From 1cd32f7db4f359c789379d809af2943e5b2aebd6 Mon Sep 17 00:00:00 2001 From: bushuhui Date: Sat, 19 Nov 2022 18:10:56 +0800 Subject: [PATCH] Improve descriptions --- .../1-numpy_tutorial.ipynb | 58 +++++------ .../2-matplotlib_tutorial.ipynb | 2 +- .../4-scipy_tutorial.ipynb | 52 ++++------ .../5-sympy_tutorial.ipynb | 96 +++++++----------- .../images/scipy.png | Bin 0 -> 149121 bytes .../images/sympy.png | Bin 0 -> 137564 bytes 6 files changed, 90 insertions(+), 118 deletions(-) create mode 100644 1_numpy_matplotlib_scipy_sympy/images/scipy.png create mode 100644 1_numpy_matplotlib_scipy_sympy/images/sympy.png diff --git a/1_numpy_matplotlib_scipy_sympy/1-numpy_tutorial.ipynb b/1_numpy_matplotlib_scipy_sympy/1-numpy_tutorial.ipynb index 8f1ea56..d0ea975 100644 --- a/1_numpy_matplotlib_scipy_sympy/1-numpy_tutorial.ipynb +++ b/1_numpy_matplotlib_scipy_sympy/1-numpy_tutorial.ipynb @@ -406,7 +406,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "如果我们试图给一个numpy数组中的元素赋一个错误类型的值,我们会得到一个错误:" + "如果给一个numpy数组中的元素赋一个错误类型的值,会得到一个错误:" ] }, { @@ -415,7 +415,7 @@ "metadata": {}, "outputs": [], "source": [ - "M[0,0,0] = \"Hello\"\n" + "M[0,0,0] = \"Hello\"" ] }, { @@ -468,7 +468,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "对于较大的数组,使用显式的Python列表人为地初始化数据是不切实际的。除此之外可以用`numpy`的很多函数得到不同类型的数组。有一些常用的分别是:" + "对于较大的数组,使用显式的Python列表人为地初始化数据效率比较低。生成有规律的数组,可以使用下面的函数:" ] }, { @@ -650,7 +650,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### random 数据" + "#### 随机数据" ] }, { @@ -855,7 +855,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "对于数据文件来说一种非常常见的文件格式是逗号分割值(CSV),或者有关的格式例如TSV(制表符分隔的值)。为了从这些文件中读取数据到Numpy数组中,我们可以用`numpy.genfromtxt`函数。例如:" + "为了方便不同程序直接交互数据,可以将数组存储到文件,常见的文件格式是逗号分割值(CSV)、制表符分隔的值(TSV)。为了从这些文件中读取数据到Numpy数组中,可以用`numpy.genfromtxt`函数。例如:" ] }, { @@ -954,7 +954,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "使用`numpy.savetxt`我们可以将一个Numpy数组以CSV格式存入:" + "使用`numpy.savetxt`,可以将一个Numpy数组以CSV格式存入:" ] }, { @@ -1036,7 +1036,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### 3.2 numpy 的本地文件格式" + "### 3.2 numpy 数据文件格式" ] }, { @@ -1225,7 +1225,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "如果我们省略了一个多维数组的索引,它将会返回整行(或者,总的来说,一个 N-1 维的数组)" + "如果省略了一个多维数组的索引,它将会返回整行(或者,总的来说,一个 N-1 维的数组)" ] }, { @@ -1321,7 +1321,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们可以用索引赋新的值给数组中的元素:" + "可以用索引赋新的值给数组中的元素:" ] }, { @@ -1403,7 +1403,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "切片索引是语法 `M[lower:upper:step]` 的技术名称,用于提取数组的一部分:" + "为了访问一部分数据,可以使用切片索引,其语法是 `M[lower:upper:step]`。" ] }, { @@ -1451,7 +1451,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "切片索引到的数据是 *可变的* : 如果它们被分配了一个新值,那么从其中提取切片的原始数组将被修改:" + "切片索引到的数据是 **可变的**,如果它们被分配了一个新值,那么从其中提取切片的原始数组将被修改:" ] }, { @@ -1732,7 +1732,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Fancy索引是一个名称时,一个数组或列表被使用在一个索引:" + "可以使用列表作为访问的索引,一个数组或列表被使用在一个索引:" ] }, { @@ -1788,7 +1788,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们也可以使用索引掩码:如果索引掩码是一个数据类型`bool`的Numpy数组,那么一个元素被选择(True)或不(False)取决于索引掩码在每个元素位置的值:" + "也可以使用索引掩码:如果索引掩码是一个数据类型`bool`的Numpy数组,那么一个元素被选择(`True`)或否(`False`)取决于索引掩码在每个元素位置的值:" ] }, { @@ -2025,7 +2025,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "使用diag函数,我们还可以提取一个数组的对角线和亚对角线:" + "使用diag函数,可以提取一个数组的对角线和亚对角线:" ] }, { @@ -2105,7 +2105,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们可以使用常用的算术运算符来对标量数组进行乘、加、减和除运算。" + "可以使用常用的算术运算符来对标量数组进行乘、加、减和除运算。" ] }, { @@ -2202,7 +2202,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "当我们对数组进行加法、减法、乘法和除法时,默认的行为是**element-wise**操作:" + "对数组进行加法、减法、乘法和除法时,默认的行为是**element-wise**操作:" ] }, { @@ -2253,7 +2253,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "如果我们用兼容的形状进行数组的乘法,我们会得到每一行的对位相乘结果:" + "如果用兼容的形状进行数组的乘法,会得到每一行的对位相乘结果:" ] }, { @@ -2409,7 +2409,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "另外,我们可以将数组对象投到`matrix`类型上。这将改变标准算术运算符`+, -, *` 的行为,以使用矩阵代数。" + "另外,可以将数组对象投到`matrix`类型上。这将改变标准算术运算符`+, -, *` 的行为,以使用矩阵代数。" ] }, { @@ -2517,7 +2517,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "如果我们尝试用不相配的矩阵形状加,减或者乘我们会得到错误:" + "如果尝试用不相配的矩阵形状加,减或者乘则会得到错误:" ] }, { @@ -2643,7 +2643,7 @@ "metadata": {}, "source": [ "#### 数据统计\n", - "通常将数据集存储在Numpy数组中是非常有用的。Numpy提供了许多函数用于计算数组中数据集的统计。\n", + "通常将数据集存储在Numpy数组中是非常有用的,Numpy提供了许多函数用于计算数组中数据集的统计。\n", "\n", "例如,让我们从上面使用的斯德哥尔摩温度数据集计算一些属性。" ] @@ -2957,9 +2957,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们可以使用索引、花式索引和从数组中提取数据的其他方法(如上所述)来计算数组中的数据子集。\n", + "可以使用索引、花式索引和从数组中提取数据的其他方法(如上所述)来计算数组中的数据子集。\n", "\n", - "例如,让我们回到温度数据集:" + "例如,针对温度数据集,进行处理。" ] }, { @@ -2987,7 +2987,7 @@ "source": [ "数据集的格式是:年,月,日,日平均气温,低,高,位置。\n", "\n", - "如果我们对某个特定月份的平均温度感兴趣,比如二月,然后我们可以创建一个索引掩码,使用它来选择当月的数据:" + "如果对某个特定月份的平均温度感兴趣,比如二月,可以创建一个索引掩码,使用它来选择当月的数据:" ] }, { @@ -3052,7 +3052,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "有了这些工具,我们就有了非常强大的数据处理能力。例如,提取每年每个月的平均气温只需要几行代码:" + "有了这些工具,就拥有了非常强大的数据处理能力。例如,提取每年每个月的平均气温只需要几行代码:" ] }, { @@ -3484,7 +3484,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "当矩阵乘法的时候,需要两个矩阵的对应的纬度保持一致才可以正确执行,有了`newaxis`,我们可以在数组中插入新的维度,例如将一个向量转换为列或行矩阵:" + "当矩阵乘法的时候,需要两个矩阵的对应的纬度保持一致才可以正确执行,有了`newaxis`,可以在数组中插入新的维度,例如将一个向量转换为列或行矩阵:" ] }, { @@ -4228,7 +4228,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "正如前面多次提到的,为了获得良好的性能,我们应该尽量避免对向量和矩阵中的元素进行循环,而应该使用向量化算法。