GPH 503 Mathematical Methods in Geophysics
                                                                                 Fall 2011
Syllabus
OFFICE: New Geophysics Building, 2nd floor
OFFICE HOURS: Thursdays 15:00-17:00
E-MAIL ADDRESS: ozgun.konca@boun.edu.tr
COURSE WEB PAGE:http://www.koeri.boun.edu.tr/jeofizik/kisiler/personal/ozgun/gph503/
CLASS HOURS: Mondays 13:00-16:00
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Description: The aim of this course is to teach the basic mathematics for Master's level earth science students with applications to earth sciences. The subjects covered include linear algebra, complex analysis and integral transforms.

Prerequisites: Undergraduate level linear algebra, and calculus.

Goal: The goal is to obtain the mathematical background necessary for geophysical studies and other geophysics classes. Successful students are expected to attend all the classes (except with medical report).  Quizzes and homework will be assigned  every week (except midterm week and holidays).

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Topics
Linear Systems and Matrices

  • Systems of Equations and Matrices
  • Inverse of a Matrix
  • LU decomposition
  • Least Squares solutions
  • Eigenvalues and Eigenvectors
  • Singular Value Decompositon
  • Generalized Inverses
Complex Analysis

  • Complex Numbers
  • Polar Representation
  • Roots of a Complex Number
  • Branch points and Branch Cuts
  • Complex Derivative
  • Analyticity
  • Residue Theory
  • Complex Integration
Integral Transforms
  • Fourier Series
  • Fourier Transform
  • Convolution, Correlation
  • Z-transform, Hilbert Transform
  • Fourier Transform in Cylindrical Coordinates

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Grading Plan

Homework assignments 20%
Quizzes 20%
Midterm 20%
Final 40%

Homework assigments: Homework assignments will be given throughout the term. The assignments are supposed to be returned on time, in class. 10 points (out of 100) will be deducted from your homework for each day of late return after the assignment deadline.  No homework will be accepted 2 days after the deadline. The lowest graded homework will be dropped (it will not be included in your grade).

Quizzes:  Quizzes will be given in class. Quizzes may or may not be announced before. This will also be a way to measure the attendance. The lowest graded quiz will be dropped (it will not be included in your grade).

Collaboration: Collaboration is welcome and strongly encouraged for the homework assignments. It is not OK to copy answers from each other without putting some thought into it. 

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Homework Assignments

AssignmentsDue Date
Assignment 103/10/2011
Assignment 210/10/2011
Assignment 317/10/2011
Assignment 424/10/2011
Assignment 531/10/2011
Assignment 614/11/2011
Assignment 728/11/2011
Assignment 85/12/2011

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