There will be weekly homework assignments to be collected through Gradescope, due at 11:59pm on the indicated date. No late homeworks will be accepted, however the lowest homework score will be dropped.

Homework Schedule

All assignments are from [Stein-Shakarchi].

Note that there are two types of problems in the textbook: Exercises and Problems.

(Submit in Gradescope)

# Due Date Homework Assignment  
6. Due Thur, 03/5: Chap 4: Exercises 7, 10, 11; Problem 5(a,b)  
5. Due Thur, 02/26: Chap 3: Exercises 11, 12, 19; Chap 4: Exercises 1, 4
Hint to the Hint for Ch 4 Ex 4: (Wirtinger $\Rightarrow$ Isoper. Ineq) Assume W.L.O.G. that the curve \(\gamma\) is oriented counterclockwise; use that $\mathcal{A}=-\int_\gamma ydx=-\int_0^{2\pi}x’(s)y(s)ds$ and note that both displayed integrals are nonnegative (second one by Wirtinger).
(Isoper. Ineq $\Rightarrow$ Wirtinger) Take $y(s)=f(s)$ and $x(s)=-F(s)$, where $F(s)$ is an antiderivative of $f(s)$. Condition $\int_0^{2\pi} f(s)ds=0$ ensures $F(s)$ is 2$\pi$-periodic.		  
4. Due Thur, 02/19: Chap 3: Exercises 2, 3, 6, 13, 15 [Partial Solutions]
3. Due Tue, 02/10: Chap 2: Exercises 12, 13(a), 15, 17(a,b) [Partial Solutions]
2. Due Tue, 02/03: Chap 2: Exercises 2, 3, 6, 10, 11
Note: The reverse implication in 2(e) may not hold at every point, but holds at points of continuity of \(f\). Hint: Express Fourier coefficients of \(\bar f\) in terms of those of \(f\) and apply the Uniqueness Theorem.		  
1. Due Thur, 01/22: Chap 1: Exercises 5, 7, 8, 9, 11; Problem 1 [Partial Solutions]

Gradescope Help

  • Gradescope Student Hub
  • Gradescope Tips:
    • Write different problems on separate pages.
    • Don’t forget to match the pages for each question after the upload. Unmatched questions will not be considered as submitted.