将标量算法转换为向量化算法的第一步是确保我们编写的函数使用向量输入。" + "正如前面多次提到的,为了获得良好的性能,我们应该尽量避免对向量和矩阵中的元素进行循环,而应该使用向量化算法。将标量算法转换为向量化算法的第一步是确保编写的函数使用向量输入。" ] }, { @@ -4279,7 +4279,7 @@ "source": [ "这个操作并不可行,因为所实现的 `Theta` 函数不能接收向量输入。\n", "\n", - "为了得到向量化的版本,我们可以使用Numpy函数 `vectorize` 。在许多情况下,它可以自动向量化一个函数:" + "为了得到向量化的版本,可以使用Numpy函数 `vectorize` 。在许多情况下,它可以自动向量化一个函数:" ] }, { @@ -4317,7 +4317,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们也可以实现从一开始就接受矢量输入的函数(需要更多的计算,但可能会有更好的性能):" + "也可以实现从一开始就接受矢量输入的函数(需要更多的计算,但可能会有更好的性能):" ] }, { @@ -4636,7 +4636,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.4" + "version": "3.7.9" } }, "nbformat": 4, diff --git a/1_numpy_matplotlib_scipy_sympy/2-matplotlib_tutorial.ipynb b/1_numpy_matplotlib_scipy_sympy/2-matplotlib_tutorial.ipynb index d22dc10..1f01bbf 100644 --- a/1_numpy_matplotlib_scipy_sympy/2-matplotlib_tutorial.ipynb +++ b/1_numpy_matplotlib_scipy_sympy/2-matplotlib_tutorial.ipynb @@ -450,7 +450,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.4" + "version": "3.7.9" } }, "nbformat": 4, diff --git a/1_numpy_matplotlib_scipy_sympy/4-scipy_tutorial.ipynb b/1_numpy_matplotlib_scipy_sympy/4-scipy_tutorial.ipynb index f7416fd..7211abc 100644 --- a/1_numpy_matplotlib_scipy_sympy/4-scipy_tutorial.ipynb +++ b/1_numpy_matplotlib_scipy_sympy/4-scipy_tutorial.ipynb @@ -7,29 +7,6 @@ "# SciPy - Library of scientific algorithms for Python" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "最新的[IPython notebook](http://ipython.org/notebook.html) 课程可以在这里找到: [http://github.com/jrjohansson/scientific-python-lectures](http://github.com/jrjohansson/scientific-python-lectures).\n", - "\n", - "其他的这个课程系列的笔记在这里[http://jrjohansson.github.io](http://jrjohansson.github.io)." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# 这一行的作用会在第四节讲到\n", - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "from IPython.display import Image" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -41,7 +18,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "SciPy框架建立在用于多维数组的低级NumPy框架之上,并提供了大量的高级科学算法。SciPy涵盖的一些主题是:\n", + "SciPy框架建立在用于多维数组的低级NumPy框架之上,并提供了大量的高级科学算法。\n", + "\n", + "![cover](images/scipy.png)\n", + "\n", + "SciPy涵盖的一些主题是:\n", "\n", "* Special functions ([scipy.special](http://docs.scipy.org/doc/scipy/reference/special.html))\n", "* Integration ([scipy.integrate](http://docs.scipy.org/doc/scipy/reference/integrate.html))\n", @@ -57,16 +38,26 @@ "\n", "这些子模块中的每一个都提供了许多可用于解决各自主题中的问题的函数和类。\n", "\n", - "在这节课中,我们将看看如何使用这些子包。\n", - "\n", "为了在Python程序中获得这些SciPy程序包,我们首先从调用`scipy`模块开始。" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# 这一行的作用会在第四节讲到\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "from IPython.display import Image" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ - "如果我们只使用SciPy框架的一部分,我们可以选择性地包含那些我们感兴趣的模块。例如,为了将线性代数包包含在`la`名词下,我们可以这样做:" + "如果只使用SciPy框架的一部分,可以选择性地包含那些我们感兴趣的模块。例如,为了将线性代数包包含在`la`名词下,可以这样做:" ] }, { @@ -77,7 +68,8 @@ }, "outputs": [], "source": [ - "import scipy.linalg as la" + "import scipy.linalg as la\n", + "\n" ] }, { @@ -91,7 +83,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "有很多数学的特殊函数对于很多计算物理问题都很重要。SciPy提供了一组非常广泛的特殊函数的实现。有关具体的细节,参见参考文档中的函数列表http://docs.scipy.org/doc/scipy/reference/special.html#module-scipy.special. \n", + "有很多数学的特殊函数对于很多计算物理问题都很重要。SciPy提供了一组非常广泛的特殊函数的实现。有关具体的细节,参见参考文档中的函数列表 http://docs.scipy.org/doc/scipy/reference/special.html#module-scipy.special. \n", "\n", "为了演示特殊函数的典型用法我们将会将会更多的讲到贝塞尔函数的细节:" ] @@ -2425,7 +2417,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.4" + "version": "3.7.9" } }, "nbformat": 4, diff --git a/1_numpy_matplotlib_scipy_sympy/5-sympy_tutorial.ipynb b/1_numpy_matplotlib_scipy_sympy/5-sympy_tutorial.ipynb index a7d925b..82cb4c6 100644 --- a/1_numpy_matplotlib_scipy_sympy/5-sympy_tutorial.ipynb +++ b/1_numpy_matplotlib_scipy_sympy/5-sympy_tutorial.ipynb @@ -7,27 +7,6 @@ "# Sympy - Python中的符号代数" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "这门课的最新版本[IPython notebook](http://ipython.org/notebook.html) 可以在这里获得[http://github.com/jrjohansson/scientific-python-lectures](http://github.com/jrjohansson/scientific-python-lectures).\n", - "\n", - "这节课其他的参考书可以在这里找到[http://jrjohansson.github.io](http://jrjohansson.github.io) 。" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -39,26 +18,29 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "有两个值得注意的Python计算机代数系统(CAS):\n", + "SymPy 是一个由 Python 语言编写的符号计算库。处理数学对象的计算称为符号计算,在符号计算中,数学对象是精确表示的,而不是近似的,未计算的数学表达式会以符号形式保留;与符号计算相对应的是数值计算。\n", + "\n", + "![cover](images/sympy.png)\n", + "\n", + "有两个比较有名的Python计算机代数系统(CAS):\n", "\n", "* [SymPy](http://sympy.org/en/index.html) - 这是一个python模块可以被用在任意的Python程序或者是IPython会话中,它提供了强大的计算机代数系统(CAS)特征。\n", "* [Sage](http://www.sagemath.org/) - Sage 是一个全功能的且非常强大的CAS环境,它的目的是提供一个与Mathematica和Maple竞争的开源系统。Sage并不是一个常规的Python模块,而是一个CAS环境用Python作为其编程语言。\n", "\n", "Sage在某些方面比SymPy更加强大,但是他们都提供非常完善的CAS功能。SymPy的优点是,它是一个常规的Python模块而且和IPython notebook集成的很好。\n", "\n", - "在这个课上我们将会学会如何运用SymPy和IPython notebooks。如果你对CAS开源环境感兴趣,我也推荐你去阅读更多关于Sage的内容。