SIO 215a Math Methods for Oceanographers 2009
M. Hendershott - mhendershott@ucsd.edu
G. Ierley - grierley@ucsd.edu
C. Winant - cwinant@ucsd.edu

Class meets in the Munk conference room (west end of IGPP bldg) on Tu-Th @9:30
There will be a CAS session scheduled for Fr. pm (tbd)
Text: Hildebrand - Advanced Calculus for Applications
http://www.alibris.com/booksearch?qwork=132940&matches=36&wquery=Hildebrand%2C+francis&cm_sp=works*listing*titleClinton 

www.math.uic.edu/~jan/mcs494f02/Lec34/pde1.html

Participation
Think of learning as consisting of two parts: passive learning, which is what you do when you sit in the lectures or read source material, and active learning which is what you do when you work  out a problem, or when you re-create some of the plots drawn in the class room.  This first is important, but nothing happens without the second.  Making the information yours comes about during the active process.  This is why we motivate, or even coerce you to  complete homework and exams.  In this class, the active learning consists of homework, due on each Thursday, and will not be accepted late.  We expect the homework to be emailed to us as pdf files. Hand-written homework will not be read. I suggest you consider using latex or lyx as word processors, as they will soon become essential tools for your work. Homework assignments can be found beneath this paragraph.
Due date
Assignment
 1 Oct
Homework 1                           latex version                      Solution
 8 Oct
Homework 2                           Solution
15 Oct.
Homework 3                           Solution

CAS homework 1                    Solution
22 Oct
Homework 4                           Solution
 3 Nov
Mid-term                                 Solution
10 Nov
Homework 5                           Solution
13 Nov
CAS homework 2                    Solution
20 Nov
CAS homework 3                    Solution
30 Nov
CAS homework 4                   Solution
 7 Dec.
Homework 6                            Solution


In addition there will be a mid-term and final exam at tbd dates

Department of further amplification

Mid-term is on 3 Nov.
GRI CASS session 3 matlab file
GRI CASS session 2 text file
GRI CASS session 1 text file



 
We expect that an average student (?) will devote 12-16 hours each week to this material.  If you fall behind in this class, you will probably fail the class.
Syllabus (H=Hildebrand)

Date
Tentative Topic
Reading
 24 Sept
Variables, coordinates, vectors
H. Chap 6
 29
Differentiation
H. 7.1; 6.5-6.8
  1 Oct.
Matrices and tensors

 6
Complex quantities
H. 10.1-10.4
 8
Linear ordinary differential equations
H. 1.1-1.7
13
Non-homogeneous ordinary differential equations
H 1.9
15
Analytical solutions to the heat equation
H 9.2-9.4
20
“Best fit” Least squares H 5.6
22
Fourier series H 5.7
27
Fourier transforms H 5.10
29
Eigenvectors H 5.11
 3 Nov
Mid-term

 5
Numerical solutions to the heat equation I
10
Numerical solutions to the heat equation II
12
Numerical solutions to the heat equation III
17
Numerical solutions to the heat equation IV
19
Regular expansions

24
Singular expansions

 1 Dec
Boundary layers: The Blasius solution

 3
Boundary layers: the Falkner-Skan solution

Resources
The SIO library has set up a reserve list in the reserve room on the second floor, with several copies of the Hildebrand text.  That is an ideal place for you to meet as a group to discuss assignments etc...  While I expect the work you turn in to be your own effort, I encourage you to talk together and learn from each other to the maximum extent possible. 
Tools
We expect you to be (or very soon become) fluent in matlab, latex or lyx, and one of the CAS systems (Maple, Maxima or Mathematica)