CRN 13593: Weeks

Week 9

• 20. Fourier Analysis II

• 21. Fourier Analysis III

• Start reading Multi-Resolution Analysis for the Haar Wavelet.

Week 8

• Read pp.334-344.
• 19. Fourier Analysis I (15 min.) [Disclaimer: There are a few "typos" - sorry!]

Week 7

• Your first test will be on Thursday, October 8. I will email the test to you at 17:00; you will need to return it to me via email in PDF format by 18:30. You are allowed to use a hand-held calculator and writing utensils only. The test will cover the material up to Video 16, including the "traditional Fourier series" homework I assigned last week.
• Read pp.322-334.
• 17. Complex numbers (23 min.):

• 18. The complex exponential function (21 min.):

Week 6

• A new project has been posted. Deadline is October 16. Watch the next video for help on some Mathematica commands.
• 14. Some advanced Mathematica commands (18 min.):

• 15. Traditional Fourier Analysis (20 min.):

• 16. An example (8 min.):

• Your first test will be on Thursday, October 8. I will email the test to you at 17:00; you will need to return it to me via email in PDF format by 18:30. You are allowed to use a hand-held calculator and writing utensils only. The test will cover the material up to this point, including the homework I assigned today:
  1. Show that \(\int_{-\pi}^\pi \sin(kt) \cos(nt)\, dt=0\) for all values of k and n.
  2. Compute \(\int_{-\pi}^\pi \cos(kt) \cos(nt)\, dt\) for all values of k and n.
  3. (a) Compute \(\|\sin(t)\|_2\). (b) Can you find c such that \(\|c\sin(kt)\|_2=1\) or all k?
  4. Compute the Fourier coefficients of \(f(t)=|t|\)
  5. Can every function \(f:\mathbb{R}\to\mathbb{R}\) be written as the sum of an odd function and an even function?

Week 5

• Towards Shannon's Entropy Theorem
• 13. Shannon's Entropy Theorem (13 min.):

Week 4

• Read pp. 91-96, 106-120
• Homework: p.106: 3.26ab; p.113: 3.27, 3.28, 3.29, 3.30, 3.33
• 9. Color Images (16 min.):

• 10. Huffman Encoding (17 min.):

• 11. Huffman Encoding II (6 min.):

• 12. Quantitative and Qualitative Measures (12 min.):

Week 3

• Project 2 has been posted.
• 8. Creating Large Matrices with the SparseArray Command (13 min.):

• Project 1 is due on Friday, September 11: Project 1. Please email the project to me at hknaust@utep.edu. Name the notebook "<your last name> 1.nb", e.g. "Smith 1.nb".

Week 2

• Read pp.69-85
• Photo set
• 5. Loading Photos into Mathematica (14 min.):

• 6. Introduction to Digital Images I: (14 min.)

• 7. Introduction to Digital Images II: (16 min.)

Week 1

• 1. Course Overview and Syllabus (28 min.):
  

• Read pp.15-40 (skip Example 2.9)
• 2. Section 2.1 (9 min.):
  

• 3. Section 2.2 (18 min.):

• How to display matrices the "right" way
• 4. Project 1 (6 min.):