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.
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Week #1 |
Jan. 11 |
Review of Calculus |
- Functions and Derivatives, - More on Derivatives, Maxima, and Mimima |
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Week #2 |
Jan. 18 |
Review of Statistics Linear Regression Model I |
- Expectation Value, Variance, and Covariance - Least Squares |
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Week #3 |
Jan. 25 |
- Error Bounds - More on Error Analysis |
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Week #4 |
Feb. 1 |
- Correlation - Variance Associated with Least Square |
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Week #5 |
Feb. 8 |
Linear Regression Model II |
- Limitation of Least Square Estimation - Major Axis Method |
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Week #6 |
Feb. 15 |
- Geometric Mean Method -Arithmetic Mean Method |
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Week #7 |
Feb. 22 |
Review and Mid-term Exam |
- Bias and Error |
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Week #8 |
Mar. 15 |
Other Regression Methods |
- Quadratic and Cubic Curve Fitting - Variance in Polynomial Regression |
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Week #9 |
Mar. 22 |
- More on Variance in Polynomial Regression - Linear Multiple Regression |
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Week #10 |
Mar. 29 |
- More on Linear Multiple Regression - Nonlinear Least Squares |
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Week #11 |
Apr. 5 |
Numerical Integration |
- Gauss-Newton Iteration - Mid-Point Rule and Trapezoid Rule |
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Week #12 |
Apr. 12 |
- Taylor Series - Simpson's Rule, Runge-Kutta Method |
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Week #13 |
Apr. 19 |
Introduction to Box Models |
- Pelagic Food Chain Model - Perturbation Theory and Stability |
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Week #14 |
Apr. 26 |
Introduction to Time Series |
- Time Series, Time Domain Techniques - Frequency Domain Techniques |
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Week #15 |
May 3 |
Final Exam (Project and Presentation) |
