diff --git a/quarto/basics/vectors.qmd b/quarto/basics/vectors.qmd index 9a5442e..dafa9b9 100644 --- a/quarto/basics/vectors.qmd +++ b/quarto/basics/vectors.qmd @@ -926,7 +926,7 @@ The latter using *splatting* to iterate over each value in `xs` and pass it to ` A few reductions work with *predicate* functions---those that return `true` or `false`. Let's use `iseven` as an example, which tests if a number is even. -We can check if *all* the alements of a container are even or if *any* of the elements of a container are even with `all` and `even`: +We can check if *all* the elements of a container are even or if *any* of the elements of a container are even with `all` and `even`: ```{julia} xs = [1, 1, 2, 3, 5] diff --git a/quarto/differentiable_vector_calculus/matrix_calculus_notes.qmd b/quarto/differentiable_vector_calculus/matrix_calculus_notes.qmd index cb65b27..bee6d93 100644 --- a/quarto/differentiable_vector_calculus/matrix_calculus_notes.qmd +++ b/quarto/differentiable_vector_calculus/matrix_calculus_notes.qmd @@ -88,7 +88,7 @@ Vectors and matrices have properties that are generalizations of the real number * Viewing a vector as a matrix is possible. The association chosen here is common and is through a *column* vector. -* The *transpose* of a matrix comes by permuting the rows and columns. The transpose of a column vector is a row vector, so $v\cdot w = v^T w$, where we use a superscript $T$ for the transpose. The transpose of a product, is the product of the transposes---reversed: $(AB)^T = B^T A^T$; the tranpose of a transpose is an identity operation: $(A^T)^T = A$; the inverse of a transpose is the tranpose of the inverse: $(A^{-1})^T = (A^T)^{-1}$. +* The *transpose* of a matrix comes by permuting the rows and columns. The transpose of a column vector is a row vector, so $v\cdot w = v^T w$, where we use a superscript $T$ for the transpose. The transpose of a product, is the product of the transposes---reversed: $(AB)^T = B^T A^T$; the transpose of a transpose is an identity operation: $(A^T)^T = A$; the inverse of a transpose is the transpose of the inverse: $(A^{-1})^T = (A^T)^{-1}$. * Matrices for which $A = A^T$ are called symmetric. @@ -133,7 +133,7 @@ The referenced notes identify $f'(x) dx$ as $f'(x)[dx]$, the latter emphasizing We take the view that a derivative is a linear operator where $df = f(x+dx) + f(x) = f'(x)[dx]$. -In writing $df = f(x + dx) - f(x) = f'(x)[dx]$ generically, some underlying facts are left implicit: $dx$ has the same shape as $x$ (so can be added) and there is an underlying concept of distance and size that allows the above to be made rigorous. This may be an abolute value or a norm. +In writing $df = f(x + dx) - f(x) = f'(x)[dx]$ generically, some underlying facts are left implicit: $dx$ has the same shape as $x$ (so can be added) and there is an underlying concept of distance and size that allows the above to be made rigorous. This may be an absolute value or a norm. ##### Example: directional derivatives diff --git a/quarto/differentiable_vector_calculus/vectors.qmd b/quarto/differentiable_vector_calculus/vectors.qmd index cf16f5c..8e625c1 100644 --- a/quarto/differentiable_vector_calculus/vectors.qmd +++ b/quarto/differentiable_vector_calculus/vectors.qmd @@ -1790,7 +1790,7 @@ plotly() nothing ``` -Parallelogram formed by two vectors $\vec{v}$ and $\vec{w}$. What is desription of red diagonal? +Parallelogram formed by two vectors $\vec{v}$ and $\vec{w}$. What is a description of red diagonal? ::: One diagonal is given by $\vec{v} + \vec{w}$. What is the other (as in the figure)? diff --git a/quarto/integrals/area_between_curves.qmd b/quarto/integrals/area_between_curves.qmd index 4088acc..ac7db6a 100644 --- a/quarto/integrals/area_between_curves.qmd +++ b/quarto/integrals/area_between_curves.qmd @@ -118,7 +118,7 @@ p = let # axis plot!([(A,0),(B,0)]; axis_style...) - # hightlight + # highlight x0, x1 = xp[marked], xp[marked+1] _style = (;line=(:gray, 1, :dash)) plot!([(a,0), (a, f(a))]; _style...) diff --git a/quarto/integrals/ftc.qmd b/quarto/integrals/ftc.qmd index 16bb31f..48c104f 100644 --- a/quarto/integrals/ftc.qmd +++ b/quarto/integrals/ftc.qmd @@ -1247,7 +1247,7 @@ Why is $F'(x) = \text{erf}'(x)$? ```{julia} #| echo: false -choices = ["The integrand is an *even* function so the itegral from ``0`` to ``x`` is the same as the integral from ``-x`` to ``0``", +choices = ["The integrand is an *even* function so the integral from ``0`` to ``x`` is the same as the integral from ``-x`` to ``0``", "This isn't true"] radioq(choices, 1; keep_order=true) ``` diff --git a/quarto/integrals/volumes_slice.qmd b/quarto/integrals/volumes_slice.qmd index 72a5f5b..be4af39 100644 --- a/quarto/integrals/volumes_slice.qmd +++ b/quarto/integrals/volumes_slice.qmd @@ -493,7 +493,7 @@ plt = let gr() # Follow lead of # https://github.com/SigurdAngenent/WisconsinCalculus/blob/master/figures/221/09surf_of_rotation2.py # plot surface of revolution around x axis between [0, 3] - # best if r(t) descreases + # best if r(t) decreases rad(x) = 2/(1 + exp(x)) trange = (0, 3) @@ -585,7 +585,7 @@ plotly() nothing ``` -Modification of earlier figure to show washer method. The interior volumn would be given by $\int_a^b \pi r(x)^2 dx$, the entire volume by $\int_a^b \pi R(x)^2 dx$. The difference then is the volume computed by the washer method. +Modification of earlier figure to show washer method. The interior volume would be given by $\int_a^b \pi r(x)^2 dx$, the entire volume by $\int_a^b \pi R(x)^2 dx$. The difference then is the volume computed by the washer method. ::: @@ -883,7 +883,7 @@ Consider a sphere with an interior cylinder bored out of it. (The [Napkin](http plt = let # Follow lead of # https://github.com/SigurdAngenent/WisconsinCalculus/blob/master/figures/221/09surf_of_rotation2.py # plot surface of revolution around x axis between [0, 3] - # best if r(t) descreases + # best if r(t) decreases rad(t) = (t = clamp(t, -1, 1); sqrt(1 - t^2)) rad2(t) = 1/2