範例：求解非線性方程式系統

解題指令群 > 範例：求解非線性方程式系統

範例：求解非線性方程式系統

使用解題指令群，求解 n 個未知數的 n 方程式系統。

1. 插入解題指令群，然後定義估值、條件約束及求解器函數 Find。

按一下以複製此運算式

<region id="ID0EJPFKB" top="192" left="24" width="300" height="238.475485342492" xmlns="http://schemas.mathsoft.com/worksheet50">
  <solveblock>
    <regions>
      <region id="" top="24" left="24" solve-block-category="guess-value">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id label="Variable">x</id>
            <real>1</real>
          </define>
        </math>
      </region>
      <region id="" top="48" left="24" solve-block-category="guess-value">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id label="Variable">y</id>
            <real>1</real>
          </define>
        </math>
      </region>
      <region id="" top="72" left="24" solve-block-category="guess-value">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id label="Variable">z</id>
            <real>0</real>
          </define>
        </math>
      </region>
      <region id="" top="120" left="24" solve-block-category="constraint">
        <math disable-calc="false">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <plus />
              <apply>
                <mult />
                <real>2</real>
                <id>x</id>
              </apply>
              <id>y</id>
            </apply>
            <apply>
              <minus />
              <real>5</real>
              <apply>
                <mult />
                <real>2</real>
                <apply>
                  <pow />
                  <id>z</id>
                  <real>2</real>
                </apply>
              </apply>
            </apply>
          </apply>
        </math>
      </region>
      <region id="" top="144" left="24" solve-block-category="constraint">
        <math disable-calc="false">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <plus />
              <apply>
                <pow />
                <id>y</id>
                <real>3</real>
              </apply>
              <apply>
                <mult />
                <real>4</real>
                <id>z</id>
              </apply>
            </apply>
            <real>4</real>
          </apply>
        </math>
      </region>
      <region id="" top="168" left="24" solve-block-category="constraint">
        <math disable-calc="false">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <plus />
              <apply>
                <mult />
                <id>x</id>
                <id>y</id>
              </apply>
              <id>z</id>
            </apply>
            <apply>
              <pow />
              <id>e</id>
              <id>z</id>
            </apply>
          </apply>
        </math>
      </region>
      <region id="" top="216" left="24" solve-block-category="solver">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id label="Variable">vec</id>
            <apply>
              <id label="Keyword">尋找</id>
              <sequence>
                <id>x</id>
                <id>y</id>
                <id>z</id>
              </sequence>
            </apply>
          </define>
        </math>
      </region>
    </regions>
  </solveblock>
</region>

2. 計算 vec：

求解矩陣式方程式

您可以使用本徵分析或解題指令群，求解矩陣方程式。

1. 求解下列非線性方程式：

2. 使用 eigenvecs 函數計算矩陣 M 的特徵向量：

3. 使用 eigenvals 計算矩陣 M 的特徵向量以及 diag 函數，以沿著矩陣 Vals 的對角放置這些值：

4. 使用 Vectorization 與 Transpose 運算子尋找 X：

5. 使用解題指令群中的求解器函數 Find 尋找 X：

按一下以複製此運算式

<region id="ID0E53FKB" top="1320" left="24" width="300" height="210.573851031992" xmlns="http://schemas.mathsoft.com/worksheet50">
  <solveblock>
    <regions>
      <region id="" top="24" left="24" solve-block-category="guess-value">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id label="Variable">Xsb</id>
            <id>M</id>
          </define>
        </math>
      </region>
      <region id="" top="120" left="24" solve-block-category="constraint">
        <math disable-calc="false">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <pow />
              <id>Xsb</id>
              <real>2</real>
            </apply>
            <id>M</id>
          </apply>
        </math>
      </region>
      <region id="" top="192" left="24" solve-block-category="solver">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id label="Variable">Xsb</id>
            <apply>
              <id label="Keyword">尋找</id>
              <id>Xsb</id>
            </apply>
          </define>
        </math>
      </region>
    </regions>
  </solveblock>
</region>

