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Fall 2016: MATH 464 Transformed Methods for Scientists and Engineers

Instructor:
Radu Balan
Contact:
  • Office hours: Thurs. 2:00-3:15 pm in CSIC 4131 (CSCAMM)
  • Email: rvbalan at math.umd.edu
  • Office: Math 2308 / CSCAMM 4131
  • Office phone: 301 405 5492 / 301 405 1217

Lectures: 12:30pm-1:45pm on Tue., Thr., in CSIC 4122. Except when a CSCAMM workshop takes place.

Prerequisites: MATH 246

Textbook:
Required Textbook: "A First Course in Fourier Analysis" by David W. Kammler, Cambridge University Press 2000 (1st Edition), or 2007 (2nd Edition).

Additional References:

  • Charles L. Epstein, "Introduction to the Mathematics of Medical Imaging", SIAM 2008.
  • Elliott H. Lieb and Michael Loss, "Analysis", AMS 2001.
  • John J. Benedetto, "Harmonic Analysis and Applications", CRC Press 1996.

Description: MATH 464 is an introduction to transformed methods used in science and engineering applications. Lectures will cover topics including: Fourier transform, Fourier series, discrete and fast Fourier transform (DFT and FFT), Laplace transform, Poisson Summation, and sampling. Optional Topics: Distributions and operational calculus, PDEs, Wavelet transform, Radon transforms. Applications: Imaging, Speech Processing, PDEs of Mathematical Physics, Communications, Inverse Problems.

Assignments: Homework must be submitted on the date assigned. Homework must be prepared without consulting any other person. You may however consult any written reference. In this case you should cite the reference. Results taken from the reference should be (re)stated to the notation used in the course. Explanation should be given in complete English sentences. Written work must be legible and clear.

Exams: One midterm will be scheduled during regular class (1h15min long). You are allowed with one one-side formula sheet. The final exam will be 2-hour long, and currently it is scheduled for TBA. For the final exam you are allowed with one two-side formula sheet.
Review Sessions: TBA in TBD.

Grading:

  • 25%: homeworks
  • 25%: midterm
  • 50%: final exam