Differential Geometry and Its Visualization

《微分幾何及其可視化》適用於微分幾何的研究生課程，旨在為學生和教師提供參考。同時，它也可以作為數學、自然科學和工程科學研究的補充參考資料。

微分幾何是使用數學分析方法研究幾何物體及其性質的學科。本書的前三章介紹了三維歐幾里得空間中曲線和曲面的經典理論。最後兩章則探討了張量代數、黎曼空間和張量分析等抽象和現代主題。書中包含了大量的實例、可視化圖像和由作者自己的軟件創建的真實圖形，以支持讀者對所介紹的概念和結果的理解，並培養對幾何物體形狀、性質及其之間關係的適當感知。

特點：
- 大量全彩色可視化圖像
- 多個練習題
- 自成體系且全面的主題處理

Eberhard Malkowsky is a Full Professor of Mathematics in retirement at the State University of Novi Pazar in Serbia. He earned his Ph.D. degree and habilitation at the Department of Mathematics of the Justus-Liebig Universität Giessen in Germany in 1982 and 1988, respectively. He was a professor of mathematics at universities in Germany, South Africa, Jordan, Turkey and Serbia, and a visiting professor in the USA, India, Hungary and France. Furthermore, he participated as an invited or keynote speaker with more than 100 lectures in international scientific conferences and congresses. He is a member of the editorial boards of twelve journals of international repute. His list of publications contains 175 research papers in international journals. He is the author or co-author of nine books, and the editor or co-editor of six proceedings of international conferences. He supervised 6 Ph.D. theses and a great number of B.Sc. and M.Sc. theses in mathematics. His research and work areas include functional analysis, differential geometry and software development for the visualization of mathematics.

Ćemal Dolicanin is a Professor Emeritus at the Department of Sciences and Mathematics at the State University of Novi Pazar in Serbia and a member of the Serbian Academy of Non-linear Sciences. He was dean of the Electro-Technical Faculty and the Faculty of Technical Sciences in Pristina, vice-rector of the University of Pristina and founder and rector of the State University of Novi Pazar, Serbia. He obtained his M.Sc. degree at the Faculty of Mathematics of the University of Belgrade in 1974, and his Ph.D. degree at the Faculty of Sciences and Mathematics of the University of Pristina in 1980. He published more than 20 books, 23 papers in national scientific journals, 41 papers in international scientific journals, and gave more than 50 lectures at international scientific conferences.

He was a visiting professor in Germany, Belorussia and Russia. He supervised 14 PhD theses and a great number of B.Sc. and M.Sc. theses in mathematics. His research and work areas include Euclidean and non-Euclidean geometry, differential geometry and applied mathematics. He is very active in promoting mathematics, and has established the Center for the Advancement and Popularization of Mathematics at the State University of Novi Pazar. He participated in the implementation of several national scientific projects TEMPUS projects and was the coordinator of Master's study programs with the World University Service Austria (WUS).

Vesna Veličkovic is a Professor at the Department of Computer Science at the Faculty of Sciences and Mathematics of the University of Nis, Serbia. She obtained her magister degree at the Faculty of Mathematics of the University of Belgrade in 1996, and her Ph.D. degree at the Faculty of Sciences and Mathematics of the University of Nis in 2012. She published 3 books, 30 papers in international scientific journals, 12 papers in national scientific journals, and gave more than 50 lectures at international scientific conferences. She participated in 3 international scientific and 4 software projects, and 7 study visits in Serbia, Germany, Bulgaria, Romania and Turkey. Together with Professor Malkowsky, she is developing the software MV-Graphics for visualization of mathematics. With large-format graphics, they participated in three exhibitions of mathematical art. For ten years she worked with pupils talented in mathematics and programming. Her students won a number of medals at International Olympiads in Informatics. She is still very active in organizing contests in programming and promoting of mathematics. Her research areas are software development, computer graphics and visualization of mathematics.

Eberhard Malkowsky是塞爾維亞諾維帕薩爾州立大學的退休數學教授。他於1982年和1988年在德國吉森大學數學系獲得博士學位和資格教授資格。他曾在德國、南非、約旦、土耳其和塞爾維亞的大學擔任數學教授，並在美國、印度、匈牙利和法國擔任訪問教授。此外，他還在國際科學會議上以邀請或主題演講嘉賓的身份發表了100多場演講。他是12本國際知名期刊的編輯委員會成員。他的發表論文清單包含175篇國際期刊上的研究論文。他是9本書的作者或合著者，以及6個國際會議議程的編輯或合編者。他指導了6個博士論文和大量的數學學士和碩士論文。他的研究和工作領域包括函數分析、微分幾何和數學可視化軟件開發。

Ćemal Dolicanin是塞爾維亞諾維帕薩爾州立大學科學與數學系的名譽教授，也是塞爾維亞非線性科學學院的成員。他曾擔任普里什蒂納的電氣技術學院和技術科學學院的院長，普里什蒂納大學的副校長，以及塞爾維亞諾維帕薩爾州立大學的創辦人和校長。他於1974年在貝爾格萊德大學數學學院獲得碩士學位，並於1980年在普里什蒂納大學科學與數學學院獲得博士學位。他出版了20多本書，23篇國內科學期刊論文，41篇國際科學期刊論文，並在國際科學會議上發表了50多場演講。他曾在德國、白俄羅斯和俄羅斯擔任訪問教授。他指導了14個博士論文和大量的數學學士和碩士論文。他的研究和工作領域包括歐幾里得和非歐幾里得幾何、微分幾何和應用數學。他在塞爾維亞諾維帕薩爾州立大學成立了數學推廣中心，積極推動數學發展。他參與了多個國家科學項目TEMPUS項目的實施，並擔任世界大學服務奧地利（WUS）碩士學習計劃的協調人。

Vesna Veličković是塞爾維亞尼什大學理學與數學學院計算機科學系的教授。她於1996年在貝爾格萊德大學數學學院獲得碩士學位，並於2012年在尼什大學理學與數學學院獲得博士學位。她出版了3本書，30篇國際科學期刊論文，12篇國內科學期刊論文，並在國際科學會議上發表了50多場演講。她參與了3個國際科學和4個軟件項目，並在塞爾維亞、德國、保加利亞、羅馬尼亞和土耳其進行了7次學習訪問。她與Malkowsky教授一起開發了數學可視化軟件MV-Graphics。通過大尺寸圖形，他們參加了三個數學藝術展覽。她與數學和編程方面有才華的學生合作了十年。她的學生在國際信息學奧林匹克競賽中獲得了多個獎牌。她仍然積極組織編程比賽和推廣數學。她的研究領域包括軟件開發、計算機圖形和數學可視化。