An Introduction to Partial Differential Equations with MATLAB
暫譯: MATLAB 偏微分方程入門

這第三版改變了書籍的結構，將計算部分的角色提升至更接近修訂過的分析部分。對於希望專注於使用偏微分方程（PDEs）理論進行建模的數學、物理和工程學生來說，這本書非常有用，並且在後續的數值分析課程中也能派上用場。

Dr. Matthew P. Coleman is a Professor Emeritus of Mathematics at Fairfield University, CT, where he taught from 1989 until his retirement in 2019. He received his Ph.D. in Applied Mathematics from Penn State University in 1989 under the guidance of Dr. Goong Chen. While at Fairfield, Dr. Coleman taught almost every undergraduate course in the curriculum, along with a number of graduate courses. In addition, he was department chair for ten years, did a brief stint as associate dean (though he was happy when it was over!), and was a visitor at Texas A&M, NYU, and National Taiwan University.

Dr. Coleman's main research area is Control Theory and, more specifically, the vibration and damping of distributed systems. He has published numerous articles in this area, while collaborating with people from numerous universities, in mathematics, physics, and various branches of engineering. In addition, he has authored the first two editions of the textbook "An Introduction to Partial Differential Equations with MATLAB".

Dr. Vladislav Bukshtynov is an Assistant Professor at the Dept. of Mathematical Sciences of Florida Institute of Technology (Florida Tech) since 2015 after finishing his 3-year postdoctoral term at the Dept. of Energy Resources Engineering at Stanford University and having his Ph.D. degree in Computational Engineering & Science at McMaster University in 2012. As a Professor, he actively teaches and advises students from various fields: applied and computational math, operations research, and different engineering majors. His teaching experience includes Multivariable Calculus, Honors ODE/PDE courses for undergrad students, Applied Discrete Math, and Linear/Nonlinear Optimization for senior undergrads and graduates. As a researcher, Dr. Bukshtynov leads his research group with several dynamic scientific directions and ongoing collaborations for various cross-institutional and interdisciplinary projects. His current interests lie in but are not limited to the areas of applied and computational mathematics focusing on combining theoretical and numerical methods for various problems in computational/numerical optimization, control theory, and inverse problems.

Besides being an expert in applying numerous optimization techniques, either analytically or numerically, Dr. Bukshtynov's expertise includes PDE-based modeling for various engineering applications. For example, he pioneered system reduction techniques using a 4D VAR method and earned the 2012 Cecil Graham Doctoral Dissertation Award from Canadian Applied and Industrial Mathematics Society (CAIMS). At Stanford, he was part of a large collaborative research project to develop efficient computational and optimization algorithms for solving oil field management problems for petroleum reservoir models.

At Florida Tech, Dr. Bukshtynov develops novel techniques suitable for reconstructing medical/computational images via solving inverse problems using multiscale simulation and optimization, optimal solution space multilevel parameterization, dynamical re-parameterization, and numerical methods for regularization. In addition, he has profound expertise in HPC programming. His particular strength is his ability to create hybrid computational frameworks by combining and tuning for optimal joint work scientific software of various types. As one of many examples, Dr. Bukshtynov is an author and active developer of EIT-OPT, an all-purpose open-structure multifaceted optimization framework for reconstructing biomedical images and early cancer detection via electrical impedance tomography. In 2023, Dr. Bukshtynov published a book "Computational Optimization: Success in Practice" with CRC Press to share his extensive experience in practical aspects of computational optimization with graduate students of math, computer science, engineering, and all who explore optimization techniques at different levels for educational or research purposes.

馬修·P·科爾曼博士是康乃狄克州費爾菲爾德大學的數學名譽教授，自1989年起任教，直到2019年退休。他於1989年在賓州州立大學獲得應用數學博士學位，指導教授為陳公博士。在費爾菲爾德大學期間，科爾曼博士教授了幾乎所有本科課程，並開設了多門研究生課程。此外，他擔任了十年的系主任，短暫擔任過副院長（雖然他對結束這段經歷感到高興！），並曾在德州農工大學、紐約大學和國立台灣大學擔任訪問學者。

科爾曼博士的主要研究領域是控制理論，特別是分佈系統的振動和阻尼。他在這一領域發表了大量文章，並與來自多所大學的數學、物理學和各種工程分支的學者合作。此外，他還是教科書《使用MATLAB的偏微分方程導論》前兩版的作者。

弗拉基斯拉夫·布克什季諾夫博士自2015年起擔任佛羅里達理工學院數學科學系的助理教授，此前他在斯坦福大學能源資源工程系完成了三年的博士後研究，並於2012年在麥克馬斯特大學獲得計算工程與科學博士學位。作為教授，他積極教授和指導來自不同領域的學生：應用與計算數學、運籌學以及不同的工程專業。他的教學經驗包括多變量微積分、榮譽常微分方程/偏微分方程課程、應用離散數學，以及針對高年級本科生和研究生的線性/非線性優化。作為研究者，布克什季諾夫博士領導他的研究小組，開展多個動態科學方向的研究，並進行各種跨機構和跨學科項目的合作。他目前的研究興趣包括但不限於應用與計算數學，專注於將理論方法與數值方法結合，解決計算/數值優化、控制理論和反問題等各種問題。

除了在分析或數值上應用多種優化技術的專業知識外，布克什季諾夫博士的專長還包括基於偏微分方程的各種工程應用建模。例如，他開創了使用4D VAR方法的系統簡化技術，並於2012年獲得加拿大應用與工業數學學會（CAIMS）頒發的塞西爾·格雷厄姆博士論文獎。在斯坦福大學，他參與了一個大型合作研究項目，旨在為石油儲層模型開發高效的計算和優化算法，以解決油田管理問題。

在佛羅里達理工學院，布克什季諾夫博士開發了適合通過解決反問題來重建醫療/計算圖像的新技術，這些技術包括多尺度模擬和優化、最佳解空間的多層次參數化、動態重新參數化以及正則化的數值方法。此外，他在高性能計算（HPC）編程方面擁有深厚的專業知識。他的特長在於能夠通過結合和調整各類科學軟體來創建混合計算框架，以實現最佳的聯合工作。舉例來說，布克什季諾夫博士是EIT-OPT的作者和活躍開發者，這是一個多用途的開放結構多面向優化框架，用於通過電阻抗斷層掃描重建生物醫學圖像和早期癌症檢測。2023年，布克什季諾夫博士與CRC Press出版了《計算優化：實踐中的成功》一書，旨在與數學、計算機科學、工程的研究生分享他在計算優化實踐方面的豐富經驗，以及為不同層次的教育或研究目的探索優化技術的所有人。