Complex Analysis: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=2881
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 04 Mar 2021 19:12:15 GMTThu, 04 Mar 2021 19:12:15 GMTNew applications in the Complex Analysis categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgComplex Analysis: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=2881
Fractal Leaf Generator
https://www.maplesoft.com/applications/view.aspx?SID=154086&ref=Feed
This application generates Barnsley Fern fractals, using the number of iterations specified by the user.<img src="https://www.maplesoft.com/view.aspx?si=154086/fractalleafThumb.jpg" alt="Fractal Leaf Generator" style="max-width: 25%;" align="left"/>This application generates Barnsley Fern fractals, using the number of iterations specified by the user.https://www.maplesoft.com/applications/view.aspx?SID=154086&ref=FeedWed, 20 Apr 2016 04:00:00 ZMaplesoftMaplesoftThe Schwarz-Christoffel panel method: a computational kit
https://www.maplesoft.com/applications/view.aspx?SID=153963&ref=Feed
The so-called Schwarz-Christoffel Panel Method devised and developed by Prof. E. Morishita for the analysis of aerodynamics of airfoils with arbitrary geometry is built as a hidden code in this document. Given the airfoil geometry, the Schwarz-Christoffel transform that maps the unit circle onto the polygon that represents the airfoil, is obtained. Some Maple resources are included to handle and visualize the computed results.<img src="https://www.maplesoft.com/view.aspx?si=153963/temporaryAirfoils.png" alt="The Schwarz-Christoffel panel method: a computational kit" style="max-width: 25%;" align="left"/>The so-called Schwarz-Christoffel Panel Method devised and developed by Prof. E. Morishita for the analysis of aerodynamics of airfoils with arbitrary geometry is built as a hidden code in this document. Given the airfoil geometry, the Schwarz-Christoffel transform that maps the unit circle onto the polygon that represents the airfoil, is obtained. Some Maple resources are included to handle and visualize the computed results.https://www.maplesoft.com/applications/view.aspx?SID=153963&ref=FeedWed, 03 Feb 2016 05:00:00 ZLuis Sainz de los TerrerosLuis Sainz de los TerrerosExponential map fractal viewer
https://www.maplesoft.com/applications/view.aspx?SID=153953&ref=Feed
Static fractal viewer for the Julia sets of the exponential map lambda*exp(z), with variable lambda. Allows adjustable viewing window, zoom-in and display of periodic attractors up to period 5. Dynamic version can generate animated views, like the Knaster explosion of period 3 shown on the figure.<img src="https://www.maplesoft.com/view.aspx?si=153953/3djulia.png" alt="Exponential map fractal viewer" style="max-width: 25%;" align="left"/>Static fractal viewer for the Julia sets of the exponential map lambda*exp(z), with variable lambda. Allows adjustable viewing window, zoom-in and display of periodic attractors up to period 5. Dynamic version can generate animated views, like the Knaster explosion of period 3 shown on the figure.https://www.maplesoft.com/applications/view.aspx?SID=153953&ref=FeedTue, 19 Jan 2016 05:00:00 ZRobert Israel, Carl LoveRobert Israel, Carl LoveClassroom Tips and Techniques: Real and Complex Derivatives of Some Elementary Functions
https://www.maplesoft.com/applications/view.aspx?SID=153726&ref=Feed
The elementary functions include the six trigonometric and hyperbolic functions and their inverses. For all but five of these 24 functions, Maple's derivative (correct on the complex plane) agrees with the real-variable form found in the standard calculus text. For these five exceptions, this article explores two issues: (1) Does Maple's derivative, restricted to the real domain, agree with the real-variable form; and (2), to what extent do both forms agree on the complex plane.<img src="https://www.maplesoft.com/view.aspx?si=153726/thumb.jpg" alt="Classroom Tips and Techniques: Real and Complex Derivatives of Some Elementary Functions" style="max-width: 25%;" align="left"/>The elementary functions include the six trigonometric and hyperbolic functions and their inverses. For all but five of these 24 functions, Maple's derivative (correct on the complex plane) agrees with the real-variable form found in the standard calculus text. For these five exceptions, this article explores two issues: (1) Does Maple's derivative, restricted to the real domain, agree with the real-variable form; and (2), to what extent do both forms agree on the complex plane.https://www.maplesoft.com/applications/view.aspx?SID=153726&ref=FeedWed, 10 Dec 2014 05:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Branch Cuts for a Product of Two Square-Roots
