Mathematical Modeling and Simulation

This textbook is relevant to BSc/MSc students interested in mathematical modeling and simulation. It brings together analysis, calculus and numerical methods presented in a single coherent volume.
Particular attention is given to engineering mathematics, addressing modeling, analysis, method development, implementation and testing of algorithms, as well as application to actual problems and critical interpretation of the results. The book can be used throughout bachelor programs and parts of masters programs, presenting a comprehensive suite of courses that link formal abstract thinking on the one hand to intuitive model formulation, critical algorithm development and interpretation of results on the other hand. The books contains numerous examples of practical applications from physics, technology, biology and chemistry. It also contains an introduction to Matlab and C for algorithm development and computational analysis. Software and solutions to selected problems are included.

這本教科書適用於對數學建模和模擬感興趣的學士/碩士學生。它將分析、微積分和數值方法結合在一個統一的卷中呈現。

特別關注工程數學，涵蓋建模、分析、方法開發、實施和算法測試，以及應用於實際問題和對結果的關鍵解釋。本書可在學士課程和部分碩士課程中使用，提供了一套全面的課程，將正式的抽象思維與直觀的模型制定、關鍵算法開發和結果解釋相結合。該書包含了來自物理學、技術學、生物學和化學的許多實際應用示例。它還包含了Matlab和C的介紹，用於算法開發和計算分析。書中還包含了選定問題的軟件和解答。

Bernard Geurts is the Chair of the Multiscale Modeling and Simulation (MMS) group at the University of Twente, The Netherlands. The big dream behind their work is to help open entirely new worlds of understanding and application in science and technology, by creating advanced computational methods. The impact of their work is increased by close collaboration with other disciplines.The main research focus is on the mathematical development of computational methods forsystems of nonlinear differential equations. The models studied at MMS represent complexphysical mechanisms acting simultaneously at micro- and macro scales. Much of the workis motivated by fluid-mechanical problems, from nano- and micro fluidics to macroscopicturbulence.The three directions of MMS expertise, i.e., (i) mathematical models, (ii) numerical methods and (iii) advanced reduction and regularisation techniques, are exploited in multi-disciplinary research. The work is characterised by balancing fundamental orientation and application perspective. Specific targets are derived from unresolved issues in science and technology.Main application areas are in fluid technology, health and energy such as: - multi-phase turbulence and heat transfer, - aerosol formation and phase transitions, - biomedical flows in complex domains, - nano-engineered materials for energy systemsSpecific challenges range from understanding the physics of boiling and turbulence modulation, to novel methods of controlled respiratory drug delivery. Moreover, new methods are forgedfor the prediction and mitigation of cerebral haemorrhages and the optimisation of nanostructured inclusions for new materials in energy harvesting.While these applications and research fields appear diverse, the binding element is his interest in mathematical elegance and abstraction to discover and exploit the simplicity behind apparent complexity in physical systems.
Ruud van Damme is associate professor in numerical analysis in the Multiscale Modeling and Simulation. This group is part of the Department of Applied Mathematics at the University of Twente.

His research interests are in mathematics, physics and numerics. The main topics lie in fields such as fluid mechanics, quantum mechanics, graph theory and stochastic processes. His recent research concentrates on advanced numerical techniques and their application, such as splines and wavelets, adaptive grid methods and high dimensional integration.

Bernard Geurts是荷蘭特溫特大學多尺度建模和模擬（MMS）組的主席。他們的工作背後的大夢想是通過創建先進的計算方法，幫助開啟科學和技術領域的全新理解和應用。他們與其他學科的密切合作增加了他們工作的影響力。主要研究重點是數學方法的發展，用於非線性微分方程系統。MMS研究的模型代表了同時在微觀和宏觀尺度上作用的複雜物理機制。他們的許多工作都受到流體力學問題的啟發，從納米和微流體到宏觀紊流。MMS專業的三個方向，即（i）數學模型，（ii）數值方法和（iii）高級簡化和正則化技術，在多學科研究中得到了應用。這項工作的特點是平衡基礎導向和應用觀點。具體目標來自科學和技術中未解決的問題。主要應用領域包括流體技術、健康和能源，例如：- 多相紊流和熱傳遞，- 氣溶膠形成和相變，- 複雜領域中的生物醫學流體，- 用於能源系統的納米工程材料具體挑戰範圍從理解沸騰和紊流調制的物理學，到控制呼吸藥物傳遞的新方法。此外，還開發了預測和減輕腦出血以及優化用於能源收集的納米結構添加劑的新方法。儘管這些應用和研究領域看似多樣，但其共同點是他對數學優雅和抽象的興趣，以發現和利用物理系統中明顯複雜性背後的簡單性。

Ruud van Damme是特溫特大學應用數學系多尺度建模和模擬組的副教授。他的研究興趣涉及數學、物理和數值計算。主要研究領域包括流體力學、量子力學、圖論和隨機過程。他最近的研究集中在先進的數值技術及其應用，如樣條和小波、自適應網格方法和高維積分。