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1、单元知识知识点知识点说明precalculus（微积分预备）functions（函数）functions and their graphs函数和函数图像，微积分必备基础linear and quadratic functions一次函数与二次函数，国内初中内容polynomial and rational functions多项式函数与有理函数，因式分解部分国内初中曾学过exponential and logarithmic functions指数函数与对数函数，学生需学会使用计算器进行计算，重视实际运用。trigonometric functions三角函数，除了正余弦、正切余切函数，还要求
2、掌握正割余割polar coordinates（极坐标）polar coordinates and graphs极坐标与图像，需掌握极坐标与普通坐标的互相转换the complex plane复平面，重点是复数的三角形式与极坐标形式的互相转换the demoivres theoremdemoivre定理，复数计算法则vectors（向量）the dot product向量内积，模长的求法，根据坐标求向量夹角，向量投影的计算方法the cross product向量外积的坐标运算，比较容易记错vector in space空间向量analytic geometry（解析几何）conics圆锥曲线
3、the parabola抛物线the ellipse椭圆the hyperbola双曲线polar equations of conics圆锥曲线的极坐标方程systems of equations and inequalities（方程组与不等式组）substitution and elimination代入消元法matrices矩阵，高斯消元法解方程组determinants行列式，三阶以内行列式的计算systems of nonlinear inequations非线性方程组systems of inequations不等式组，一元不等式组linear programming线性规划，用
4、线性规划解决实际问题sequences induction （数列、数学归纳法）arithemetic sequences and series等差数列，通项公式和求和公式geometric sequences and series等比数列，通项公式和求和公式binomial theorem二项式定理mathematical induction数学归纳法counting and probability（计数原理和排列组合）counting计数原理permutuations and combinations排列组合probability概率calculus（微积分-先修课程）limits and
5、 rates of changethe limit of a function函数的极限one-sided limits单边极限velocity and other rates of change极限的运用：速度和变化率infinite sequences无限级数infinite series无限数列derivativesthe power rule多项式求导the sum and difference rules函数和与差的求导法则the product rule函数乘积的求导法则the quotient rule函数商的求导法则the chain rule复合函数求导法则implicit
6、differentiation隐函数微分higher derivatives高阶导数integralsthe definite integral积分的定义the fundamental theorem of calculus微积分基本定义the substitution rule代换法integration by parts分布积分法trigonometric substitution三角代换法extreme valuesincrasing and decreasing functions函数单调性maximum and minimum values最大最小值applied maximum a
7、nd minimum problems最值问题的应用trigonometric functions and their derivativestrigonometric formulas三角公式trigonometric identities三角恒等式solving trgonometric equations解三角方程derivatives of sine and cosine functions正弦函数与余弦函数的求导derivatives of other trigonometric functions其他三角函数的求导applications三角函数微分的应用exponential and logarithmic functions and their derivativesexponential functions指数函数derivatives of exponential functions指数函数求导logarithmetic functions对数函数derivatives of logarithmetic functions对数函数求导exponential growth and decay指数增长指数衰减模型logarithmic differentiation对数微分