一本数学书的英语 (含例句)

1. 数学符号和术语

数学书的英语中包含了大量的数学符号和术语，需要学生掌握。

例句：

- The square root of 2 is an irrational number.

- The equation y = mx + b represents a line in slope-intercept form.

- The derivative of a function f(x) is denoted by f'(x).

- The Pythagorean theorem states that a² + b² = c².

- The area of a circle is pi times the radius squared.

2. 独特的语法结构

数学书的英语使用了一些独特的语法结构和句型，需要学生掌握和理解。

例句：

- If a line intersects two parallel lines, then corresponding angles are congruent.

- The limit of a function as x approaches a is denoted by lim x→a f(x).

- A function f(x) is continuous at x = c if and only if the limit of f(x) as x approaches c exists and is equal to f(c).

- A matrix is a rectangular array of numbers, usually enclosed in brackets.

- A polynomial is a sum of terms, where each term consists of a coefficient and a variable raised to a power.

3. 阅读理解和推理

数学书的英语不仅要求学生具备基本的阅读理解能力，还需要学生能够进行推理和推导。

例句：

- Given that angle A is congruent to angle B and angle B is congruent to angle C, we can conclude that angle A is congruent to angle C.

- If a function is odd, then f(-x) = -f(x) for all x in the domain of the function.

- The Fundamental Theorem of Calculus states that if F(x) is an antiderivative of f(x), then the definite integral from a to b of f(x) dx is equal to F(b) - F(a).

- A system of linear equations can be solved using matrix algebra.

- The Intermediate Value Theorem states that if a function is continuous on a closed interval [a,b], and f(a) and f(b) have opposite signs, then there exists at least one value c in the interval (a,b) such that f(c) = 0.

翻译例句：

- 平方根2是无理数。

- 方程y=mx+b表示连结斜率和截距的直线。

- 函数f(x)的导数用f'(x)表示。

- 毕达哥拉斯定理规定a² + b² = c²。

- 圆的面积是半径的平方乘以π。

- 如果一条线与两条平行线相交，则对应角相等。

- 函数f(x)在x=c处连续当且仅当f(x)当x趋于c时存在极限并且等于f(c)。

- 系数和变量的幂次之和构成的项的和即为一个多项式。

- 如果一个函数是奇函数，则对于函数定义域中的所有x，f(-x)=-f(x)。

- 计算基本定理规定，如果F(x)是f(x)的原函数，则从a到b的定积分f(x)dx等于F(b)-F(a)。