https://www.maplesoft.com/applications/view.aspx?SID=153697&ref=Feed
Naive simplification of f(z) = sqrt(z - 1) sqrt(z + 1) to F(z) = sqrt(z<sup>2</sup> - 1) results in a pair of functions that agree on only part of the complex plane. The enhanced ability of Maple 18 to find and display branch cuts of composite functions is used in this article to explore the branch cuts and regions of agreement/disagreement of f and F.<img src="https://www.maplesoft.com/view.aspx?si=153697/thumb.jpg" alt="Classroom Tips and Techniques: Branch Cuts for a Product of Two Square-Roots" style="max-width: 25%;" align="left"/>Naive simplification of f(z) = sqrt(z - 1) sqrt(z + 1) to F(z) = sqrt(z<sup>2</sup> - 1) results in a pair of functions that agree on only part of the complex plane. The enhanced ability of Maple 18 to find and display branch cuts of composite functions is used in this article to explore the branch cuts and regions of agreement/disagreement of f and F.https://www.maplesoft.com/applications/view.aspx?SID=153697&ref=FeedTue, 11 Nov 2014 05:00:00 ZDr. Robert LopezDr. Robert LopezHopalong Attractor
https://www.maplesoft.com/applications/view.aspx?SID=153557&ref=Feed
<p>Hopalong attractors are fractals, introduced by Barry Martin of Aston University in Birmingham, England. This application allows you to explore the Hopalong by varying the parameters, the number of iterations, the iterates' symbol size, and the background color choice. You can also change the starting values of each of the three orbits by dragging the cross symbols appearing in the plot. Full details on how this application was created using the Explore command with a user-defined module are included.</p><img src="https://www.maplesoft.com/view.aspx?si=153557/95fa944692de1fb724cb7e758e6c56e5.gif" alt="Hopalong Attractor" style="max-width: 25%;" align="left"/><p>Hopalong attractors are fractals, introduced by Barry Martin of Aston University in Birmingham, England. This application allows you to explore the Hopalong by varying the parameters, the number of iterations, the iterates' symbol size, and the background color choice. You can also change the starting values of each of the three orbits by dragging the cross symbols appearing in the plot. Full details on how this application was created using the Explore command with a user-defined module are included.</p>https://www.maplesoft.com/applications/view.aspx?SID=153557&ref=FeedMon, 28 Apr 2014 04:00:00 ZDave LinderDave LinderClassroom Tips and Techniques: Mathematical Thoughts on the Root Locus
https://www.maplesoft.com/applications/view.aspx?SID=153452&ref=Feed
Under suitable assumptions, the roots of the equation <em>f</em>(<em>z, c</em>) = 0, namely, <em>z</em> = <em>z</em>(<em>c</em>), trace a curve in the complex plane. In engineering feedback-control, such curves are called a <em>root locus</em>. This article examines the parameter-dependence of roots of polynomial and transcendental equations.<img src="https://www.maplesoft.com/view.aspx?si=153452/thumb.jpg" alt="Classroom Tips and Techniques: Mathematical Thoughts on the Root Locus" style="max-width: 25%;" align="left"/>Under suitable assumptions, the roots of the equation <em>f</em>(<em>z, c</em>) = 0, namely, <em>z</em> = <em>z</em>(<em>c</em>), trace a curve in the complex plane. In engineering feedback-control, such curves are called a <em>root locus</em>. This article examines the parameter-dependence of roots of polynomial and transcendental equations.https://www.maplesoft.com/applications/view.aspx?SID=153452&ref=FeedTue, 29 Oct 2013 04:00:00 ZDr. Robert LopezDr. Robert Lopez