Homework 6

Due: Mar 28th, 2021

Note: Due date extended to Sunday, March 28 (instead of Wednesday, March 24)

These exercises are on sequences and series of functions.

Exercises

1. Choose: either Lebl 6.1.4+6.1.5 (both exercises together) or TBB 9.3.4+9.3.5 (both exercises together)

2. Lebl 6.1.6

3. Choose one: Lebl 6.1.10, 6.1.11

4. Choose one: Lebl 6.2.7, 6.2.12

Instructions

If you don’t have LaTeX on your computer, you can use Overleaf. Upload the PDF to Gradescope. Don’t submit the LaTeX source, just the PDF.

• When you upload to Gradescope, please mark which page of the PDF has your answer to each question!

Email your instructor (that’s me) if you have questions or need help.

Some additional formatting instructions are in the syllabus. To summarize:

• Use a new page (\newpage) for each problem.
• State which question you are answering and the actual question. Then, start your answer in a new paragraph.
• Use environments such as proof and theorem (via \begin{proof}...\end{proof}).
• Use 12pt option \documentclass[12pt]{amsart} and \linespread{2.4}.

Please find and use the LaTeX template linked on the course website.

You are encouraged to work together on the homework!

Additional reading

• Visit the Mathematics Colloquium web page: https://math.boisestate.edu/colloquium/
  Visit the Mathematics seminars web page: https://math.boisestate.edu/seminars/
  You are invited to attend colloquium and seminar talks!

• You might enjoy the articles:

  1. Connections in Mathematical Analysis: the Case of Fourier Series

  2. Fourier series in the College Math Journal (and you can do a similar search for Taylor series, which also finds lots of nice results)

  3. Taylor series in Mathematics Magazine (similarly, you can try searching for Fourier series or Maclaurin series)

  4. The Convergence of Fourier Series