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Mathematical Methods for Oceanographers: An Introduction



Mathematical Methods for Oceanographers: An Introduction

Edward A. Laws

ISBN: 978-0-471-16221-6 March 1997 343 Pages


Oceanography calls for a wide variety of mathematical andstatistical techniques, and this accessible treatment provides thebasics every oceanographer needs to know, including
* Practical ways to deal with chemical, geological, and biologicaloceanographic data
* Instructions on detecting the existence of patterns in whatappears to be noise
* Numerous examples from the field that highlight the applicationof the methods presented

Written by an oceanographer and based on his successful course atthe University of Hawaii, the volume is well suited to atwo-semester course at the graduate level. The book reviews thenecessary calculus, clarifies statistical concepts, and includesend-of-chapter problems that illustrate and expand the varioustopics. Tips on using MATLAB(r) software in matrix operationscomplement chapters that deal with the formulation of relationshipsin terms of matrices.

The main body of the text covers the actual methods of dealing withdata--including least squares and linear regression, correlationfunctions and analysis of variance, means and error bounds,nonlinear techniques and weighted least squares, numericalintegration, and other modeling techniques. Unlike mostintroductory texts, Mathematical Methods for Oceanographersdiscusses regression methods in great detail, and includes ananalysis of why certain methods produce unbiased parameterestimates. Finally, the chapter on time series analysis covers anarea of particular interest to physical oceanographers.

The numerous problems and solutions included in the book enablereaders to check their understanding of concepts and techniques aswell as their ability to apply what they have learned.

A must-read for students of oceanography, this text/reference isalso useful for professionals in the field, as well as forfisheries scientists, biologists, and those in the environmentalsciences.

A systematic introduction to the mathematics oceanographersneed

Topics covered in Mathematical Methods for Oceanographers include:
* A review of the necessary calculus
* Model I linear regression
* Correlation analysis
* Model II linear regression
* Polynomial curve fitting, linear multiple regression analysis,and nonlinear least squares
* Numerical integration
* Box models
* Time series analysis
Calculus Review.

Model I Linear Regression.


Model II Linear Regression.

Polynomial Curve Fitting, Linear Multiple Regression Analysis, andNonlinear Least Squares.

Numerical Integration.

Box Models.

Time Series Analysis.


Answers to Exercises.

"...It presents many well discussed and illustrative examples..." (Zentralblatt Math, Vol.988, No.13, 2002)