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- ...function now established, we can now introduce the differentiability of a complex function. Let f be a complex valued funtion defined in a neighborhood of <math>z_0</math>. Then the ''' ...1 KB (236 words) - 19:25, 25 February 2007
- ...inequality|triangle inequality]]''' is a useful inequality that holds for complex numbers: This is obvious geometrically, but a formal proof can be found [[Complex Analysis/Appendix/Proofs/Triangle Inequality|here]]. ...3 KB (566 words) - 14:28, 20 July 2006
- ...worked out solutions, please see the [[Algebra/Complex numbers|Wikibook on complex numbers]]. A '''complex number''' ''z'' is a number written in the form: ...4 KB (732 words) - 11:47, 4 November 2007
- ...point <math>z_0</math> of <math>\mathfrak{G}</math> exists and equals the complex number ''L'' if, for any real number <math>\epsilon >0</math> we can find a ...n can be made using open sets: we say that the limit exists and equals the complex number ''L'' if, for any real number <math>\epsilon >0</math> we can find a ...2 KB (291 words) - 11:40, 25 February 2007
- From our look at complex derivatives, we now examine the analytic functions, the Cauchy-Riemann Equa A complex valued function f(z) is '''[[analytic]]''' on an open set ''G'' if it has a ...3 KB (464 words) - 12:22, 7 March 2008
- ...explicitly stated, whenever the term ''function'' appears, we will mean a complex function. A function can also be '''multi-valued''' - for example, <math>z^ ...on Z Squared Plot.png|thumb|A plot of Abs(''z''²) as ''z'' ranges over the complex plane.]] ...2 KB (290 words) - 00:51, 31 August 2007
- ...omplex analysis''' is the study of functions of complex variables. Complex analysis is a widely used and powerful tool in certain areas of electrical engineeri Before we begin, you may want to review [[Algebra/Complex numbers|Complex numbers]] ...12 KB (2,016 words) - 22:10, 12 October 2007
- == Complex Conjugate == Let: <math>\bar{z}</math> be the complex conjugate of <math>z\ </math> then ...1 KB (228 words) - 10:26, 24 June 2006
- {{Merge|Complex Analysis/Complex Functions/Continuous Functions |The page is very short, there are other pag [[Category:Complex Analysis]] ...668 bytes (113 words) - 14:01, 26 September 2007
- {{Merge |Complex Analysis/Complex Functions/Complex Derivatives|The page is very short, there are other page about this topic}} [[Category:Complex Analysis]] ...2 KB (348 words) - 13:58, 26 September 2007
- [[Category:Complex Analysis]] ...1 KB (213 words) - 10:24, 24 June 2006
- Let <math>z</math> and <math>w</math> be complex numbers. Since we have: [[Category:Complex Analysis]] ...733 bytes (126 words) - 10:24, 24 June 2006
- We want to extend the exponential function <math>\exp</math> to the complex numbers in ...667 bytes (139 words) - 12:21, 29 October 2006
Page text matches
- {{Merge|Complex Analysis/Complex Functions/Continuous Functions |The page is very short, there are other pag [[Category:Complex Analysis]] ...668 bytes (113 words) - 14:01, 26 September 2007
- ===[[Real analysis/Section 1 Exercises|Exercises]]=== # Show that the complex numbers <math>\mathbb C</math> cannot be made into an ordered field. ...900 bytes (146 words) - 22:03, 12 October 2007
- ...explicitly stated, whenever the term ''function'' appears, we will mean a complex function. A function can also be '''multi-valued''' - for example, <math>z^ ...on Z Squared Plot.png|thumb|A plot of Abs(''z''²) as ''z'' ranges over the complex plane.]] ...2 KB (290 words) - 00:51, 31 August 2007
- ===What is Analysis?=== ...basic concepts needed for the idea of functions, then move on to the more analysis-based topics. ...2 KB (362 words) - 00:59, 19 October 2007
- ...point <math>z_0</math> of <math>\mathfrak{G}</math> exists and equals the complex number ''L'' if, for any real number <math>\epsilon >0</math> we can find a ...n can be made using open sets: we say that the limit exists and equals the complex number ''L'' if, for any real number <math>\epsilon >0</math> we can find a ...2 KB (291 words) - 11:40, 25 February 2007
- ...function now established, we can now introduce the differentiability of a complex function. Let f be a complex valued funtion defined in a neighborhood of <math>z_0</math>. Then the ''' ...1 KB (236 words) - 19:25, 25 February 2007
- ...inequality|triangle inequality]]''' is a useful inequality that holds for complex numbers: This is obvious geometrically, but a formal proof can be found [[Complex Analysis/Appendix/Proofs/Triangle Inequality|here]]. ...3 KB (566 words) - 14:28, 20 July 2006
- {{Engineering Analysis}} == Complex Eigenvalues == ...3 KB (378 words) - 20:00, 17 April 2007
- Let <math>z</math> and <math>w</math> be complex numbers. Since we have: [[Category:Complex Analysis]] ...733 bytes (126 words) - 10:24, 24 June 2006
- {{Merge |Complex Analysis/Complex Functions/Complex Derivatives|The page is very short, there are other page about this topic}} [[Category:Complex Analysis]] ...2 KB (348 words) - 13:58, 26 September 2007
- == Complex Conjugate == Let: <math>\bar{z}</math> be the complex conjugate of <math>z\ </math> then ...1 KB (228 words) - 10:26, 24 June 2006
- ...worked out solutions, please see the [[Algebra/Complex numbers|Wikibook on complex numbers]]. A '''complex number''' ''z'' is a number written in the form: ...4 KB (732 words) - 11:47, 4 November 2007
- The subject of real analysis is concerned with the real numbers, <math>\mathbb R</math>, and associated ...<math>\frac{1}{0}</math>? It turns out that they are not (the first is a ''complex'' number and the second is undefined) but we need to be able to explain why ...1 KB (188 words) - 22:03, 12 October 2007
- ...ate without actually 'integrating'. ''Note: Its derivation is in Complex Analysis, which is listed as a prerequisite for these more advanced tricks.'' ...eorem (Cauchy really did do a lot of this stuff, a running joke in Complex Analysis classes is, "Isn't every proof done by Cauchy?"): ...4 KB (636 words) - 10:55, 27 July 2007
- ...alysts use today (e.g., complex analysis, a partition of unity, functional analysis). No attention has been given with regard to the organization of the conten * In this book, an analytic function is always complex-valued. ...3 KB (398 words) - 22:43, 10 October 2007
- Using [[Algebra/Complex numbers#Euler's theorem|Euler's formula]],<br/> A complex exponential can also be expressed as<br/> ...2 KB (407 words) - 10:02, 1 July 2006
- The vast majority of this book is going to be focused on (2), the analysis of the mathematical systems. This chapter alone will be devoted to a discus == Complex Descriptions == ...5 KB (823 words) - 22:11, 1 November 2007
- {{Engineering Analysis}} #If λ is a complex eigenvalue of A, then λ<sup>*</sup> (the complex conjugate) is also an eigenvalue of A. ...5 KB (791 words) - 03:24, 10 October 2006
- =Some Graphical Analysis= A spiral point (spirals in or away from a point): a complex eignevalues. ...1 KB (165 words) - 22:06, 11 July 2006
- From our look at complex derivatives, we now examine the analytic functions, the Cauchy-Riemann Equa A complex valued function f(z) is '''[[analytic]]''' on an open set ''G'' if it has a ...3 KB (464 words) - 12:22, 7 March 2008