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Calculus with Complex Numbers by John B. Reade

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Published by Taylor & Francis Inc in London .
Written in English


Book details:

The Physical Object
FormatElectronic resource
ID Numbers
Open LibraryOL24262987M
ISBN 101420023462

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Calculus with Complex Numbers - CRC Press Book This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and th. The book Visual Complex Analysis by Tristan Needham is a great introduction to complex analysis that does not skip the fundamentals that you mentioned. In particular, the first chapter includes detailed sections on the roots of unity, the geometry of the complex plane, Euler's formula, and a very clear proof of the fundamental theorem of algebra. Book Description. This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of. A good book is the one which teaches you how things work. A good book is one which aims to teach you the concept, and give you some challenging questions which in turn, will boost your understanding and confidence. A book with just loads of formul.

Complex numbers can be multiplied and divided. To multiply complex numbers, distribute just as with polynomials. See,, and. To divide complex numbers, multiply both the numerator and denominator by the complex conjugate of the denominator to eliminate the complex number from the denominator. See, . This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is. Complex numbers are unreal. Yes, that’s the truth. A complex number has a term with a multiple of i, and i is the imaginary number equal to the square root of –1. Many of the algebraic rules that apply to real numbers also apply to complex numbers, but you have to be careful because many [ ]. Constructing the complex numbers One way of introducing the field C of complex numbers is via the arithmetic of 2×2 matrices. DEFINITION A complex number is a matrix of the form x −y y x, where x and y are real numbers. Complex numbers of the form x 0 0 x are scalar matrices and are called real complex numbers and are denoted by File Size: KB.

Calculus of Complex functions. Laurent Series and Residue Theorem Review of complex numbers. A complex number is any expression of the form x+iywhere xand yare real numbers. xis called the real part and yis called the imaginary part of the complex number x+iy:The complex number x iyis said to be complex conjugate of the number x+iy:File Size: KB.   Hint: You know how to do the operation with polynomials so you can do the operation here! Just recall that you need to be careful to deal with any \(i\) . Multiplying Complex Numbers. Multiplying complex numbers is much like multiplying binomials. The major difference is that we work with the real and imaginary parts separately. Multiplying a Complex Number by a Real Number. Let’s begin by multiplying a complex number by a real number. We distribute the real number just as we would with a binomial. Complex analysis is one of the classical branches in mathematics, with roots in the 18th century and just prior. Important mathematicians associated with complex numbers include Euler, Gauss, Riemann, Cauchy, Weierstrass, and many more in the 20th x analysis, in particular the theory of conformal mappings, has many physical applications and is also used throughout analytic number.