Book:Morris Tenenbaum/Ordinary Differential Equations/Errata

Errata for 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations

Historical Note on Radiocarbon Dating

Chapter $1$: Basic Concepts: Lesson $1$: How Differential Equations Originate

*Dr. Willard F. Libby was awarded the $1960$ Nobel Physics Prize for developing this method of ascertaining the age of ancient objects. His $C^{14}$ half-life figure is $5600$ years, ...

Arbitrary Function

Chapter $1$: Basic Concepts: Lesson $2 \text B$: The Meaning of the Term Function of One Independent Variable

The relationship between two variables $x$ and $y$ is the following. If $x$ is between $0$ and $1$, $y$ is to equal $2$. If $x$ is between $2$ and $3$, $y$ is equal to $\sqrt x$. The equations which express the relationship between the two variables are, with the end points of the interval included,

\(\text {(a)}: \quad\)

\(\ds y\)

\(=\)

\(\ds 2,\)

\(\ds 0 \le x \le 1,\)

\(\ds y\)

\(=\)

\(\ds \sqrt x,\)

\(\ds 2 \le x \le 3.\)

These two equations now define $y$ as a function of $x$. For each value of $x$ in the specified intervals, a value of $y$ is determined uniquely. The graph of this function is shown in Fig. $2.211$. Note that these equations do not define $y$ as a function of $x$ for values of $x$ outside the two stated intervals.

Figure $2.211$