Keywords:
Marine sciences Mathematical models
;
Aquatic sciences Mathematical models
;
Marine sciences ; Mathematical models..
;
Aquatic sciences ; Mathematical models
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Electronic books
Description / Table of Contents:
An advanced textbook on modeling, data analysis and numerical techniques for advanced students and researchers in chemical, biological, geological and physical oceanography.
Type of Medium:
Online Resource
Pages:
1 online resource (590 pages)
ISBN:
9781139141406
URL:
https://ebookcentral.proquest.com/lib/kxp/detail.action?docID=802941
URL:
https://ebookcentral.proquest.com/lib/kxp/detail.action?docID=802941
URL:
http://site.ebrary.com/lib/academiccompletetitles/home.action
URL:
http://site.ebrary.com/lib/alltitles/docDetail.action?docID=10506224
URL:
http://gbv.eblib.com/patron/FullRecord.aspx?p=802941
DDC:
551.46015118
Language:
English
Note:
Description based on publisher supplied metadata and other sources
,
Cover; Title; Copyright; Dedication; Contents; Preface; 1 Resources, MATLAB primer, and introduction to linear algebra; 1.1 Resources; 1.2 Nomenclature; 1.3 A MATLAB primer; 1.4 Basic linear algebra; 1.5 Problems; 2 Measurement theory, probability distributions, error propagation and analysis; 2.1 Measurement theory; 2.1.1 Systems of measurements (scales); 2.1.2 Precision versus accuracy; 2.1.3 Systematic versus random errors; 2.1.4 Significant figures and roundoff; 2.1.5 Computational roundoff and truncation; 2.2 The normal distribution; 2.2.1 Parent versus sample distributions
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2.2.2 Mean/median/mode/moments2.2.3 The normal (Gaussian) distribution; 2.2.4 Testing a normal distribution; 2.2.5 Standardization and normalization (Z-scores); 2.2.6 Calculating normal probabilities; 2.3 Doing the unspeakable: throwing out data points?; 2.3.1 Chauvenet's criterion; 2.4 Error propagation; 2.4.1 The general equation; 2.4.2 Assumptions regarding independence or orthogonality; 2.5 Statistical tests and the hypothesis; 2.5.1 Hypothesis building and test; 2.5.2 Example 1: testing a null hypothesis; 2.5.3 Example 2: testing for a normal distribution; 2.6 Other distributions
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2.6.1 Student's t-distribution2.6.2 The F-distribution; 2.6.3 Poisson distribution; 2.6.4 Weibull distributions; 2.6.5 Log-normal transformations; 2.7 The central limit theorem; 2.8 Covariance and correlation; 2.8.1 Analysis of variance (ANOVA); 2.9 Basic non-parametric tests; 2.9.1 Spearman rank-order correlation coefficient; 2.9.2 Kendall's tau; 2.9.3 Wilcoxon signed-rank test; 2.9.4 Kruskal-Wallis ANOVA; 2.9.5 Mann-Whitney rank-sum test; 2.10 Problems; 3 Least squares and regression techniques, goodness of fit and tests, and nonlinear least squares techniques
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3.1 Statistical basis for regression3.1.1 The chi-squared (?2) defined (and goodness of fit); 3.1.2 Look at your residuals; 3.2 Least squares fitting a straight line; 3.2.1 Doing things the hard way (the normal equations); 3.2.2 Uncertainties in coefficients; 3.2.3 Uncertainties in an estimated y-value; 3.2.4 Example: ocean heat content; 3.2.5 Type II regressions (two dependent variables); 3.3 General linear least squares technique; 3.3.1 Choose your model functions wisely; 3.3.2 There is an easier way: the design matrix approach; 3.3.3 Solving the design matrix equation with SVD
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3.3.4 Multi-dimensional regressions3.3.5 Transformably linear models; 3.3.6 Non-coefficients; 3.4 Nonlinear least squares techniques; 3.4.1 Iterative techniques; 3.4.2 Uncertainties in nonlinear coefficients; 3.4.3 Example: Exponential phytoplankton growth; 3.4.4 Example: Gaussian on a constant background; 3.5 Problems; 4 Principal component and factor analysis; 4.1 Conceptual foundations; 4.1.1 The data matrix and the covariance matrix; 4.1.2 Standardization and normalization; 4.1.3 Linear independence and basis functions; 4.2 Splitting and lumping; 4.2.1 Discriminant analysis
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4.2.2 Cluster analysis
