle: If f is analytic and not constant in a given domain D, then |f(z)| has no maximum value in D. That is, there is no z 0 in the domain such that |f(z)| ? |f(z 0 )| for all points z in D. Proof: Assume that |f(z)| does have a maximum value in D. R. z 0. C R.

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The z-Transform

The z-Transform. ECON 397 Macroeconometrics Cunningham. z-Transform. The z-transform is the most general concept for the transformation of discrete-time series. The Laplace transform is the more general concept for the transformation of continuous time processes.

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RESIDUE THEOREM

RESIDUE THEOREM. Presented By Osman Toufiq Ist Year Ist SEM. RESIDUE THEOREM Calculus of residues. Suppose an analytic function f ( z ) has an isolated singularity at z 0 . Consider a contour integral enclosing z 0. z 0.

1.68k views • 10 slides