Dr. Yasuyuki Nakamura: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=927
en-us2015 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 03 Mar 2015 16:36:56 GMTTue, 03 Mar 2015 16:36:56 GMTNew applications published by Dr. Yasuyuki Nakamurahttp://www.mapleprimes.com/images/mapleapps.gifDr. Yasuyuki Nakamura: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=927
Geometrical View of Differential Equation dy/dx=f(x, y)
http://www.maplesoft.com/applications/view.aspx?SID=6423&ref=Feed
This worksheet gives you geometrical view of differential equations dy/dx=f(x, y). Direction vectors on all lattice points in a defined range are displayed. This shows direction field of a differential equation. If you try to draw direction field by hand, it is convenient to draw direction vectors on isoclines. The isoclines are lines defined as f(x, y)=C and all vectors on the same isocline have same dirrection. This worksheet illustrates how to draw vector fields on isoclines.<img src="/view.aspx?si=6423/1.gif" alt="Geometrical View of Differential Equation dy/dx=f(x, y)" align="left"/>This worksheet gives you geometrical view of differential equations dy/dx=f(x, y). Direction vectors on all lattice points in a defined range are displayed. This shows direction field of a differential equation. If you try to draw direction field by hand, it is convenient to draw direction vectors on isoclines. The isoclines are lines defined as f(x, y)=C and all vectors on the same isocline have same dirrection. This worksheet illustrates how to draw vector fields on isoclines.6423Thu, 10 Jul 2008 00:00:00 ZDr. Yasuyuki NakamuraDr. Yasuyuki NakamuraFourier Series Expansion
http://www.maplesoft.com/applications/view.aspx?SID=6398&ref=Feed
This worksheet is designed for students to study how to expand a function into Fourier series. If you set a function, Fourier coefficients for the function are calcurated and a partial sum of the series are displayed together with the original function. Furthermore, animation in which a partial sum of the series are plotted as the number of sums increased.<img src="/view.aspx?si=6398/1.jpg" alt="Fourier Series Expansion" align="left"/>This worksheet is designed for students to study how to expand a function into Fourier series. If you set a function, Fourier coefficients for the function are calcurated and a partial sum of the series are displayed together with the original function. Furthermore, animation in which a partial sum of the series are plotted as the number of sums increased.6398Wed, 02 Jul 2008 00:00:00 ZDr. Yasuyuki NakamuraDr. Yasuyuki NakamuraStability of a fixed point in a system of ODE
http://www.maplesoft.com/applications/view.aspx?SID=6320&ref=Feed
This worksheet is designed for students to study how to analyze the stability of a fixed point in a system of ODE. Especially, a system of autonomous ODE with two variables are considered. When ODE are input by students, following calculation is performed: seek fixed points, linearize original ODEs, calculate eigen values of coefficient matrix, determine a kind of fixed point, draw a direction field, animate of solution curves.<img src="/view.aspx?si=6320/thumb.gif" alt="Stability of a fixed point in a system of ODE" align="left"/>This worksheet is designed for students to study how to analyze the stability of a fixed point in a system of ODE. Especially, a system of autonomous ODE with two variables are considered. When ODE are input by students, following calculation is performed: seek fixed points, linearize original ODEs, calculate eigen values of coefficient matrix, determine a kind of fixed point, draw a direction field, animate of solution curves.6320Wed, 28 May 2008 00:00:00 ZDr. Yasuyuki NakamuraDr. Yasuyuki NakamuraSolution of a System of Differential Equations
http://www.maplesoft.com/applications/view.aspx?SID=6323&ref=Feed
<p>In this worksheet, we show some examples of behavior of solutions of a system of differential equations and if you put DEs and an initial condition, an orbit of a solution with a vector field are shown. All parameters input by you are recorded and they can be easily reused. <strong>Note:</strong> There are some features in this application that are new to Maple 12 and will not work in older versions. To see the Maple 11 version, <a href="http://www.maplesoft.com/applications/app_center_view.aspx?AID=2225" class="plainlink">follow this link</a>.</p><img src="/view.aspx?si=6323/thumb.gif" alt="Solution of a System of Differential Equations" align="left"/><p>In this worksheet, we show some examples of behavior of solutions of a system of differential equations and if you put DEs and an initial condition, an orbit of a solution with a vector field are shown. All parameters input by you are recorded and they can be easily reused. <strong>Note:</strong> There are some features in this application that are new to Maple 12 and will not work in older versions. To see the Maple 11 version, <a href="http://www.maplesoft.com/applications/app_center_view.aspx?AID=2225" class="plainlink">follow this link</a>.</p>6323Tue, 27 May 2008 04:00:00 ZDr. Yasuyuki NakamuraDr. Yasuyuki NakamuraSolution of a System of Differential Equations
http://www.maplesoft.com/applications/view.aspx?SID=5699&ref=Feed
In this worksheet, we show some examples of behavior of solutions of a system of differential equations and if you put DEs and an initial condition, an orbit of a solution with a vector field are shown. All parameters input by you are recorded and they can be easily reused.
<b>Note:</b> If you would like to see the application using new features available in Maple 12, <a href="http://www.maplesoft.com/applications/app_center_view.aspx?AID=2246" class="plainlink">follow this link</a>.<img src="/view.aspx?si=5699/phase_doc_en_3.gif" alt="Solution of a System of Differential Equations" align="left"/>In this worksheet, we show some examples of behavior of solutions of a system of differential equations and if you put DEs and an initial condition, an orbit of a solution with a vector field are shown. All parameters input by you are recorded and they can be easily reused.
<b>Note:</b> If you would like to see the application using new features available in Maple 12, <a href="http://www.maplesoft.com/applications/app_center_view.aspx?AID=2246" class="plainlink">follow this link</a>.5699Mon, 10 Mar 2008 00:00:00 ZDr. Yasuyuki NakamuraDr. Yasuyuki NakamuraThree Body Problem
http://www.maplesoft.com/applications/view.aspx?SID=1663&ref=Feed
A Three body problem (3BP) considers three mutually interacting particles. It is a problem that is surprisingly difficult to solve. This simple Maplet application simulates the 3BP numerically. Users can set paramters and see how the particles behave. Some examples are included in the application such as a line solution, triangle solution and figure 8 solution.
1. Select a particular example from the pull down menu and the simulation starts automatically.
2. You can also set parameters, mass, position, velocity of three particles. After setting the parameters, press the Start button to start the simulation.<img src="/view.aspx?si=1663/FigEight-3bodysmall.JPG" alt="Three Body Problem" align="left"/>A Three body problem (3BP) considers three mutually interacting particles. It is a problem that is surprisingly difficult to solve. This simple Maplet application simulates the 3BP numerically. Users can set paramters and see how the particles behave. Some examples are included in the application such as a line solution, triangle solution and figure 8 solution.
1. Select a particular example from the pull down menu and the simulation starts automatically.
2. You can also set parameters, mass, position, velocity of three particles. After setting the parameters, press the Start button to start the simulation.1663Wed, 07 Sep 2005 00:00:00 ZDr. Yasuyuki NakamuraDr. Yasuyuki Nakamura