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National Taiwan Normal University Course Outline Spring , 2022 |
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| I.Course information |
| Serial No. | 2713 | Course Level | Undergraduate |
| Course Code | MAU0181 | Chinese Course Name | 微積分乙（二） |
| Course Name | Calculus B (II) | ||
| Department | Department of Mathematics | ||
| Two/one semester | 1 | Req. / Sel. | Req. |
| Credits | 3.0 | Lecturing hours | Lecture hours: 3 |
| Prerequisite Course | Prerequisite course: 【MAU0180 Calculus B (I)】 ◎1. This is a cross-level course and is available for junior and senior undergraduate students, master's students and PhD students. 2. If the listed course is a doctroal level course, it is only available for master's students and PhD students. | ||
| Comment | |||
| Course Description | |||
| Time / Location | Thur. 6-8 Gongguan S2-02 | ||
| 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. Improve the ability of 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 | |||
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一、無窮級數 (2週) (1) 級數的意義及其斂散性質 (2) 冪級數、Taylor級數、Maclaurin級數 二、向量值函數 (3週) (1) 平面曲線、參數方程式 (2) 極坐標、圓柱坐標、球面坐標 (3) 向量值函數的微積分 (切向量、法向量、弧長及曲率) 三、多變數函數的微分 (5週) (1) 多變數函數的極限與連續 (2) 偏導數 (3) 方向導數與梯度 (多變數函數的鏈鎖法則) (4) 切平面與法平面 (5) 多變數函數的極值 (Lagrange 乘子法、最小平方法) 四、多變數函數的積分 (6週) (1) 二重積分的意義與應用 (2) 二重積分的計算 (極坐標變數代換法、Fubini定理) (3) 線積分及其應用 (4) 曲面積分及其應用 (5) Green定理及其應用 |
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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 | |
| Assignments | 10 % | 隨堂指定之習題。 | |
| Midterm Exam | 30 % | 命題形式包括名詞解釋、問答題與計算題。 | |
| Final exam | 30 % | 命題形式包括名詞解釋、問答題與計算題。 | |
| Attendances | 10 % | 上課點名。 | |
| other: | 20 % | 命題形式包括名詞解釋、問答題與計算題。 | |
| Required and Recommended Texts/Readings with References |
1. R. Larson and B.H. Edwards, Calculus 2. 3. Stewart, Calculus, early transcendentals |
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