Course Announcement for OCE 693(03)

Data Analysis in Oceanography

CRN #: 19783

Dr. Huijie Xue

School of Marine Sciences

University of Maine

Phone: 581-4318

hjx@apollo.umeoce.maine.edu

This course covers some of the techniques commonly used in the analysis of data collected in the field of Oceanography. It discusses regression methods in great details, followed by numerical integration, and brief introductions to box models and time series analysis. The goal is to provide theoretical and computational guidance on these techniques, emphasis on developing a hands-on understanding of the methods and correct interpretation of results. Two lectures per week (TBA). Term project required. Prerequisites: undergraduate calculus.

Textbook:

Edward Laws (1997): Mathematical Methods for Oceanographers. John Wiley & Sons, Inc.

Syllabus

Week #1

Jan. 11

Review of Calculus

- Functions and Derivatives,

- More on Derivatives, Maxima, and Mimima

Week #2

Jan. 18

Review of Statistics

Linear Regression Model I

- Expectation Value, Variance, and Covariance

- Least Squares

Week #3

Jan. 25

- Error Bounds

- More on Error Analysis

Week #4

Feb. 1

- Correlation

- Variance Associated with Least Square

Week #5

Feb. 8

Linear Regression Model II

- Limitation of Least Square Estimation

- Major Axis Method

Week #6

Feb. 15

- Geometric Mean Method

-Arithmetic Mean Method

Week #7

Feb. 22

 

Review and Mid-term Exam

- Bias and Error

Week #8

Mar. 15

Other Regression Methods

- Quadratic and Cubic Curve Fitting

- Variance in Polynomial Regression

Week #9

Mar. 22

- More on Variance in Polynomial Regression

- Linear Multiple Regression

Week #10

Mar. 29

- More on Linear Multiple Regression

- Nonlinear Least Squares

Week #11

Apr. 5

 

Numerical Integration

- Gauss-Newton Iteration

- Mid-Point Rule and Trapezoid Rule

Week #12

Apr. 12

- Taylor Series

- Simpson's Rule, Runge-Kutta Method

Week #13

Apr. 19

Introduction to Box Models

- Pelagic Food Chain Model

- Perturbation Theory and Stability

Week #14

Apr. 26

Introduction to Time Series

- Time Series, Time Domain Techniques

- Frequency Domain Techniques

Week #15

May 3

Final Exam (Project and Presentation)