課程資訊

CALCULUS (2)

109-1

MATH4007

201 49820

05

2.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1091MATH4007_05

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, finding areas and volumes, solving elementary differential equations and more.
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 make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.

Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus 1, 2, 3, 4" provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations.

Students participating in the course should be already skilled in high school mathematics. They 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% 1/9(六) 09:00~11:30 2. 小考1 20% 暫定 第14週 舉行 3. 小考2 20% 暫定 第17週 舉行 4. WeBWorK作業 10%

 課程進度
 週次 日期 單元主題 第9週 11/09,11/10,11/12 11/10: 5.2 The Definite Integral and 5.3 The Fundamental Theorem of Calculus 11/12: 5.4, 5.5 the substitution rule, and the area of the region enclosed by a circle ============================ 5.1 The Area and Distance Problems 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 11/13(五) 微積分2退選截止 第10週 11/16,11/17,11/19 11/17: 6.1 Areas Between Curves, 6.2 Volumes (by slicing and by disk method), and the beginning of 6.3 Volumes by Cylindrical Shells 11/19: 6.3, 6.5, and 7.1 ============================== 5.4 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule 第11週 11/23,11/24,11/26 11/24: Reduction formulas and 7.2 11/26: 7.2, 7.3, and 7.4 (the case of distinct linear factors) =============== 6.1 Areas Between Curves 6.2 Volumes 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function 第12週 11/30,12/01,12/03 12/01: 7.4 Integration of Rational Functions by Partial Fractions 12/03: 7.5 and 7.8 (type 1 improper integrals) ===================================== 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 第13週 12/07,12/08,12/10 12/08: 7.8 Tests by comparison, limit comparison, and its extension 12/10: Absolute convergence, more examples, linear differential equations, and 8.1 arc length ============== 7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration 7.8 Improper Integrals 第14週 12/14,12/15,12/17 12/15: 8.1 Arc Length and 8.2 Area of a Surface of Revolution 12/17: 9.1, 9.3, and 9.5 =============================== 9.1 Modeling with Differential Equations 9.3 Separable Equations 第15週 12/21,12/22,12/24 12/22: 10.1 and 10.2 12/24: 10.2 curvature and 10.3 polar coordinates ============================== 9.4 Models for Population Growth (✽) 9.5 Linear Equations 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 第16週 12/28,12/29,12/31 12/29: 10/4, and the definitions of logarithmic and exponential functions 12/31: Basic topology (I) ====================== 10.3 Polar Coordinates 10.4 Calculus in Polar Coordinates 第17週 1/04,1/05,1/07 1/5: Basic topology II 1/7: Quiz ====================== 期末考 1/9(六) 09:00~11:30