SIO 221B is the second quarter of the physical oceanography data analysis sequence. You do not need to be a physical oceanographer to enroll in the course, but you should have some mathematical background. If you can't answer the questions indicated with bullets, then you probably will need to plan on spending time reviewing this material before the start of SIO 221B.

- What is a Fourier transform?
- What is the relationship between a time series
**x**and its transform? - If
**x**has N elements, how many Fourier modes can be defined?

Bendat and Piersol,

Bracewell,

Matlab manual,

Numerical Recipes,

any complex variables textbook.

- How do you integrate by parts?
- How do you define a Taylor series? What is the Taylor series expansion of cos(x) for small x?
- How do you use a table of integrals such as Gradshteyn and Ryzhik?

undergraduate calculus textbooks.

- What is a matrix? What is a vector?
- For the matrix
**A**, what is**A**^{-1}? When can**A**^{-1}be defined? - What is the matrix
**I**? How is it related to**A**and**A**^{-1}? - If
**A**is a 4x3 matrix, and**b**is a 3 element vector, how big is**Ab**? - If
**A**is an NxN matrix, how many vectors are required to span the space defined by**A**?

Resources for linear algebra:

Strang,

links and exercises in Gilbert Strang's web site for his undergraduate linear algebra class: http://web.mit.edu/18.06/www/

Matlab manual,

Linpack/Lapack manual,

tutorial websites (see for example http://www.math.duke.edu/education/ccp/materials/linalg/index.html)

some textbooks with Matlab exercises (suggested by the Mathworks)

-- ATLAST Computer Exercises for Linear Algebra http://www.mathworks.com/support/books/book1347.jsp

-- Linear Algebra LABS with MATLAB, 2e http://www.mathworks.com/support/books/book1341.jsp

-- The MATLAB Project Book for Linear Algebra http://www.mathworks.com/support/books/book1352.jsp

- How do you read a data file?
- How do you create a line plot?
- How do you define a matrix or a vector?
- How do you iterate through all the elements of a vector or a matrix?
- How do you invert a matrix?

*Octave*: a freeware imitator of Matlab, uses almost the same commands. (http://www.octave.org/)*Scilab*: another freeware imitator of Matlab (http://www-rocq.inria.fr/scilab/)*Fortran*,*c*, or*c++*: compiled languages. Run faster than Matlab for some applications,*Julia*: Offers some of the efficiencies of a compiled language with the structure of python.*Lapack/linpack*: Fortran-based matrix inversion packages. (http://www.netlib.org/lapack/)*csh, awk, perl*: Non-compiled scripting languages. Sometimes very efficient for transforming columns of numbers. (Not good for matrix inversion.)*GMT*: Generic Mapping Tool. Free unix command-line software developed for geophysical graphics. (http://gmt.soest.hawaii.edu/)

If you aren't comfortable with Matlab or Python (or the software package of your choice) work through its tutorials before the end of the first week of class. You'll need some experience to tackle the first problem sets.

Sarah Gille, December 2002, updated January 2023.

Back to SIOC 221B web site.