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Introduction to PDEs and Waves for the Atmosphere and Ocean
Andrew Majda, New York University-Courant Institute of Mathematical Sciences, New York
A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University.

Courant Lecture Notes
2003; 234 pp; softcover
Volume: 9
ISBN-10: 0-8218-2954-8
ISBN-13: 978-0-8218-2954-7
List Price: US$38
Member Price: US$30.40
Order Code: CLN/9
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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.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.


Graduate students and researchers working in partial differential equations and their applications to atmosphere/ocean science (AOS); applied mathematicians.


"The author presents rigorous mathematical theory and offers deep insights ... contribution of these notes to the modern literature is very valuable and unique ... essentially self-contained 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

Table of Contents

  • Introduction
  • Some remarkable features of stratified flow
  • Linear and nonlinear instability of stratified flows with strong stratification
  • Rotating shallow water theory
  • Linear and weakly nonlinear theory of dispersive waves with geophysical examples
  • Simplified equations for the dynamics of strongly stratified flow
  • The stratified quasi-geostrophic equations as a singular limit of the rotating Boussinesq equations
  • Introduction to averaging over fast waves for geophysical flows
  • Waves and PDEs for the equatorial atmosphere and ocean
  • Bibliography
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