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商品描述
Accessible to advanced undergraduate students, Physical Oceanography: A Mathematical Introduction with MATLAB(R) demonstrates how to use the basic tenets of multivariate calculus to derive the governing equations of fluid dynamics in a rotating frame. It also explains how to use linear algebra and partial differential equations (PDEs) to solve basic initial-boundary value problems that have become the hallmark of physical oceanography. The book makes the most of MATLAB's matrix algebraic functions, differential equation solvers, and visualization capabilities.
Focusing on the interplay between applied mathematics and geophysical fluid dynamics, the text presents fundamental analytical and computational tools necessary for modeling ocean currents. In physical oceanography, the fluid flows of interest occur on a planet that rotates; this rotation can balance the forces acting on the fluid particles in such a delicate fashion to produce exquisite phenomena, such as the Gulf Stream, the Jet Stream, and internal waves. It is precisely because of the role that rotation plays in oceanography that the field is fundamentally different from the rectilinear fluid flows typically observed and measured in laboratories. Much of this text discusses how the existence of the Gulf Stream can be explained by the proper balance among the Coriolis force, wind stress, and molecular frictional forces.
Through the use of MATLAB, the author takes a fresh look at advanced topics and fundamental problems that define physical oceanography today. The projects in each chapter incorporate a significant component of MATLAB programming. These projects can be used as capstone projects or honors theses for students inclined to pursue a special project in applied mathematics.
商品描述(中文翻譯)
本書《物理海洋學：MATLAB(R)的數學入門》適合高年級本科生閱讀，展示了如何使用多變量微積分的基本原則來推導旋轉框架中的流體動力學控制方程。它還解釋了如何使用線性代數和偏微分方程（PDEs）來解決已成為物理海洋學標誌的基本初邊值問題。本書充分利用了MATLAB的矩陣代數函數、微分方程求解器和可視化功能。
本書專注於應用數學與地球物理流體動力學之間的相互作用，介紹了建模海洋洋流所需的基本分析和計算工具。在物理海洋學中，感興趣的流體流動發生在一個旋轉的行星上；這種旋轉能夠以微妙的方式平衡作用於流體粒子上的力，從而產生精緻的現象，如墨西哥灣暖流、噴流和內部波。正是因為旋轉在海洋學中的作用，使得這一領域與通常在實驗室中觀察和測量的直線流體流動根本不同。本書的許多內容討論了如何通過科里奧利力、風應力和分子摩擦力之間的適當平衡來解釋墨西哥灣暖流的存在。
通過使用MATLAB，作者重新審視了當今定義物理海洋學的高級主題和基本問題。每章中的項目都包含了MATLAB編程的重要組成部分。這些項目可以作為學生追求應用數學特殊項目的畢業設計或榮譽論文。
作者簡介
Reza Malek-Madani is a professor in the Department of Mathematics at the U.S. Naval Academy. He earned a Ph.D. in applied mathematics from Brown University. His research interests include mathematical modeling and stability analysis in fluid flows and dynamical systems.
作者簡介(中文翻譯)
Reza Malek-Madani 是美國海軍軍官學院數學系的教授。他在布朗大學獲得應用數學的博士學位。他的研究興趣包括流體流動和動態系統中的數學建模與穩定性分析。
