微积分英文专业术语

Question

我需要比较全的（最好A~z）我学AP课程老师要 O(∩_∩)O谢谢你们帮助
地址是qq邮箱

Answer 1

下面提供AP最常用的微积分词汇，如果需要翻译，请Hi我：
antiderivative 原函数
a representation, usually in symbolic form, of any function whose derivative is a given function.

tangent 切线，斜率，正切
a line or a plane that touches a curve or a surface at a single point.

chain rule 链式求导法
the theorem that defines the method for taking the derivative of a composite function.

concave downward 向下开口
part of a graph resembling an upside down bowl.

concave upward 向上开口
part of a graph resembling a right side up bowl.

continuous 连续
being in immediate connection or spatial relationship.

critical point 临界点
point on the graph where the derivative is either 0 or undefined.

cylindrical shell method 旋转体积圆筒积分法
technique for finding the volume of a solid of revolution.

definite integral 定积分
the representation of the difference in values of a primitive of a given function evaluated at two designated points.

derivative 导数，求导，导函数
the change of a function with respect to an infinitesimally small change in the independent variable, or the slope of the point's tangent line.

differentiable 可导的，可微的
a function whose graph is curve that is smooth and contains no discontinuities or cusps.

disk method 旋转体积圆盘法
technique for finding the volume of a solid of revolution when integrating along the axis of revolution.

extreme value theorem 极值理论
guarantees an absolute max and an absolute min

first derivative test 极值点、拐点的确定法
determines whether an inflection point is a minimum, maximum, or neither.

higher order derivatives 高阶导数，高阶导函数
any derivatives beyond the first derivative.

implicit differentiation 隐函数求导、微分
method for finding the derivative of an implicitly defined function or relation using the chain rule.

indefinite integral 不定积分
another way of saying antiderivative.

instantaneous rate of change 瞬时牵连变化率、相关变化率
rate of change at a particular moment.

instantaneous velocity 瞬时速度
rate at which an object is moving at a particular moment.

integration by parts 分部积分
a method of evaluating an integral by use of the formula, ∫udv = uv − ∫vdu.

limit 极限
value that a function approaches as the domain variable approach a specific value.

mean value theorem 中值定理
the theorem that there is a point in a continuous curve where the derivative is equal to the average derivative of the entire arc.

normal line 法线
line that is at a 90 degree angle, perpendicular to a surface.

point-slope form 直线方程点斜式
form used the most when finding the equation of a line.

riemann sum 黎曼积分
method for approximating the definite integral.

second derivative test 用二阶导数检查是否是极大值点或极小值点
determines whether a critical point is a relative minimum or maximum using the value of the second derivative at the point.

u-substitution U型变量代换
integration method that involves using the chain rule in reverse.

trigonometric substitution 三角函数变量代换
substitution of trigonometric functions for other expressions to eliminate radicals in integrals.

washer method 旋转体积的圆筒积分法
similar to the disk method but using washers instead of disks.