摘 要 對大一學生微積分課程的級數主題裏要學習各種判斷級數收斂性的測試法，學生若不知為什麼要學級數，容易造成學生的學習動力的缺乏。為促進學生對級數學習的動機，本研究目標在於設計「欣賞級數之美與應用」之微積分先導型作業。此作業的教材包括三個單元，即第一單元「級數之美」、第二單元「級數之應用」、第三單元「級數之蹤跡─過去與未來」，其中「級數之應用」單元亦附加「偏微分方程組的級數解」的附錄提供有興趣探索的學生自由取用。在先導型作業的設計上，本研究首先檢視微積分相關的通俗數學史、高中數學、微積分、工程數學及大四或研究所的應用數學等課程教材在數列、級數、冪級數、及傅立葉級數之主題的內容，作為先導型作業的主軸設計參考。本文也提供一個配合微積分教學進度來使用「欣賞級數之美與應用」之微積分先導型作業的建議構想。

Abstract For the freshman calculus course in the chapter of Series to learn a variety of Convergence tests, when students not knowing at the beginning why they need to learn Series, they are likely to cause a lack of student motivation for learning. In order to promote student motivation for learning Series, the research goal is to design "appreciate the beauty of Series and its applications" pilot-type assignment of calculus. This assignment consists of three units of teaching materials, the first unit "the beauty of Series ", the second unit "applications on Series ", the third unit "traces of Series ─ Past and Future ", where the unit of "applications on Series" also comes with a Series solution of partial differential equations in Appendix for interested students to explore freely access. In the assignment design, this study related to calculus history of mathematics, high school mathematics, calculus, engineering mathematics and senior or graduate level Applied Mathematics courses and all their corresponding topics of Sequence, Series, Power Series, and Fourier Series, serves as the main axis of design references for pilot-type assignment ofcalculus. About the assignment, this paper prepares a suggestive proposal for a modified curriculum of calculus with the usage of the pilot-type assignment of calculus, "the Beauty of Series and its Applications."