| Symbol |
Description |
Location |
| \(p_0\) |
the initial value of a quantity \(p\) in a DTDS |
Example 1.1.4 |
| \(p_t\) |
the value of a quantity \(p\) after \(t\) steps in a DTDS |
Example 1.1.4 |
| \(f(x)\) |
the output value associated with an input value of \(x\) in the function relationship represented by \(f\)
|
Item 1 |
| \((f \circ g)(x)\) |
\(f\) composed with the function \(g\text{,}\) or \(f(g(x))\)
|
Definition 1.2.7 |
| \(f^{-1}(x)\) |
the inverse function of an invertible function \(f(x)\)
|
Definition 1.2.9 |
| \(AROC_{[a,b]}\) |
the average rate of change between \(x\) values \(a\) and \(b\) for a given function |
Definition 1.2.13 |
| \(t_d\) |
the doubling time for a given exponential growth model |
Assemblage |
| \(t_h\) |
the half life for a given exponential decay model |
Assemblage |
| \(b^*\) |
an equilibrium value for a DTDS whose dependent variable is \(b\)
|
Definition 1.8.3 |
| \(\lim_{x \to a}f(x)\) |
The limit of \(f(x)\) as \(x\) approaches \(a\)
|
Definition 2.1.2 |
| \(\lim_{x \to a^-}f(x)\) |
The limit of \(f(x)\) as \(x\) approaches \(a\) from the left |
Definition 2.1.4 |
| \(\lim_{x \to a^+}f(x)\) |
The limit of \(f(x)\) as \(x\) approaches \(a\) from the right |
Definition 2.1.4 |
| \(f'(a)\) |
The derivative of \(f(x)\) at the \(x\) value \(a\)
|
Definition 2.2.3 |
| \(f'(x)\) |
The derivative function of \(f(x)\) with respect to the variable \(x\)
|
Definition 2.3.2 |
| \(f''(x)\) |
The second derivative function of \(f(x)\) with respect to the variable \(x\)
|
Definition 2.4.4 |
| \(\frac{dy}{dx}\) |
The derivative function of \(y\) with respect to the variable \(x\)
|
Paragraph |
| \(\frac{d}{dx}[f]\) |
The derivative function of \(f\) with respect to the variable \(x\)
|
Paragraph |
| \(\frac{d^2 f}{dx^2}\) |
The second derivative function of \(f\) with respect to the variable \(x\)
|
Paragraph |
| \(L(x)\) |
The linear approximation of a function centered at an \(x\) value |
Paragraph |
| \(Q(x)\) |
The quadratic approximation of a function centered at an \(x\) value |
Assemblage |
| \(\lim_{x \to \infty}f(x)\) |
The limit of \(f(x)\) as \(x\) gets arbitrarily large |
Paragraph |
| \(f_\infty(x)\) |
The leading behavior of \(f(x)\) at \(\infty\)
|
Definition 3.7.1 |
| \(f_{-\infty}(x)\) |
The leading behavior of \(f(x)\) at \(-\infty\)
|
Definition 3.7.3 |
| \(\int f(x) dx\) |
The indefinite integral of \(f(x)\) with respect to the variable \(x\)
|
Assemblage |
| \(\sum_{k=1}^n f(k)\) |
The sum of expressions of the form \(f(k)\) as \(k\) goes from \(1\) to \(n\)
|
Paragraph |
| \(L_n\) |
A left Riemann sum for a function on an interval using \(n\) rectangles |
Paragraph |
| \(R_n\) |
A right Riemann sum for a function on an interval using \(n\) rectangles |
Paragraph |
| \(M_n\) |
A middle Riemann sum for a function on an interval using \(n\) rectangles |
Paragraph |
| \(\int_a^b f(x) dx\) |
The definite integral of \(f(x)\) as \(x\) values range from \(a\) to \(b\)
|
Definition 4.4.3 |
| \(f_{\operatorname{AVG} [a,b]}\) |
The average value of \(f(x)\) on the interval \([a,b]\)
|
Assemblage |
| \(\left. F(x) \right|_a^b\) |
The function \(F(x)\) evaluated from \(a\) to \(b\text{:}\) \(F(b) - F(a)\)
|
Paragraph |
| \(\frac{dy}{dx}\bigg\vert_{(x,y)}\) |
The derivative of \(y\) with respect to \(x\) evaluated at the point \((x,y)\)
|
Warm-Up 4.6.1 |
| \(E_{\Delta t}\) |
An approximate value of the solution to an initial value problem using Euler’s method with a step size of \(\Delta t\)
|
Paragraph |
