typos
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@ -9,6 +9,7 @@ ABD = "ABD"
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DNE = "DNE"
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Hass = "Hass"
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Strang = "Strang"
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multline = "multline"
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@ -15,7 +15,7 @@ The *forward error* is $||f(x+\delta_x) - f(x)||$, the *relative forward error*
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The *backward error* is $||\delta_x||$, the *relative backward error* is $||\delta_x|| / ||x||$.
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The *absolute condition number* $\hat{\kappa}$ is worst case of this ratio $||\delta_f||/ ||\delta_x||$ as the pertubation size shrinks to $0$.
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The *absolute condition number* $\hat{\kappa}$ is worst case of this ratio $||\delta_f||/ ||\delta_x||$ as the perturbation size shrinks to $0$.
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The relative condition number $\kappa$ divides $||\delta_f||$ by $||f(x)||$ and $||\delta_x||$ by $||x||$ before taking the ratio.
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@ -669,7 +669,7 @@ integrate(rho(x,y), (y, h(x), g(x)), (x, -a, a))
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##### Example (Strang)
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Integrate $\int_0^1 \int_y^1 \cos(x^2) dx dy$ avoiding the *impossible* integral of $\cos(x^2)$. As the integrand is continuous, Fubini's Theorem allows the interchange of the variable of integraton. The region, $R$, is a triangle in the first quadrant below the line $y=x$ and left of the line $x=1$. So we have:
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Integrate $\int_0^1 \int_y^1 \cos(x^2) dx dy$ avoiding the *impossible* integral of $\cos(x^2)$. As the integrand is continuous, Fubini's Theorem allows the interchange of the variable of integration. The region, $R$, is a triangle in the first quadrant below the line $y=x$ and left of the line $x=1$. So we have:
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$$
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@ -114,7 +114,7 @@ The notebook interface has "cells" where one or more commands can be entered.
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In `IJulia`, a block of commands is sent to the kernel (the `Julia` interpreter) by typing "shift+return" or clicking on a "run" button. The output is printed below a cell, including graphics.
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When a cell is evaluating, the leading `[]` has an asterick (`[*]`) showing the notebook is awaiting the results of the calculation.
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When a cell is evaluating, the leading `[]` has an asterisk (`[*]`) showing the notebook is awaiting the results of the calculation.
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Once a cell is evaluated, the leading `[]` has a number inserted (e.g., `[1]`, as in the figure). This number indicates the order of cell evaluation. Once a notebook is interacted with, the state of the namespace need not reflect the top-to-bottom order of the notebook, but rather reflects the order of cell evaluations.
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@ -663,7 +663,7 @@ numericq(val)
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##### Question
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Credit card numbers have a check digit to ensure data entry of a 16-digit number is correct. How does it work? The [Luhn Alogorithm](https://en.wikipedia.org/wiki/Luhn_algorithm).
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Credit card numbers have a check digit to ensure data entry of a 16-digit number is correct. How does it work? The [Luhn Algorithm](https://en.wikipedia.org/wiki/Luhn_algorithm).
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Let's see if `4137 8947 1175 5804` is a valid credit card number?
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