Mathematical Physics by Derek Raine

Author:Derek Raine
Language: eng
Format: epub, mobi
ISBN: 9781683922056
Publisher: Mercury Learning and Information
Published: 2018-02-09T05:00:00+00:00

where the integrals are taken around closed curves within the annulus A, and that

The quantity b1 is called the residue of f(z) at z0. Equation (7.16) can be used to evaluate integrals which are often difficult to obtain by other means. (The technique is called contour integration.)

REVISION NOTES

After completing this chapter you should be able to

•Add, subtract, multiply and divide complex numbers

•Find the complex conjugate of an algebraic expression

•Find the real and imaginary parts of a complex algebraicexpression

•Solve quadratic equations with real or complexcoefficients

•Find the argument and modulus of a complex numberand indicate it on the Argand diagram

•Express a complex number in the form

z = r(cos(θ) + i sin(θ)) = reiθ

•Recall

•Quote de Moivre’s theorem and use it to derive trigonometric identities

•Find the nth roots of unity

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