大学物理学-电大同步上课进度更新

港控/mmm° 2022-10-23 11:11 120阅读 0赞

# 大学物理-简介及补充知识 #

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70][]

### ![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 1][] ###

# **数理基础** #

**1****、高等数学（向量，偏微分，梯度，散度，旋度等）**

**2****、高中物理（力学、电磁学等）**

**一、向量（矢量）**

**1、概念    既有大小，又有方向，且满足向量相加的平行四边形法则，如位移、速度、加速度、力、力矩等**

**2****、表示**

**有向线段**

**带箭头的字母（手书应采用的格式）**

**加粗的字母（出版方便，不宜手书）**

**向量的大小（向量的模）**

![20210305074211347.png][]

**单位向量（模等于****1****）**

![20210305074223726.png][]![20210305074228215.png][]![20210305074231326.png][]

**3****、向量的运算**

**A****、向量的加减法**

![20210305074242638.png][]![20210305074305888.png][]

**向量的加减法满足交换率和结合率**

![2021030507431419.png][]![20210305074317300.png][]

**B****、向量与实数的乘积还是一个向量，且满足结合率和分配律**

![20210305074328242.png][]

![20210305074332604.png][]

![20210305074334864.png][]

**C****、向量的内积、向量积、混合积**

**内积**

![2021030507434917.png][]![20210305074407604.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 2][]

**向量的内积满足交换律和分配律**

![20210305074435961.png][]![2021030507443968.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 3][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 4][]

**向量积**

![20210305074611499.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 5][]

**向量的向量积满足：**

![20210305074653751.png][]

![20210305074656772.png][]

![2021030507470131.png][]

**例****4****：力矩是一种向量积**

![20210305074707599.png][]

![20210305074710195.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 6][]

**例****5****：动量矩（角动量）是一种向量积**

![20210305074803932.png][]

![20210305074807155.png][]![2021030507481161.png][]![20210305074814608.png][]![20210305074817415.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 7][]

**向量的向量积在直角坐标系中的表示：**

![20210305075122278.png][]![20210305075125426.png][]![2021030507513771.png][]

![20210305075128951.png][]

![20210305075132139.png][]

![20210305075134385.png][]

![20210305075157468.png][]

![202103050752048.png][]

**例****6****：直角坐标系单位向量之间的内积和向量积**

![20210305075233190.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 8][]

**向量的混合积**

![2021030507531645.png][]

**表示三个矢量为三条邻边的六面体的体积**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 9][]

**二、偏导数**

**1.****定义**

**设函数**![20210305075348132.png][]**在点**![20210305075355495.png][]**某一邻域有定义，当  y  固定在  ![y\_0\{\}][y_0] ，而  x  在 ![x\_\{0\}][x_0] 有增量 ![\\Delta x][Delta x] 时，相应的函数有增量**

![20210305075447777.png][]

**如果**![20210305075459599.png][]

**存在，则称此极限为 **![20210305075508332.png][]**  在 **![20210305075514858.png][]**  的偏导数，记作**

![20210305075521208.png][]**或**![20210305075526602.png][]**或**![2021030507553391.png][]

**2.****偏导函数**

**如果函数  **![20210305075550518.png][] **在区域D内任意一点  **![20210305075554391.png][]**都有偏导数，那么这个偏导数就是   **![20210305075558896.png][]**     的函数，称为偏导函数，记为：**

![20210305075602554.png][]**或**![20210305075607535.png][]

**3.****全微分**

**设函数  **![20210305075619652.png][]**    在点  **![20210305075623584.png][]**   某一邻域有定义，如果函数在 **![20210305075627359.png][]**  的全增量可表示为**

![20210305075633184.png][]![20210305075643210.png][]

![20210305075646550.png][]

**其中  **![20210305075653401.png][]**    不依赖于  **![2021030507565794.png][]**  而仅与**![20210305075700310.png][] **有关，  则称函数可微分， **![20210305075706677.png][]**   称为函数的全微分                    **

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 10][]

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# 1.1 参考系，坐标系和时间坐标轴 #

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# 1.2+1.3描述质点运动的线参量和角参量 #

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