# 微积分网课代修|偏微分方程代写Partial Differential Equation代考|TMA026/MMA430 Open the PDE App

• 单变量微积分
• 多变量微积分
• 傅里叶级数
• 黎曼积分
• ODE
• 微分学

## 微积分网课代修|偏微分方程代写Partial Differential Equation代考|Open the PDE App

For basic information on 2-D geometry construction, see “Create 2-D Geometry” on page $2-17$

Partial Differential Equation Toolbox software includes the PDE app, which covers all aspects of the PDE solution process. You start it by typing
pdetool
at the MATLAB command line. It may take a while the first time you launch the PDE app during a MATLAB session. The following figure shows the PDE app as it looks when you start it.

At the top, the PDE app has a pull-down menu bar that you use to control the modeling. Below the menu bar, a toolbar with icon buttons provide quick and easy access to some of the most important functions.

To the right of the toolbar is a pop-up menu that indicates the current application mode. You can also use it to change the application mode. The upper right part of the PDE app also provides the $x$ – and $y$-coordinates of the current cursor position. This position is updated when you move the cursor inside the main axes area in the middle of the PDE app.
The edit box for the set formula contains the active set formula.
In the main axes you draw the 2-D geometry, display the mesh, and plot the solution.
At the bottom of the PDE app, an information line provides information about the current activity. It can also display help information about the toolbar buttons.

## 微积分网课代修|偏微分方程代写Partial Differential Equation代考|Specify Geometry Using a CSG Model

For basic information on 2-D geometry construction, see “Create 2-D Geometry” on page $2-17$
You can specify complex geometries by overlapping solid objects. This approach to representing geometries is called Constructive Solid Geometry (CSG).
Use these four solid objects to specify a geometry for your problem:

• Circle – Represents the set of points inside and on a circle.
• Polygon – Represents the set of points inside and on a polygon given by a set of line segments.
• Rectangle – Represents the set of points inside and on a rectangle.
• Ellipse – Represents the set of points inside and on an ellipse. The ellipse can be rotated.

When you draw a solid object in the PDE app, each solid object is automatically given a unique name. Default names are C1, C2, C3, etc., for circles; P1, P2, P3, etc. for polygons; R1, R2, R3, etc., for rectangles; E1, E2, E3, etc., for ellipses. Squares, although a special case of rectangles, are named SQ1, SQ2, SQ3, etc. The name is displayed on the solid object itself. You can use any unique name, as long as it contains no blanks. In draw mode, you can alter the names and the geometries of the objects by double-clicking them, which opens a dialog box. The following figure shows an object dialog box for a circle.

You can use the name of the object to refer to the corresponding set of points in a set formula. The operators $+, *$, and – are used to form the set of points $\Omega$ in the plane over which the differential equation is solved. The operators $+$, the set union operator, and *, the set intersection operator, have the same precedence. The operator $-$, the set difference operator, has higher precedence. The precedence can be controlled by using parentheses. The resulting geometrical model, $\Omega$, is the set of points for which the set formula evaluates to true. By default, it is the union of all solid objects. We often refer to the area $\Omega$ as the decomposed geometry.

pdetool来启动它。

## 微积分网课代修|偏微分方程代写Partial Differential Equation代考|Specify Geometry Using a CSG Model

• 圆 – 表示圆内和圆上的点集。
• 多边形 – 表示由一组线段给出的多边形内部和上面的一组点。
• 矩形 – 表示矩形内部和矩形上的点集。
• 椭圆 – 表示椭圆内部和椭圆上的点集。椭圆可以旋转。