# 微积分网课代修|AP微积分代写AP calculus辅导|MT600A/MT600B THE COURSES

• 单变量微积分
• 多变量微积分
• 傅里叶级数
• 黎曼积分
• ODE
• 微分学

## 微积分网课代修|AP微积分代写AP calculus辅导|THE COURSES

Calculus $\mathrm{AB}$ and $\mathrm{BC}$ are both full-year courses in the calculus of functions of a single variable. Both courses emphasize:
(1) student understanding of concepts and applications of calculus over manipulation and memorization;
(2) developing the student’s ability to express functions, concepts, problems, and conclusions analytically, graphically, numerically, and verbally, and to understand how these are related; and
(3) using a graphing calculator as a tool for mathematical investigations and problem-solving.

Both courses are intended for students who have already studied college-preparatory mathematics: algebra, geometry, trigonometry, analytic geometry, and elementary functions (linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise). The $\mathrm{AB}$ topical course outline that follows can be covered in a full high-school academic year even if some time is allotted to studying elementary functions. The BC course assumes that students already have a thorough knowledge of all the topics noted above.

## 微积分网课代修|AP微积分代写AP calculus辅导|TOPICS THAT MAY BE TESTED ON THE CALCULUS AB EXAM

1. Functions and Graphs
Rational, trigonometric, inverse trigonometric, exponential, and logarithmic functions.
2. Limits and Continuity
Intuitive definitions; one-sided limits; functions becoming infinite; asymptotes and graphs; limit of a quotient; $\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}$; estimating limits using tables or graphs.Definition of continuity; kinds of discontinuities; theorems about continuous functions; Extreme Value and Intermediate Value Theorems.
1. Differentiation
Definition of derivative as the limit of a difference quotient and as instantaneous rate of change; derivatives of power, exponential, logarithmic, trig and inverse trig functions; product, quotient, and chain rules; differentiability and continuity; estimating a derivative numerically and graphically; implicit differentiation; derivative of the inverse of a function; the Mean Value Theorem; recognizing a given limit as a derivative.
2. Applications of Derivatives
Rates of change: slope; critical points; average velocity; tangents and normals; increasing and decreasing functions; using the first and second derivatives for the following: local (relative) max or min, inflection points, curve sketching, global (absolute) max or min and optimization problems; relating a function and its derivatives graphically; motion along a line; local linearization and its use in approximating a function; related rates; differential equations and slope fields.
3. The Definite Integral
Definite integral as the limit of a Riemann sum; area; definition of definite integral; properties of the definite integral; Riemann sums using rectangles or sums using trapezoids; comparing approximating sums; average value of a function; Fundamental Theorem of Calculus; graphing a function from its derivative; estimating definite integrals from tables and graphs; accumulated change as integral of rate of change.
4. Integration
Antiderivatives and basic formulas; antiderivatives by substitution; applications of antiderivatives; differential equations; motion problems.
5. Applications of Integration to Geometry
Area of a region, including between two curves; volume of a solid of known cross section, including a solid of revolution.
6. Further Applications of Integration and Riemann Sums
Velocity and distance problems involving motion along a line; other applications involving the use of integrals of rates as net change or the use of integrals as accumulation functions; average value of a function over an interval.
7. Differential Equations
Basic definitions; geometric interpretations using slope fields; solving first-order separable differential equations analytically; exponential growth and decay.

## 微积分网课代修| AP微积分代写AP calculus辅导| THE COURSES

（1）学生对微积分概念和应用的理解，而不是操纵和记忆;
（2）培养学生以分析，图形，数字和口头方式表达功能，概念，问题和结论的能力，并理解这些功能，概念，问题和结论之间的关系;
（3）使用图形计算器作为数学调查和解决问题的工具。

## 微积分网课代修| AP微积分代写AP calculus辅导| TOPICS THAT MAY BE TESTED ON THE CALCULUS AB EXAM

1. 函数和图形有理函数
、三角函数、反三角函数、指数函数和对数函数。
2. 限制和连续性
直观的定义;片面限制;函数变得无限;渐近线和图形;商的极限;limi→0sini i i;使用表格或图形估计极限。连续性的定义;不连续性的种类;关于连续函数的定理;极值和中间值定理。
1. 微分
导数的定义是差商的极限和瞬时变化率;幂、指数、对数、三角函数和反三角函数的导数;产品、商和链规则;可微性和连续性;以数字和图形方式估计导数;隐性分化;函数逆的导数;均值定理;将给定的极限识别为导数。
2. 衍生品
变化率的应用：斜率;关键点;平均速度;切线和法线;增加和减少功能;将第一导数和第二导数用于以下值：局部（相对）最大值或最小值，拐点，曲线草绘，全局（绝对）最大值或最小值和优化问题;以图形方式关联函数及其导数;沿直线的运动;局部线性化及其在近似函数中的应用;相关费率;微分方程和斜率场。
3. 定积分
定积分 作为黎曼和的极限;面积;定积分的定义;定积分的性质;黎曼使用矩形求和或使用梯形求和;比较近似和;函数的平均值;微积分基本定理;从其导数绘制函数;从表格和图形中估计确定的积分;累积变化作为变化率的积分。
4. 整合
反导数和基本公式;通过替代进行反导数;抗衍生物的应用;微分方程;运动问题。
5. 积分在一个区域的几何
区域中的应用，包括两条曲线之间的应用;已知横截面的固体的体积，包括旋转的固体。
6. 积分和黎曼求和
速度和距离问题的进一步应用涉及沿线的运动;涉及使用汇率积分作为净变化或使用积分作为累积函数的其他应用;函数在某个区间内的平均值。
7. 微分方程
基本定义;使用斜率场的几何解释;解析求解一阶可分微分方程;指数增长和衰减。