6. 計算 Xsb2 或 M：

求解含有單位的數量

您可以使用解題指令群求解含有單位的數量。以下範例可決定通過直線管長的流速。

1. 定義流動物質的密度與磁導率：

2. 定義管路的直徑與長度：

3. 定義管路內的壓力與重力：

按一下以複製此運算式

<region id="ID0ETFGKB" top="2616" left="24" width="300" height="411" xmlns="http://schemas.mathsoft.com/worksheet50">
  <solveblock>
    <regions>
      <region id="" top="24" left="24" solve-block-category="guess-value">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id label="Variable">f</id>
            <apply>
              <mult />
              <real>1</real>
              <apply>
                <pow />
                <real>10</real>
                <real>-3</real>
              </apply>
            </apply>
          </define>
        </math>
      </region>
      <region id="" top="72" left="24" solve-block-category="guess-value">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id label="Variable">v</id>
            <apply>
              <mult />
              <real>10</real>
              <apply>
                <div />
                <id>ft</id>
                <id>s</id>
              </apply>
            </apply>
          </define>
        </math>
      </region>
      <region id="" top="120" left="24" solve-block-category="guess-value">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id label="Variable">NRe</id>
            <apply>
              <mult />
              <real>1</real>
              <apply>
                <pow />
                <real>10</real>
                <real>4</real>
              </apply>
            </apply>
          </define>
        </math>
      </region>
      <region id="" top="168" left="24" solve-block-category="constraint">
        <math disable-calc="false">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <id>NRe</id>
            <apply>
              <div />
              <apply>
                <mult />
                <apply>
                  <mult />
                  <id>ρ</id>
                  <id>v</id>
                </apply>
                <id>D</id>
              </apply>
              <id>μ</id>
            </apply>
          </apply>
        </math>
      </region>
      <region id="" top="216" left="24" solve-block-category="constraint">
        <math disable-calc="false">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <div />
              <id label="Variable">ΔP</id>
              <id>ρ</id>
            </apply>
            <apply>
              <mult />
              <apply>
                <mult />
                <real>4</real>
                <id>f</id>
              </apply>
              <apply>
                <div />
                <apply>
                  <mult />
                  <apply>
                    <pow />
                    <id>v</id>
                    <real>2</real>
                  </apply>
                  <id label="Variable">ΔL</id>
                </apply>
                <apply>
                  <mult />
                  <apply>
                    <mult />
                    <real>2</real>
                    <id>D</id>
                  </apply>
                  <id>gc</id>
                </apply>
              </apply>
            </apply>
          </apply>
        </math>
      </region>
      <region id="" top="264" left="24" solve-block-category="constraint">
        <math disable-calc="false">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <div />
              <real>1</real>
              <apply>
                <nthRoot />
                <placeholder />
                <apply>
                  <div />
                  <id>f</id>
                  <real>2</real>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus />
              <apply>
                <mult />
                <real>2.5</real>
                <apply>
                  <id>ln</id>
                  <apply>
                    <mult />
                    <id>NRe</id>
                    <apply>
                      <nthRoot />
                      <placeholder />
                      <apply>
                        <div />
                        <id>f</id>
                        <real>8</real>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <real>1.75</real>
            </apply>
          </apply>
        </math>
      </region>
      <region id="" top="360" left="24" solve-block-category="solver">
        <math disable-calc="false">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <matrix rows="3" cols="1">
              <id label="Variable">vsol</id>
              <id label="Variable">fsol</id>
              <id label="Variable">NRe_sol</id>
            </matrix>
            <apply>
              <id label="Keyword">尋找</id>
              <sequence>
                <id>v</id>
                <id>f</id>
                <id>NRe</id>
              </sequence>
            </apply>
          </define>
        </math>
      </region>
    </regions>
  </solveblock>
</region>

4. 求解 v、f 及 NRe

按一下以複製此運算式

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