\n", - "\n", "为了开始在Python程序或笔记本中使用SymPy,首先导入模块`sympy`:" ] }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, + "execution_count": 1, + "metadata": {}, "outputs": [], "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "\n", "import sympy as sp" ] }, @@ -96,7 +78,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "在SymPy中我们需要为需要处理的变量创造符号。我们可以创建一个新的符号用`Symbol`类:" + "在SymPy中需要为需要处理的变量定义为符号,可以创建一个新的符号用`Symbol`类:" ] }, { @@ -171,7 +153,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们可以给符号加上假设当我们创造他们的时候:" + "在定义符号的时候,可以给其设置属性,例如:" ] }, { @@ -440,9 +422,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "SymPy使用任意精度的库作为数值后端,而且预定义了许多数学常数,例如:`pi`, `e`,和用`oo`代表无限。\n", + "`SymPy`使用任意精度的库作为数值后端,而且预定义了许多数学常数,例如:`pi`, `e`,和用`oo`代表无限。\n", "\n", - "为了数值地衡量一个表达,我们可以用`evalf`方程(或者`N`)。它使用了一个参数`n`确定了有效数字的数量。" + "为了数值地衡量一个表达,可以用`evalf`方程(或者`N`),它使用了一个参数`n`确定了有效数字的数量。" ] }, { @@ -509,7 +491,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "当我们数值地衡量代数表达式,我们通常希望带入一个具有数值的符号。在SymPy中我们用`subs`方程来这样做:" + "当给符号赋予一个确定的数值的,可以使用 `subs` 函数:" ] }, { @@ -597,7 +579,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们也可以将表达式的数值演化和NumPy数组结合:" + "也可以将表达式的数值演化和NumPy数组结合:" ] }, { @@ -661,7 +643,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "然而,这个类型的数值演化会是非常慢的,有一种非常有效的方式去做:使用函数`lambdify`去“编译”一个SymPy表达并代入函数再进行数值计算是非常高效的。" + "然而,这个类型的数值计算会是非常慢的,有一种非常有效的方式去做:使用函数 `lambdify` 去“编译”一个SymPy表达并代入函数再进行数值计算是非常高效的。" ] }, { @@ -691,7 +673,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "在使用“speedup”函数而不是直接的进行数值计算时的加速是非常重要的,通常相差几个数量级。即使实在简单的例子中我们也会得到一个明显的加速:" + "在使用上述加速的实现,而不是直接的进行数值计算时的加速是非常重要的,通常相差几个数量级。即使在简单的例子中也会得到一个明显的加速:" ] }, { @@ -743,7 +725,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "CAS的一个主要用处是执行表达的代数操作。例如,我们可能想要展开一个乘积,一个表达式的因式,或者只是一个表达式。在本节中演示了在SymPy中进行这些基本操作的功能。" + "CAS的一个主要用处是执行表达的代数操作。例如,我们可能想要展开一个乘积,一个表达式的因式,或者只是一个表达式。在本节中演示SymPy中进行这些基本操作的功能。" ] }, { @@ -813,7 +795,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "`expand`函数有一些关键字参数,我们可以告诉函数我们想要执行什么样的扩展。例如,为了扩展三角函数表达式,用`trig=True`的关键字参数:" + "`expand`函数有一些关键字参数,可以告诉函数我们想要执行什么样的扩展。例如,为了扩展三角函数表达式,用`trig=True`的关键字参数:" ] }, { @@ -913,9 +895,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "`simplify`尝试使用不同的技巧,去将表达简化到易懂的形式。也有很多可以替代`simplify`的函数:`trigsimp`, `powsimp`, `logcombine`等等。\n", - "\n", - "这些函数的基本用法如下:" + "`simplify`尝试使用不同的技巧,去将表达简化到易懂的形式。也有很多可以替代`simplify`的函数:`trigsimp`, `powsimp`, `logcombine`等等,其基本用法如下:" ] }, { @@ -1005,7 +985,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "为了处理分数的符号表达式,我们可以用`apart`和`together`函数:" + "为了处理分数的符号表达式,可以用`apart`和`together`函数:" ] }, { @@ -1192,7 +1172,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "微分通常是简单的,用`diff`函数。