Softcover ISBN:  9780821829547 
Product Code:  CLN/9 
List Price:  $41.00 
MAA Member Price:  $36.90 
AMS Member Price:  $32.80 
Electronic ISBN:  9781470431105 
Product Code:  CLN/9.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
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Book DetailsCourant Lecture NotesVolume: 9; 2003; 234 ppMSC: Primary 34; 35; 65; 76; 86;
Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement them with additional information on geophysical flows, as suggested in the preface.
The book is intended for graduate students and researchers working in interdisciplinary areas between mathematics and AOS. It is excellent for supplementary course reading or independent study.ReadershipGraduate students and researchers working in partial differential equations and their applications to atmosphere/ocean science (AOS); applied mathematicians.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. Some remarkable features of stratified flow

Chapter 3. Linear and nonlinear instability of stratified flows with strong stratification

Chapter 4. Rotating shallow water theory

Chapter 5. Linear and weakly nonlinear theory of dispersive waves with geophysical examples

Chapter 6. Simplified equations for the dynamics of strongly stratified flow

Chapter 7. The stratified quasigeostrophic equations as a singular limit of the rotating Boussinesq equations

Chapter 8. Introduction to averaging over fast waves for geophysical flows

Chapter 9. Waves and PDEs for the equatorial atmosphere and ocean


Reviews

The author presents rigorous mathematical theory and offers deep insights … contribution of these notes to the modern literature is very valuable and unique … essentially selfcontained and does not require prior knowledge of fluid dynamics … should be of interest to anyone in the community of atmosphere/ocean science, from graduate students to advanced researchers.
Mathematical Reviews


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Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement them with additional information on geophysical flows, as suggested in the preface.
The book is intended for graduate students and researchers working in interdisciplinary areas between mathematics and AOS. It is excellent for supplementary course reading or independent study.
Graduate students and researchers working in partial differential equations and their applications to atmosphere/ocean science (AOS); applied mathematicians.

Chapters

Chapter 1. Introduction

Chapter 2. Some remarkable features of stratified flow

Chapter 3. Linear and nonlinear instability of stratified flows with strong stratification

Chapter 4. Rotating shallow water theory

Chapter 5. Linear and weakly nonlinear theory of dispersive waves with geophysical examples

Chapter 6. Simplified equations for the dynamics of strongly stratified flow

Chapter 7. The stratified quasigeostrophic equations as a singular limit of the rotating Boussinesq equations

Chapter 8. Introduction to averaging over fast waves for geophysical flows

Chapter 9. Waves and PDEs for the equatorial atmosphere and ocean

The author presents rigorous mathematical theory and offers deep insights … contribution of these notes to the modern literature is very valuable and unique … essentially selfcontained and does not require prior knowledge of fluid dynamics … should be of interest to anyone in the community of atmosphere/ocean science, from graduate students to advanced researchers.
Mathematical Reviews