Solve the following problem by hand. When needed, use a calculator, or write a MATLAB script file to carry out the calculations. Use MATLAB to make plots.

Expand $y=x$ where $x \in[0,3]$ in an infinite Fourier series (Eq. $f(x)=\sum_{k=0}^{\infty}\left[A_k \sin \left(\frac{\pi k x}{L}\right)+B_k \cos \left(\frac{\pi k x}{L}\right)\right]$). What is the value predicted by the Fourier series for $x=3$ ?

What commentary does Dylan Thomas make on Welsh life in '' Under Milk Wood?''

How do Colt's expectations about life at "Octagon City" compare with the reality she finds there?

Given the function $f(x)=\frac{\left(x^2+\sqrt{x}\right) \cos (x)}{\sin (x)}$, find the value of the first derivative at $x$=2. (a) Use analytical differentiation by hand. (b) Use the four-point central difference formula with $x_{i-2}$=1.96, $x_{i-1}$=1.98, $x_{i+1}$=2.02, and $x_{i+2}$=2.04. Write a MATLAB program in a script file to carry out the calculations.

Solve the following problem by hand. When needed, use a calculator, or write a MATLAB script file to carry out the calculations. If using MATLAB, do not use built-in functions for numerical solutions

Consider the second-order ODE of the form:

$$\frac{d^2 y}{d x^2}+p \frac{d y}{d x}+q y=r(x)$$

where $p$ and $q$ are constants, and $r(x)$ is a given function. Using second-order accurate central differences for the derivatives, discretize the ODE.

Solve the following problem by hand. When needed, use a calculator, or write a MATLAB script file to carry out the calculations. Use MATLAB to make plots.

Expand $y=\sin (\pi x) \cos (\pi x)$ where $x \in[0,2]$ in an infinite Fourier series (Eq. $f(x)=\sum_{k=0}^{\infty}\left[A_k \sin \left(\frac{\pi k x}{L}\right)+B_k \cos \left(\frac{\pi k x}{L}\right)\right]$).

Which elements of these poems reflect Williams's interest in portraying and celebrating everyday American life?

True or False

Avoid placing flowers on a wedding cake because you could poison the wedding guests.

Describe one method that can be used to make a hanger for a Styrofoam or straw wreath.

Select southern pine $\mathrm{(S4S)}$ simply supported joists to carry a floor live load of $120 \mathrm{~psf}$ and a superimposed dead load of $20 \mathrm{~psf}$. The joist spacing will be $16 \mathrm{~in}$. and the span will be $14 \mathrm{~ft}$.

Find all cosets of the subgroup ⟨2⟩ of

$$ℤ_{12}.$$

Find all Maclaurin polynomials $P_{n}(x) \text { for } f(x)=x^{3}$.

Find all possible functions ƒ with the given derivative. ƒ'(x) = sin x

Write the negation of the statement. All numbers are divisible by 5.