W01: 2/14
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### `基本概念`
>`print()`：函數
>`()`：內容為參數

>`=`：指定
>`x=9`：9指定給x變數

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### [Python數學運算符 (Python Operators)](https://www.w3schools.com/python/python_operators.asp)

#### Python算術運算符 (Python Arithmetic Operators)
算術運算符與數值一起使用以執行常見的數學運算：

| Operator | Name | Description | Example |
| -------- | -------------- | ----------- | ------- |
| `+` | Addition | 求和 | `x+y` |
| `-` | Subtraction | 求差 | `x-y` |
| `*` | Multiplication | 求積 | `x*y` |
| `/` | Division | 求商 | `x/y` |
| `%` | Modulus | 求餘 | `x%y` |
| `**` | Exponentiation | 次方 | `x**y` |
| `//` | Floor division | 整數商 | `x//y` |

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#### Python 賦值運算符 (Python Assignment Operators)
賦值運算符用於為變數賦值：

| Operator | Example | Same as |
| -------- | --------- | ------------ |
| `=` | `x = 5` | `x = 5` |
| `+=` | `x += 3` | `x = x + 3` |
| `-=` | `x -= 3` | `x = x - 3` |
| `*=` | `x *= 3` | `x = x * 3` |
| `/=` | `x /= 3` | `x = x / 3` |
| `%=` | `x %= 3` | `x = x % 3` |
| `**=` | `x **= 3` | `x = x ** 3` |
| `//=` | `x //= 3` | `x = x // 3` |

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#### Python 比較運算符 (Python Comparison Operators)

| Operator | Name | Description | Example |
| -------- | ------------------------ | ----------- | ------- |
| `==` | Equal | 等於 | `x == y` |
| `!=` | Not equal | 不等於 | `x != y` |
| `>` | Greater than | 大於 | `x > y` |
| `<` | Less than | 小於 | `x < y` |
| `>=` | Greater than or equal to | 不小於 | `x >= y` |
| `<=` | Less than or equal to | 不大於 | `x <= y` |

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#### Python 邏輯運算符 (Python Logical Operators)

| Operator | Description | Example |
| -------- | ---------------------------------- | ----------------------- |
| `and` | 若兩式皆為真，則回報 True | `x < 5 and x < 10` |
| `or` | 若兩式其一為真，則回報 True | `x < 5 or x < 4` |
| `not` | 反轉結果，若結果為真，則回報 False | `not(x < 5 and x < 10)` |

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### 範例：數學公式初體驗

以下範例的參考來源：https://acupun.site/lecture/python_math/index.htm#exp3_7

#引用現成的模組
from sympy import symbols, Eq, solve

x = symbols('x')

#一元多項式，相乘，展開
f = poly((x+1)*(x+1)*(x+1))
print(f)
display(f)

#二元多項式
x,y = symbols('x y')
f = poly('(x+2*y+3)**2')
display(f)

#Ex1：二元一次方程式聯立求解
from sympy import *
x, y = symbols('x y')
#二元一次聯立方程式
f1 = Eq(x + 2*y - 8, 0)
f2 = Eq(2*x - y - 6, 0)

solve((f1,f2),(x,y))

#求解兩條線的交叉點(solve(f1,f2))
p1 = None
p1 = plot_implicit(f1,show=False)
p2 = plot_implicit(f2,show=False)
p1.extend(p2)
p1.show()

print('解二元一次聯立方程式=', solve((f1,f2),(x,y)))

#Ex2：求微分，常見的幾類微積分函數基本公式
from sympy import *
x=symbols('x')
f = Function('f')(x)
#一階導數(對x) = 一階微分(對x) = diff(函數, x)
f = 1/x
print('求 y=1/x的微分=', diff(f, x))

f = 3*x**2 + 2*x + 5
print('求 y=3*x^2 + 2*x + 5的微分=', diff(f, x))

#常見的幾類微積分基本公式
f = sin(x)
print('求sin(x)的微分=', diff(f, x))
f = cos(x)
print('求cos(x)的微分=', diff(f, x))

#標準指數e的微分
f = E**x
print('求E**x的微分=', diff(f, x))
f = exp(x)
print('求exp(x)的微分=', diff(f, x))

#自然對數e的微分
#自然對數 = ln()
#10為底的對數 = log()
f = ln(x)
print('求自然對數ln(x)的微分=', diff(f, x))

#多項式的微分
#如果方程式有未知參數n,就必須要加上''
f = 'x**n'
print('求x**n的微分=', diff(f, x))
f = x**5
print('求x**5的微分=', diff(f, x))