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2019年度シラバストップ > 高Ⅱ年8組 > 数学 > AP Calculus AB

教科
科目
学年・組
授業時間
担当者
数学
AP Calculus AB
高Ⅱ年8組
4hrs/ week
必修選択
Elliott

到達目標


The aim of the H2 AP Calculus AB course is for you to learn the fundamental techniques of differential and integral calculus, and to then use these techniques to solve real-world mathematics problems. Calculus is an essential tool for those students wishing to pursue a career in the sciences, particularly physics.

授業の進め方・学習方法


The course will consist of demonstrations of key points and examples by the teacher, followed by students working all practice problems from the relevant section in the textbook. Homework will be assigned each class for completion by the next scheduled class. A 50-minute term test will be conducted each term to help students prepare for examinations.

授業スケジュール


学期
学習内容
1学期
Chapter 1 - Limits and Their Properties
- 1.1 A Preview of Calculus
- 1.2 Finding Limits Graphically and Numerically
- 1.3 Evaluating Limits Analytically
- 1.4 Continuity and One-Sided Limits
- 1.5 Infinite Limits

Chapter 2 - Differentiation
- 2.1 The Derivative and the Tangent Line Problem
- 2.2 Basic Differentiation Rules and Rates of Change
- 2.3 Product and Quotient Rules and Higher-Order Derivatives
- 2.4 The Chain Rule
- 2.5 Implicit Differentiation
- 2.6 Related Rates
1学期中間試験
1学期
Chapter 3 - Applications of Differentiation
- 3.1 Extrema on an Interval
- 3.2 Rolle's Theorem and the Mean Value Theorem
- 3.3 Increasing and Decreasing Functions and the First Derivative Test
- 3.4 Concavity and the Second Derivative Test
- 3.5 Limits at Infinity
- 3.6 A Summary of Curve Sketching
1学期末試験


学期
学習内容
2学期
Chapter 3 - Applications of Differentiation
- 3.7 Optimization Problems
- 3.8 Newton’s Method
- 3.9 Differentials

Chapter 4 - Integration
- 4.1 Antiderivatives and Indefinite Integration
- 4.4 The Fundamental Theorem of Calculus
- 4.5 Integration by Substitution
- 4.6 Numerical Integration
2学期中間試験
2学期
Chapter 5 - Logarithmic, Exponential, and Transcendental Functions
- 5.1 The Natural Logarithmic Function: Differentiation
- 5.2 The Natural Logarithmic Function: Integration
- 5.3 Inverse Functions
- 5.4 Exponential Functions: Differentiation and Integration
- 5.5 Bases Other Than e and Applications
- 5.6 Inverse Trigonometric Functions: Differentiation
- 5.7 Inverse Trigonometric Functions: Integration
2学期末試験


学期
学習内容
3学期
Chapter 6 - Differential Equations
- 6.1 Slope Fields and Euler’s Method
- 6.2 Differential Equations: Growth and Decay
- 6.3 Separation of Variables and the Logistic Equation

Chapter 7- Applications of integrations
- 7.1 Area of a Region Between Two Curves
- 7.2 Volume: The Disk Method
学年末試験

成績評価方法


種別
割合(%)
評価基準など
定期試験
60
Midterm: 30%
Final: 30%
Homework: 20%
Term Tests: 10%
Notebook: 5%
Participation: 5%
レポート
20
小テストなど
10
授業での取り組み状況
10

教科書・教材/参考書/参考サイト


教科書・教材
書名
出版社
教科書番号/code
備考
Calculus of a Single Variable, Larson, 11th Edition
Cengage Learning
ISBN-13: 9781337286909

担当者からのアドバイス


Welcome to H2 mathematics! Math will be even more interesting and useful this year. You are expected to start taking more responsibility for your mathematical ability in order to become successful, independent math students. In H2 AP Calculus AB we will study the essentials of differential and integral calculus, so it very important you fully understand everything we study. If you feel you are struggling, please seek help early. My number one recommendation is to study a little bit each day, rather than cramming before the exam. Let's work hard and have a productive year. Let's learn to love math!