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National Taiwan Normal University Course Outline Fall , 2025 |
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| I.Course information |
| Serial No. | 2713 | Course Level | Undergraduate |
| Course Code | MAU0180 | Chinese Course Name | 微積分乙（一） |
| Course Name | Calculus B (I) | ||
| Department | Department of Mathematics | ||
| Two/one semester | 1 | Req. / Sel. | Req. |
| Credits | 3.0 | Lecturing hours | Lecture hours: 3 |
| Prerequisite Course | ◎Exclusive of students within this department | ||
| Comment | |||
| Course Description | |||
| Day & Class Period/Location | Mon. 6-7 Gongguan S304, Thur. 6 Gongguan S304 | ||
| Curriculum Goals | Corresponding to the Departmental Core Goal | ||
| 1. Improve understanding of basic concepts of mathematical analysis |
College: 1-1 Equipped with professional mathematics competences 2-1 Being able to communicate and express mathematically 3-3 Being willing to work collaboratively |
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| 2. Ability to advance logical reasoning and induction |
College: 1-2 Being able to reason and induct with mathematical logic 2-2 Possessing the competences of transferring and contextualizing theories in mathematics and mathematics education 3-1 Being able to seek out answers with the attitudes of patience, diligence, concentration, and curiosity |
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| 3. Improve mathematical and critical thinking skills |
College: 1-3 Being able to think mathematically and critically 1-4 Possessing the abilities to propose and solve questions in advanced mathematics 1-5 Being able to use mathematics as tools to learn other subjects 3-2 Possessing the abilities to think independently, criticize, and reflect 4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning |
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| 4. Enhance professional knowledge and attitude towards truth |
College: 1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 2-4 Possessing the competences of lifelong learning 3-5 Having good taste for mathematics 4-1 Being knowledgeable and being able to self-develop in the profession 4-2 Possessing a consistent and firm attitude toward pursuing truths 4-4 Possessing global views from both scientific and humanistic perspectives, and being able to appreciate the values of other knowledge fields |
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| II. General Syllabus |
| Instructor(s) | Daniel Spector/ 司靈得 | ||
| Schedule | |||
一、極限與連續 (1) 函數極限的定義及運算性質 (函數的挾擠定理) (2) 連續函數的定義及基本性質 (3) 中間值定理、最大最小值定理
二、單變數函數的微分及其應用 (1) 導數與導函數的意義及其求法 (2) 微分公式、鏈鎖法則 (隱微分法、均值定理) (3) 導數的應用---求切線斜率、變化率、函數的極值及繪圖 (函數的遞增、遞減、圖形的漸近線、凹性) (4) 指數、對數與三角函數的微分 (5) L’Hospital法則
三、單變數函數的積分及其應用 (1) 不定積分的意義及其計算技巧 (分部積分法、變數代換法、分項分式法) (2) 定積分的意義及其基本性質 (Riemann和、連續函數的可積分性) (3) 微積分基本定理 (4) 指數、對數與三角函數的積分 (5) 積分的均值定理 (6) 瑕積分 (7) 定積分的應用 (兩曲線間的面積、旋轉體體積、弧長) |
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| Instructional Approach | |||
| Methods | Notes | ||
| Formal lecture | 以上課講授為主，並輔以習題研討。 | ||
| Problem-based learning | 每週排定習演和討論時間。 | ||
| Grading assessment | |||
| Methods | Percentage | Notes | |
| Midterm Exam | 40 % | 命題形式包括問答題、計算題與證明題。 | |
| Final exam | 40 % | 命題形式包括問答題、計算題與證明題。 | |
| other: | 20 % | ||
| Required and Recommended Texts/Readings with References | 教科書: 1. J. Hass, C. Heil, P. Bogacki, M. Weir , and G. Thomas : University Calculus , early transcendentals 參考書目: 2. R. Larson and B.H. Edward : Calculus 3. S. Salas, E. Hille, and G. Etgen : Calculus, one and several variables 4. Stewart, Calculus, early transcendentals 5. G. Thomas, Calculus
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