AP®Calculus BC課程是大學第一學期的微積分課程和後續的單變量微積分課程。本課程的嚴謹和節奏與許多學院和大學的微積分課程一致，將幫助學生準備大學預修考試。成功完成考試後，學生可以獲得大學學分，並為額外的高等數學課程做好準備。
AP微積分BC建立在之前的數學課程工作的先驗知識上。學生將探討本課程所涵蓋的三大概念(1)變化、(2)極限和(3)函數分析。本課程讓學生通過討論、小組活動和調查來獲得概念上的理解。學生將學習如何使用圖形計算器來幫助解決問題，實驗，解釋結果，並支持結論。為了準備考試，學生將完成每周AP®練習小測驗和單元考試，這將符合AP®考試的限制。
這門AP®課程有一個必須的暑期作業。學生必須在課程開始前完成他們的暑期作業，並在第一周結束前提交作業。9月1日或之後註冊的學生將獲得延期，在第三周結束前完成暑期作業。暑期作業的目的是在適用的情況下，複習與課程的先決知識相關的關鍵內容，並讓學生更好地理解與內容相關的嚴謹性。
用變化率和局部線性逼近來解釋導數的意義，並使用導數來解決問題
解釋定積分作為黎曼和的極限和變化的淨累積的意義，並使用積分來解決問題
描述在微積分基本定理的兩部分中表示的導數和定積分之間的關係
口頭和書面表達數學並解釋問題的解決方案
用函數、微分方程或積分對物理情況的書面描述
利用技術解決問題、實驗、解釋結果和支持結論
確定解決方法的合理性，包括符號、尺寸、相對精度和測量單
秋季2020年9月2日開始，換課、退課限9月8日前
平均每周學習時間10-12小時
每周完成閱讀要求，參與課堂討論，提交作業
學生學過代數、幾何、三角、解析幾何和初等函數等內容。學生應熟悉這些初等函數的性質，包括線性函數linear、多項式函數polynomial、有理函數rational、指數函數exponential、對數函數logarithmic、三角函數trigonometric、反三角函數inverse trigonometric、分段定義函數piecewise-defined function。
學生自備圖形計算器graphing calculator ，推薦型號TI-83/TI-84。
CollegeBoard
NACC
Cognia (AdvancED)
Middle States Commission on Secondary Schools
86%的教師擁有7年以上一線教學經驗，81%的教師擁有碩士以上學位，每位教師都修完在線教學方法課程（ Online Teaching Methodologies ）。OTM是一門研究生水平的在線課程，側重於在在線課堂中建立社區、促進有意義的討論和提供有洞察力的反饋的教學策略。
本課程結合了傳統的教師主導的、小班教學的優點，同時保持了進度靈活性。每學期的課程遵循Weekly Paced 每周進度的模式，學生選擇自己最適合的時間學習，但必須每周完成指定工作量，與小組同學和老師保持溝通。
UNIT 1: Limits and Continuity
Week 1: Introduction to AP® Calculus BC
Week 2: Continuity and Limits of Trigonometric, Exponential, and Logarithmic Functions
Week 3: Infinite Limits, Limits at Infinity, and Asymptotes
UNIT 2: Differentiation – Definition and Fundamental Properties
Week 4: Rates of Change; the Derivative; Derivatives of Polynomial Functions and the Natural Exponential Function
Week 5: Product Rule and Quotient Rule; Higher-Derivatives; and Derivatives of Trigonometric Functions
UNIT 3: Differentiation – Composite, Implicit, and Inverse Functions
Week 6: The Chain Rule and Implicit Differentiation
Week 7: Derivatives of the Inverse Trigonometric Functions and Logarithmic Functions
UNIT 4: Contextual Applications of Differentiation
Week 8: Interpreting a Derivative; Differentials; Linear Approximations; and Newton’s Method
Week 9: Related Rates; Indeterminate Forms and L』Hopital’s Rule
UNIT 5: Analytical Applications of Differentiation
Week 10: Maximum and Minimum Values; Critical Numbers; Mean Value Theorem
Week 11: Local Extrema and Concavity; Using Calculus to Graph Functions
Week 12: Optimization; Antiderivatives; Differential Equations
UNIT 6: Integration and Accumulation
Week 13: Area and the Definite Integral
Week 14: The Fundamental Theorem of Calculus; Properties of the Definite Integral
Week 15: Midterm Exam; Indefinite Integral; Substitution Method; Integration by Parts
Week 16: Integrals Containing Trigonometric Functions; Integration Using Trigonometric Substitution
Week 17: Integration Using Long Division and Partial Fractions
Week 18: Approximating Integrals; Improper Integrals
UNIT 7: Differential Equations
Week 19: Ordinary Differential Equations; Separable First-Order Differentiable Equations; Slope Fields
Week 20: Euler’s Method and the Logistic Model
Unit 8: Applications of Integration
Week 21: Area Between Graphs; Volume of a Solid of Revolution – Disks and Washers
Week 22: Volume of a Solid of Revolution – Cylindrical Shells; Volume of a Solid – Slicing
Week 23: Arc Length and Work
Unit 9: Parametric Equations; Polar Coordinates; and Vector Functions
Week 24: Parametric Equations; Tangent Lines; Arc Length
Week 25: Polar Equations; Parametric Equations of Polar Equations; Area in Polar Coordinates
Week 26: Derivatives and Integrals of Vector Functions
UNIT 10: Infinite Sequences and Series
Week 27: Sequences; Infinite Series; Properties of Series
Week 28: Comparison Tests; Alternating Series; Absolute Convergence
Week 29: Ratio and Root Tests; Summary of Tests; Power Series
Week 30: Taylor Series; Maclaurin Series; Taylor Polynomial Approximations
UNIT 11: AP® Review, Practice AP® Exam, and Final Project
Week 31: Introduction to Final Project; Practice AP® Exam
Week 32: Final Project
Week 33: Final Presentations
eText Title/Name: Calculus for the AP® Course
eText ISBN: 9781319248802
Publisher: BFW Publishers
Author: Michael Sullivan; Kathleen Miranda
Edition/Date: Third Edition, 2020
報名 15601221714
掃碼，請註明課程名、學生名