用图形界面API，结合事件处理机制，编写Java Application程序，实现一个可视化的计算器（至少应具有按键和显示区，至少实现加、减、乘、除运算以及clear功能）

好的，以下是一个简单的可视化计算器的Java Application程序，实现了加、减、乘、除运算以及clear功能。

import javax.swing.*;
import java.awt.*;
import java.awt.event.*;

public class Calculator extends JFrame implements ActionListener {

    private JTextField display;
    private JButton button0, button1, button2, button3, button4, button5, button6, button7, button8, button9;
    private JButton buttonAdd, buttonSubtract, buttonMultiply, buttonDivide, buttonClear, buttonEquals;

    private double firstNum = 0.0;
    private double secondNum = 0.0;
    private char operation = ' ';

    public Calculator() {
        super("Calculator");

        // create UI components
        display = new JTextField(20);
        display.setEditable(false);

        button0 = new JButton("0");
        button1 = new JButton("1");
        button2 = new JButton("2");
        button3 = new JButton("3");
        button4 = new JButton("4");
        button5 = new JButton("5");
        button6 = new JButton("6");
        button7 = new JButton("7");
        button8 = new JButton("8");
        button9 = new JButton("9");

        buttonAdd = new JButton("+");
        buttonSubtract = new JButton("-");
        buttonMultiply = new JButton("*");
        buttonDivide = new JButton("/");
        buttonClear = new JButton("C");
        buttonEquals = new JButton("=");

        // add action listeners to buttons
        button0.addActionListener(this);
        button1.addActionListener(this);
        button2.addActionListener(this);
        button3.addActionListener(this);
        button4.addActionListener(this);
        button5.addActionListener(this);
        button6.addActionListener(this);
        button7.addActionListener(this);
        button8.addActionListener(this);
        button9.addActionListener(this);

        buttonAdd.addActionListener(this);
        buttonSubtract.addActionListener(this);
        buttonMultiply.addActionListener(this);
        buttonDivide.addActionListener(this);
        buttonClear.addActionListener(this);
        buttonEquals.addActionListener(this);

        // create layout and add components
        JPanel panelTop = new JPanel(new FlowLayout());
        panelTop.add(display);

        JPanel panelMiddle = new JPanel(new GridLayout(4, 4));
        panelMiddle.add(button7);
        panelMiddle.add(button8);
        panelMiddle.add(button9);
        panelMiddle.add(buttonAdd);
        panelMiddle.add(button4);
        panelMiddle.add(button5);
        panelMiddle.add(button6);
        panelMiddle.add(buttonSubtract);
        panelMiddle.add(button1);
        panelMiddle.add(button2);
        panelMiddle.add(button3);
        panelMiddle.add(buttonMultiply);
        panelMiddle.add(buttonClear);
        panelMiddle.add(button0);
        panelMiddle.add(buttonEquals);
        panelMiddle.add(buttonDivide);

        Container container = getContentPane();
        container.add(panelTop, BorderLayout.NORTH);
        container.add(panelMiddle, BorderLayout.CENTER);

        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        setSize(250, 250);
        setVisible(true);
    }

    public void actionPerformed(ActionEvent e) {
        if (e.getSource() == button0) {
            display.setText(display.getText() + "0");
        } else if (e.getSource() == button1) {
            display.setText(display.getText() + "1");
        } else if (e.getSource() == button2) {
            display.setText(display.getText() + "2");
        } else if (e.getSource() == button3) {
            display.setText(display.getText() + "3");
        } else if (e.getSource() == button4) {
            display.setText(display.getText() + "4");
        } else if (e.getSource() == button5) {
            display.setText(display.getText() + "5");
        } else if (e.getSource() == button6) {
            display.setText(display.getText() + "6");
        } else if (e.getSource() == button7) {
            display.setText(display.getText() + "7");
        } else if (e.getSource() == button8) {
            display.setText(display.getText() + "8");
        } else if (e.getSource() == button9) {
            display.setText(display.getText() + "9");
        } else if (e.getSource() == buttonAdd) {
            firstNum = Double.parseDouble(display.getText());
            operation = '+';
            display.setText("");
        } else if (e.getSource() == buttonSubtract) {
            firstNum = Double.parseDouble(display.getText());
            operation = '-';
            display.setText("");
        } else if (e.getSource() == buttonMultiply) {
            firstNum = Double.parseDouble(display.getText());
            operation = '*';
            display.setText("");
        } else if (e.getSource() == buttonDivide) {
            firstNum = Double.parseDouble(display.getText());
            operation = '/';
            display.setText("");
        } else if (e.getSource() == buttonClear) {
            firstNum = 0.0;
            secondNum = 0.0;
            operation = ' ';
            display.setText("");
        } else if (e.getSource() == buttonEquals) {
            secondNum = Double.parseDouble(display.getText());
            double result = 0.0;
            switch (operation) {
                case '+':
                    result = firstNum + secondNum;
                    break;
                case '-':
                    result = firstNum - secondNum;
                    break;
                case '*':
                    result = firstNum * secondNum;
                    break;
                case '/':
                    result = firstNum / secondNum;
                    break;
            }
            display.setText("" + result);
        }
    }

    public static void main(String[] args) {
        new Calculator();
    }
}

在这个程序中，我们使用了JFrame作为主窗口，JTextField作为显示区，JButton作为按键，并在其中添加了ActionListener来处理对应的事件。在按钮事件处理中，我们根据不同的按钮进行不同的操作，例如数字按钮将数字添加到显示区，运算符按钮记录第一个数字并记录要进行的运算符，等号按钮计算结果并显示在显示区。

为了简化代码，我们在这里只处理了double类型的数字，没有考虑其他类型的数字或其他错误情况。您可以根据需要进行修改和补充。