Course Syllabus
The syllabuses on both this page and the NTU online course information are synchronized.
Course Information
| Item | Content |
| Course title | Precalculus |
| Semester | 112-2 |
| Designated for | NATIONAL TAIWAN UNIVERSITY DISTANCE LEARNING |
| Instructor | YA-JU TSAI |
| Curriculum No. | MATH 4012 |
| Curriculum Id No. | 201 49870 |
| Class | |
| Credit | 1 |
| Full/Half Yr. | Half |
| Required/Elective | Elective |
| Time | Monday 0(7:10~8:00) |
| Place | |
| Remarks | 、 KWOK WING TSOI合授 |
Course Syllabus
| Item | Content |
| Course Description | 本課程以老師預錄影片的方式呈現，不會有固定的授課時間，同學可以視自己的狀況安排如何使用這些線上資源、隨時上網查看所需要的內容。 本課程將用大學數學視角，有系統的涵蓋中學數學裡和微積分相關的先備知識。課程內容包含8 個單元： 1. 函數概論 2. 多項式 3. 有理函數 4. 根函數 5. 三角函數 6. 指對數函數 7. 空間向量 8. 連加公式 This course is presented through pre-recorded videos by the instructor, without fixed lecture times. Students can arrange the use of these online resources based on their own schedules and access the necessary content at any time. From the perspective of university mathematics, this course systematically covers Calculus prerequisite knowledge. The course materials encompass the following eight topics. 1. Introduction to Functions 2. Polynomials 3. Rational Functions 4. Root Functions 5. Trigonometric Functions 6. Exponential and Logarithmic Functions 7. Space Vectors 8. Summation Formulas |
| Course Objective | 完成本課程的同學應該能夠: 1. 了解函數在數學上的嚴格定義，能善用函數圖形的幾何性質去推導函數的特性。 2. 掌握關於有理函數、指數函數、對數函數的定義、函數圖形和計算上的操作和技巧。 3. 理解三角函數廣義角的定義，推導重要的和倍角公式、正弦和餘弦定律、積化和差公式。 4. 掌握三維空間的向量、平面和直線的幾何性質和應用 5. 了解幾何級數的操作和應用，並以數學歸納法推導有限項級數的公式 Students who complete this course should be able to: 1. Understand the rigorous definition of functions in mathematics and proficiently use the geometric aspects of function graphs to derive properties of functions. 2. Master the definitions, graphs, and computational techniques related to rational functions, exponential functions, and logarithmic functions. 3. Comprehend the definition of trigonometric functions with generalized angles, derive double-angle formulas, sine and cosine laws, and product-to-sum and sum-to-product formulas. 4. Acquire a grasp of the geometric properties and applications of vectors, planes, and lines in three-dimensional space. 5. Understand the operations and applications of geometric series and deduce formulas for finite series using mathematical induction. |
| Course Requirement | |
| Student Workload (expected study time outside of class per week) | |
| References | |
| Designated Reading |
Progress
| Week | Date | Topic |
Grading
| NO | Item | Pc | Explanations for the conditions |
| 1 | 作業成績 Assessment | 30% | There are: - WeBWorK assignments (15%), - Practice quizzes (5%, only best 40 quizzes will be counted), - Weekly learning progress forms (10%). |
| 2 | 期中考 Midterm | 35% | The midterm is scheduled on 4/12 (Fri) 17:30-19:00 and will cover sections 1-1 through 5-4. Reminder. Precalculus Night (I) would be held on 4/10 (Wed) 18:00-19:30 for additional help and revision ! |
| 3 | 期末考 Final Exam | 35% | The final exam is scheduled on 6/7 (Fri) 17:30-19:00 and will cover sections 5-5 through 8-4. Reminder. Precalculus Night (II) would be held on 6/5 (Wed) 18:00-19:30 for additional help and revision ! |
| 4 | 注意 Notice | 0% | This is a pass/fail course, i.e., we will only issue either pass or fail according to the above grading scheme. You will not receive a letter grade. |
Adjustment methods for students
| Adjustment method | |
| Teaching methods | Assisted by video |
| Assignment submission methods | Extension of the deadline for submitting assignments |
| Exam methods | Final exam date postponement |
| Others | Negotiated by both teachers and students |
Office Hour
| Remarks | None |