DC 欄位 值 語言 DC.contributor 物理學系 zh_TW DC.creator 陳威澔 zh_TW DC.creator Wei-Hao Chen en_US dc.date.accessioned 2023-7-28T07:39:07Z dc.date.available 2023-7-28T07:39:07Z dc.date.issued 2023 dc.identifier.uri http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=109222024 dc.contributor.department 物理學系 zh_TW DC.description 國立中央大學 zh_TW DC.description National Central University en_US dc.description.abstract TensoriaCalc是一個使用者導向的Mathematica套件，首先是由我的導師瞿怡仁所建構的，並且由我顯著地擴展套件。經由使用者提供度量張量以及坐標系，可以快速算出重要的幾何張量如克里斯多福符號、愛因斯坦張量等，微分幾何及張量分析中的常見運算如: 張量收縮、座標轉換、投影、偏導數、協變導數、外微分、李導數亦是可使用的功能。在本文中，我將解釋TensoriaCalc的基本運作及使用方式，並展示新添加的功能與建構的思路。最後，我將呈現如何使用TensoriaCalc來計算數個廣義相對論及微分幾何中經典的問題。 zh_TW dc.description.abstract TensoriaCalc is an user-oriented Mathematica package developed to tackle tensor calculus problems. By giving a metric tensor and the coordinate set, the users can rapidly obtain tensor components of geometric objects such as Christoffel symbols, Einstein tensors, etc. Operations in tensor calculus and differential geometry, such as contraction, coordinate transformation, projection, partial derivative, covariant derivative, exterior derivative, Lie derivative, etc., are also available. In this paper, I will explain the basic structure of this package, firstly constructed by Yi-Zen Chu and significantly expanded by me. Also, the track of thought of my newly added functionality or structure will be presented. Eventually, I will show how to use TensoriaCalc to calculate several classic problems in General Relativity and Differential Geometry. en_US DC.subject TensoriaCalc zh_TW DC.subject 張量微積分 zh_TW DC.subject 廣義相對論 zh_TW DC.subject Mathematica套件 zh_TW DC.subject 微分幾何 zh_TW DC.subject TensoriaCalc en_US DC.subject tensor calculus en_US DC.subject General Relativity en_US DC.subject Mathematica package en_US DC.subject Differential Geometry en_US DC.title TensoriaCalc - 處理偽黎曼張量分析問題的使用者導向Mathematica套件 zh_TW dc.language.iso zh-TW zh-TW DC.title TensoriaCalc, an user-oriented Mathematica package to tackle semi-Riemannian tensor calculus problems en_US DC.type 博碩士論文 zh_TW DC.type thesis en_US DC.publisher National Central University en_US