Fix prose typos and grammatical errors across 26 .qmd files

Scan of all .qmd files under quarto/ found 43 genuine prose errors
in 26 files. Changes by category:

Duplicate words removed:
- alternatives/makie_plotting.qmd: 'can can' -> 'can'; 'the the' -> 'the'
- basics/vectors.qmd: 'the the' -> 'the'; 'which which' -> 'which'
- derivatives/condition.qmd: 'the the' -> 'the'
- derivatives/derivatives.qmd: 'At at' -> 'At'
- derivatives/lhospitals_rule.qmd: 'the the' -> 'the'
- derivatives/mean_value_theorem.qmd: 'the the' -> 'the'
- derivatives/more_zeros.qmd: 'the the' -> 'the'
- differentiable_vector_calculus/matrix_calculus_notes.qmd: 3 instances
- differentiable_vector_calculus/plots_plotting.qmd: 'The the' -> 'The'
- differentiable_vector_calculus/vector_fields.qmd: 'the the'; 'a a' -> 'a'
- differentiable_vector_calculus/vector_valued_functions.qmd: 'the the'
- differentiable_vector_calculus/vectors.qmd: 'the the'
- integral_vector_calculus/div_grad_curl.qmd: 'the the'
- integral_vector_calculus/double_triple_integrals.qmd: 'The the'; 'over over'
- integral_vector_calculus/line_integrals.qmd: 'the the'
- integral_vector_calculus/review.qmd: 2x 'the the'
- integral_vector_calculus/stokes_theorem.qmd: 2x 'the the'
- integrals/improper_integrals.qmd: 'the the'
- integrals/substitution.qmd: 'that that' -> 'that'
- integrals/surface_area.qmd: 'the the'
- precalc/functions.qmd: 'that that width' -> 'that the width'

Article (a/an) corrections:
- basics/calculator.qmd: 'A overview' -> 'An overview'
- basics/vectors.qmd: 'A example' -> 'An example'; 'are a implemented' -> 'are implemented'
- derivatives/optimization.qmd: 'an trigonometry-free' -> 'a trigonometry-free'
- derivatives/taylor_series_polynomials.qmd: 'a error' -> 'an error'
- differentiable_vector_calculus/scalar_functions_applications.qmd: 'a optimization' -> 'an optimization'
- differentiable_vector_calculus/vectors.qmd: 'a another' -> 'another'; 'a an angle' -> 'an angle'
- integral_vector_calculus/double_triple_integrals.qmd: 'a azimuthal' -> 'an azimuthal'
- integral_vector_calculus/line_integrals.qmd: 'an current' -> 'a current'; 'an simply' -> 'a simply'; 'an rotational' -> 'a rotational'
- limits/intermediate_value_theorem.qmd: 'an local' -> 'a local'; 'an minimum' -> 'a minimum'

Other typos:
- basics/calculator.qmd: 'is is not' -> 'is not'; 'chicken is an unfamiliar' -> 'chicken in an unfamiliar'; 'but you the oven' -> 'but the oven'
- differentiable_vector_calculus/matrix_calculus_notes.qmd: 'symmteric' -> 'symmetric'

quarto/derivatives/condition.qmd

@@ -64,7 +64,7 @@ $$
   &= 0 + f'(r)\delta + \epsilon
 \end{align*}
 $$
-Rearranging gives $\lVert\delta/\epsilon\rVert \approx 1/\lVert f'(r)\rVert$. But the $|\delta|/|\epsilon|$ ratio is related to the the condition number:
+Rearranging gives $\lVert\delta/\epsilon\rVert \approx 1/\lVert f'(r)\rVert$. But the $|\delta|/|\epsilon|$ ratio is related to the condition number:
 
 > The absolute condition number is $\hat{\kappa}_r = |f'(r)|^{-1}$.
 

quarto/derivatives/derivatives.qmd

@@ -1574,7 +1574,7 @@ radioq(choices, answ)
 ###### Question
 
 
-The rate of change of volume with respect to height is $3h$. The rate of change of height with respect to time is $2t$. At at $t=3$ the height is $h=14$ what is the rate of change of volume with respect to time when $t=3$?
+The rate of change of volume with respect to height is $3h$. The rate of change of height with respect to time is $2t$. At $t=3$ the height is $h=14$ what is the rate of change of volume with respect to time when $t=3$?
 
 
 ```{julia}

quarto/derivatives/lhospitals_rule.qmd

@@ -498,7 +498,7 @@ $$
 \lim_{x \rightarrow \infty} \frac{1 - \cos(x)}{1},
 $$
 
-as the function just oscillates. This shows that L'Hospital's rule does not apply when the limit of the the ratio of the derivatives does not exist.
+as the function just oscillates. This shows that L'Hospital's rule does not apply when the limit of the ratio of the derivatives does not exist.
 
 
 ##### Example: the assumptions matter

quarto/derivatives/mean_value_theorem.qmd

@@ -134,7 +134,7 @@ This insight holds for other types of functions:
 
 
 
-When the derivative exists, this says the tangent line is flat. (If it had a slope, then the the function would increase by moving left or right, as appropriate, a point we pursue later.)
+When the derivative exists, this says the tangent line is flat. (If it had a slope, then the function would increase by moving left or right, as appropriate, a point we pursue later.)
 
 
 For a continuous function $f(x)$, call a point $c$ in the domain of $f$ where either $f'(c)=0$ or the derivative does not exist a **critical** **point**.

quarto/derivatives/more_zeros.qmd

@@ -461,7 +461,7 @@ $$
   &= 0 + f'(r)\delta + \epsilon
 \end{align*}
 $$
-Rearranging gives $\lVert\delta/\epsilon\rVert \approx 1/\lVert f'(r)\rVert$. But the $|\delta|/|\epsilon|$ ratio is related to the the condition number:
+Rearranging gives $\lVert\delta/\epsilon\rVert \approx 1/\lVert f'(r)\rVert$. But the $|\delta|/|\epsilon|$ ratio is related to the condition number:
 
 > The absolute condition number is $\hat{\kappa}_r = |f'(r)|^{-1}$.
 

quarto/derivatives/optimization.qmd

@@ -1361,7 +1361,7 @@ radioq(choices, answ)
 ###### Question
 
 
-The ladder problem has an trigonometry-free solution. We show one attributed to [Asma](http://www.mathematische-basteleien.de/ladder.htm).
+The ladder problem has a trigonometry-free solution. We show one attributed to [Asma](http://www.mathematische-basteleien.de/ladder.htm).
 
 
 ```{julia}

quarto/derivatives/taylor_series_polynomials.qmd

@@ -1186,7 +1186,7 @@ answ = 1
 radioq(choices, answ)
 ```
 
-Assuming the above is right, find the smallest value $k$ guaranteeing a error no more than $10^{-16}$.
+Assuming the above is right, find the smallest value $k$ guaranteeing an error no more than $10^{-16}$.
 
 
 ```{julia}