Chapter 2, Mathematica's Programming Language Video Solutions, Computer science with Mathematica: theory and practice for science, mathematics, and engineering

Problem 1

1. Go through the examples given in Sections 2.1-2.3, and determine the internal forms of the expressions that occur in these examples. Mathematica can help you; see Section 2.4.3.
2. What is the internal form of these expressions before evaluation?
a. $f @\{a, b, c\}$
b. $f /@\{a, b, c\}$
c. $f @@\{a, b, c\}$

Carole Wastog

Numerade Educator

03:36

Problem 2

Investigate this expression:
$$
f^{\prime}[x+1] / 5 \text { ! }
$$
1. Write the expression in internal form, without using any operators.
2. Denote the building blocks of the expression, that is, head and elements. Continue in this way with any parts that are still composite. Give the type of atomic parts.
3. To what does this expression evaluate?

Charles Carter

Numerade Educator

05:34

Problem 3

Give the result of evaluating the following expressions. If there are any nested functions, also give the most important intermediate steps. Assume that each example is evaluated in a fresh Mathematica session. Consecutive expressions in one example are evaluated one after another in the same session.
1. $\operatorname{Sum}[z \wedge i / i !,\{i, 0,4\}]$
2. $\operatorname{Sum}[\operatorname{Product}[(x-i) \wedge j,\{i, 0,2\}],\{j, 2\}]$
3. Expand[ Product $[x-i,\{i,-2,2\}]]$
4. $\{1,2,3\} \wedge 2+1$
5.$\begin{aligned} & a=5 ; b:=6 ; \\ & c=a ; d=b ; \\ & e:=a ; f:=b ; \\ & a=7 ; b:=8 ; \\ & \{a, b, c, d, e, f\}\end{aligned}$

Willis James

Numerade Educator

12:50

Problem 4

For positive reals $a$ and $g$, the two sequences $a_i$ and $b_i$, with
$$
\begin{aligned}
a_0 & =a \\
g_0 & =g \\
a_{i+1} & =\frac{a_i+g_i}{2} \\
g_{i+1} & =\sqrt{a_i g_i}
\end{aligned}
$$
converge to a common limit. Observe that $a_{i+1}$ is the arithmetic mean of $a_i$ and $g_i$, and that $g_{i+1}$ is the geometric mean.
1. Compute the common limit numerically for a few values of $a$ and $g$ with a simple While loop.
2. Define a function AGM $[a, g]$ that computes this limit.

M Z

Numerade Educator