課程資訊

CALCULUS (2)

111-1

MATH4007

201 49820

15

2.0

Integration on functions of a single variable together with its profound applications in various subject areas are introduced in this half-semester course. Especially, this course includes the definition of integrals, the Fundamental Theorem of Calculus, techniques of integration, applications of integrals in probability, solving elementary differential equations and more. In addition to these, series and Taylor expansions are briefly introduced in the end of this course to explain how complicated functions are approximated by polynomials. Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sessions in which students are able to improve their skills in handling calculations in Calculus and complete small projects under the guidance of our teaching assistants.

Students would be familiar with Calculus as a tool and be able to apply it in Economics areas
after finishing this course.

Before taking this course, students should be already skilled in high school mathematics
and finish the online Precalculus Self Diagnostic Test which is designed for NTU freshmen.
Students are expected to attend and participate actively in lectures as well as discussion
sessions.

Office Hours

Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early
Transcendentals, 9th edition.

(僅供參考)

 No. 項目 百分比 說明 1. 期考 50% Time:12/24(Sat) 14:00~16:30 2. 小考 20% 11/17(Thu) 17:30-18:20 Quiz 1 (Range：5.1-5.5、6.1) 12/1(Thu) 17:30-18:20 Quiz 2 (Range：7.1-7.5、7.8) 12/15(Thu) 17:30-18:20 Quiz 3 (Range：8.5、9.1、9.3、9.5) 三次取最高兩次 3. Webwork 10% 請依webwork的期限完成，成績的部分將直接由系統計算 4. Worksheet 10% worksheet的內容會在演習課由助教講解。 11/17前將worksheet 1上傳至作業區，準時交最高3%，遲交1% 12/1前將worksheet 2上傳至作業區，準時交最高3%，遲交1% 12/15前將worksheet 3上傳至作業區，準時交最高3%，遲交1% 分數計算部分，完成度80%以上拿3分，50%-79%拿2分，49%以下1分。 三次都準時交者，可額外得到1%，學習單請自己完成，如有抄襲，以零分計算 5. 紙本作業 10% 題號請見課程內容，請自己完成，如有抄襲，以零分計算。每次2分，取最高5次。 6. 額外練習 0% 請見額外作業區

 上課形式 以錄影輔助 作業繳交方式 考試形式 其他 由師生雙方議定
 課程進度
 週次 日期 單元主題 第9週 11/1, 11/3 5.1 The Area and Distance Problems 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem 第10週 11/8, 11/10 5.5 The Substitution Rule 6.1 Areas Between Curves 6.5 Average Value of a Function Worksheet (Lorenz Curves and Gini Index) 第11週 11/15, 11/17 8.4 Applications to Economics (WS) 7.1 Integration by Parts 7.2 Trigonometric Integrals 11/17(Thu) 17:30-18:20 Quiz 1 (Range：5.1-5.5、6.1) 第12週 11/22, 11/24 7.3 Trigonometric Substitution 7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration Worksheet (Integrals in Economics) 第13週 11/29, 12/1 7.8 Improper Integrals 8.5 Probability(WS) 9.1 Modeling with Differential Equations 12/1(Thu) 17:30-18:20 Quiz 2 (Range：7.1-7.5、7.8) 第14週 12/6, 12/8 9.3 Separable Equations 9.5 Linear Equations Worksheet (Applications in Probability) 第15週 12/13, 12/15 11.9 Representation of Functions as Power Series 11.10 Taylor and Maclaurin Series 12/15(Thu) 17:30-18:20 Quiz 3 (Range：8.5、9.1、9.3、9.5) 第16週 12/20, 12/22 Review for the exam Exam:12/24(Sat) 14:00~16:30