GPH 503 Mathematical Methods in Geophysics Fall 2011 |

Syllabus

OFFICE: New
Geophysics Building, 2OFFICE HOURS:

E-MAIL ADDRESS: ozgun.konca@boun.edu.tr

COURSE WEB PAGE:

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

- Complex Numbers
- Polar Representation
- Roots of a Complex Number
- Branch points and Branch Cuts
- Complex Derivative
- Analyticity
- Residue Theory
- Complex Integration

- 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%

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

Assignments | Due Date |

Assignment 1 | 03/10/2011 |

Assignment 2 | 10/10/2011 |

Assignment 3 | 17/10/2011 |

Assignment 4 | 24/10/2011 |

Assignment 5 | 31/10/2011 |

Assignment 6 | 14/11/2011 |

Assignment 7 | 28/11/2011 |

Assignment 8 | 5/12/2011 |