第一个参数是求导的表达式,第二个参数是求导的符号:" + "微分通常在sympy中比较简单,可以用`diff`函数,第一个参数是求导的表达式,第二个参数是求导的符号:" ] }, { @@ -1249,7 +1229,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "对于高阶导数我们可以这样:" + "对于高阶导数可以这样:" ] }, { @@ -1306,7 +1286,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "为了计算多变量表达的导数,我们可以这样做:" + "为了计算多变量表达的导数,可以这样做:" ] }, { @@ -1432,7 +1412,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "通过提供积分变量的极限,我们可以计算定积分:" + "通过提供积分变量的极限,可以计算定积分:" ] }, { @@ -1510,7 +1490,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们可以计算加数和乘积使用函数:'Sum'" + "可以计算加数和乘积使用函数:`Sum`" ] }, { @@ -1682,7 +1662,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们可以用`limit`去检查`diff`函数的推导结果:" + "可以用`limit`去检查`diff`函数的推导结果:" ] }, { @@ -1779,7 +1759,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "我们可以改变方向,从我们接近极限点使用`dir`关键字参数:" + "可以改变方向,从接近极限点使用`dir`关键字参数:" ] }, { @@ -1841,7 +1821,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "系列扩展也是CAS最有用的特性之一。在SymPy中,我们可以用`series` 函数对表达式进行级数展开:" + "系列扩展也是CAS最有用的特性之一。在SymPy中,可以用`series` 函数对表达式进行级数展开:" ] }, { @@ -1875,7 +1855,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "默认情况下,它在$x=0$附近扩展表达式,但是我们可以通过在函数调用中显式包含一个值来扩展$x$的任何值:" + "默认情况下,它在$x=0$附近扩展表达式,但是可以通过在函数调用中显式包含一个值来扩展$x$的任何值:" ] }, { @@ -1953,7 +1933,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "级数展开式包含了近似的阶数,当我们对不同阶数的级数展开式进行计算时,这对于跟踪有效性的阶数非常有用:" + "级数展开式包含了近似的阶数,当对不同阶数的级数展开式进行计算时,这对于跟踪有效性的阶数非常有用:" ] }, { @@ -2039,7 +2019,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "如果我们想摆脱阶数信息,我们可以使用`removeO`方法:" + "如果想摆脱阶数信息,可以使用`removeO`方法:" ] }, { @@ -2121,7 +2101,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "使用`Matrix`类可以定义矩阵:" + "使用 `Matrix` 定义矩阵:" ] }, { @@ -2194,7 +2174,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "有`Matrix`类实例的基础上我们可以做常规的矩阵代数运算:" + "有`Matrix`,可以做常规的矩阵代数运算:" ] }, { @@ -2323,7 +2303,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "对于求解方程和方程组我们可以用`solve`函数:" + "对于求解方程和方程组可以用 `solve` 函数:" ] }, { @@ -2445,7 +2425,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 进一步的阅读" + "## 进一步学习" ] }, { @@ -2474,7 +2454,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.4" + "version": "3.7.9" } }, "nbformat": 4, diff --git a/1_numpy_matplotlib_scipy_sympy/images/scipy.png b/1_numpy_matplotlib_scipy_sympy/images/scipy.png new file mode 100644 index 0000000000000000000000000000000000000000..344b17e1b14d431cbbd9108d5fc03485ed9aa4fc GIT binary patch literal 149121 zcmbrlXH-+$7d@JU7K)Gn(nJUm1nC`=8VF60B8W8UO+b1tQl<9}(h-p+&4859q<5rA zZvxVLZ!g|^fB*O8z4zrM86(LV8T*{G_S$pLHRnp0s0}KYwEU7GFzCxU3w4BxL%$?ng9L)ggmM+fDW{xHS!}tII z44{BSXt+;rqZOPOr;@(74c492dqt*_Ne()h-`BR$to&#yboF+T@11FUe^!qY;k$1m 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