非同步遠距教學課程。與蔡國榮合授

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

待補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.