**Courant Lecture Notes**

Volume: 9;
2003;
234 pp;
Softcover

MSC: Primary 34; 35; 65; 76; 86;

Print ISBN: 978-0-8218-2954-7

Product Code: CLN/9

List Price: $38.00

Individual Member Price: $30.40

**Electronic ISBN: 978-1-4704-3110-5
Product Code: CLN/9.E**

List Price: $38.00

Individual Member Price: $30.40

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# Introduction to PDEs and Waves for the Atmosphere and Ocean

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*Andrew Majda*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

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.

#### Readership

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

#### Reviews & Endorsements

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

# Table of Contents

## Introduction to PDEs and Waves for the Atmosphere and Ocean

- Cover Cover11
- Title page 44
- Contents 66
- Preface 1010
- Introduction 1212
- Some remarkable features of stratified flow 2020
- Linear and nonlinear instability of stratified flows with strong stratification 4242
- Rotating shallow water theory 6060
- Linear and weakly nonlinear theory of dispersive waves with geophysical examples 9090
- Simplified equations for the dynamics of strongly stratified flow 136136
- The stratified quasi-geostrophic equations as a singular limit of the rotating Boussinesq equations 158158
- Introduction to averaging over fast waves for geophysical flows 182182
- Waves and PDEs for the equatorial atmosphere and ocean 210210
- Bibliography 244244
- Back Cover Back Cover1250