## Fourier Analysis, MTH 490-003

Instructor: |
Mark Iwen |

Time and Place: |
Lectures are Tu Th 12:40 pm -- 2:00 pm, in 2243 Engineering Building |

E-mail: |
markiwen@math.msu.edu |

Office: |
C342 WH |

Office Hours: |
Tu 2:15 pm -- 3:15 pm, W 2 pm -- 3 pm, and Th 2:15 pm -- 3:15 pm |

We will discuss Fourier series, Orthogonal Functions, Inner Product Spaces, Convergence issues, The Fourier Transform, Distributions, and Wavelets.

#### Course website for MTH490-003:

http://math.msu.edu/~markiwen/Teaching/MTH490/MTH490_S16.html

The course website is mandatory reading for the course. On it you will find the course schedule, the syllabus, and supplementary reading. Homework assignments will be posted on the schedule.

#### Textbook:

**Fourier Analysis and Its Applications**, by Gerald B. Folland.

International Thompson Publishing Company, 1992.

The majority of the course will be spent covering Chapters 2, 3, 7, and 9 of Folland's book.

#### Supplementary Texts:

We will also utilize material from **Fourier Analysis** by Elias Stein and Rami Shakarchi, and from **Wavelet Theory** by David Ruch and Patrick Van Fleet. It's not necessary to buy either of these books (though both are good).

#### D2L:

Additional reading materials and student grades are available on D2L (https://d2l.msu.edu). This website also contains a lot of good information about potential student projects.

#### Homework:

Homework assignments will be given every other week and will constitute 60% of your final grade. The homework questions will be assigned on the web with their due dates. Posting of new assignments will be announced in class. You must submit your homework solutions during the class period on the due date unless prior permission has been granted to submit otherwise. **Late homework assignments will never be graded.** The lowest homework score will be dropped when computing your average homework grade. Homework solutions must be original copies in the student's own handwriting. No other submissions will be graded. Solutions must be clear and neatly written to receive credit. A subset of the homework problems will be graded on each assignment.

#### Project:

There will be a final project consisting of two parts: **(i)** A 20 minute presentation to be delivered during the last week of class, or the final exam period (May 2nd, 12:45pm - 2:45pm), and **(ii)** a written report summarizing in 7 to 10 pages your project research topic (due the last day of class). You should expect to spend a good deal of time researching the topic in the library, looking at books and research articles. You will probably have to read some things you don't understand fully. This is an important skill to cultivate. A rough draft of the paper should be turned in to me for comments about three weeks before the semester ends. Students are encouraged to work in groups of two, three, or four. If your project involves writing any computer code, then this should also be turned in and will be graded as part of the project report.

The project grade will graded based on the project report (60%), and the project presentation and slides/notes (40%). Copies of all presentation notes/slides must be submitted the day of the presentation. A hard copy of the project report is due at the beginning of the last class. Project reports should be written in LaTeX using this template. Project presentation slides should be done in either power point or LaTeX. If a chalk talk is done instead, then a neatly written copy of the notes should be turned in beforehand.

#### Grading:

Your final course percentage will be determined by averaging your homework and project percentages with the following weights: Homework (60%) and the Project (40%). The result of this weighted average will then be rounded to the nearest integer.

Your final grade (e.g., 3.5, 4.0, etc.) will be assigned according to a class ranking. That is, the weighted averages calculated as above for all the students in the class will be rank ordered. Finally, threshold scores (e.g., a score above which a 4.0 is earned) will be determined, thereby establishing each student's final grade in the class. The threshold scores for each grade will never be higher than those indicated in following table.

90% -- 100% | A | 4.0 |

85% -- 89% | A-/B+ | 3.5 |

80% -- 84% | B | 3.0 |

75% -- 79% | B-/C+ | 2.5 |

70% -- 74% | C | 2.0 |

65% -- 69% | C-/D+ | 1.5 |

60% -- 64% | D | 1.0 |

0% -- 59% | F | 0.0 |

Incomplete grades will be given only in unusual cases of illness or other personal emergency, which causes the student to miss a significant amount of the course. This grade cannot be given for any other reason.

#### Academic Integrity:

You are encouraged to work with your peers on solving homework assignments. However, all submitted homework solutions must be written up individually in your own words. Submitting another student's written work as your own will be considered plagiarism.

**Article 2.3.3 of the Academic Freedom Report states: "The student shares with the faculty the responsibility for maintaining the integrity of scholarship, grades, and professional standards." In addition, this instructor adheres to the University regulations, policies, and ordinances on academic honesty and integrity, as specified in General Student Regulation 1.0, Protection of Scholarship and Grades; the all-University Policy on Integrity of Scholarship and Grades; and Ordinance 17.00, Examinations, all of which are available on the MSU web site (www.msu.edu). Students who violate these rules may receive a penalty grade, including, but not limited to, a failing grade on the assignment or in the course. The following conduct is specifically cited: (1) Supplying or using work or answers that are not one's own; (2) Interfering through any means with another's academic work; and (3) Faking data or results.**