fix typos

quarto/alternatives/giac.qmd

@@ -9,7 +9,7 @@ format:
 
 # Using the Giac symbolic math engine within Julia
 
-This page  describes the use of symbolic math for some topics of Calculus within `Julia` utilizing the [Giac](http://www-fourier.ujf-grenoble.fr/~parisse/giac.html) library. Giac is accessed through `Giac.jl`. Giac is a computer algebra system (CAS) implemented in C++; `Giac.jl` is an interface. See this [pdf documentation](https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/cascmd_en.pdf) for a comprehensive set of topics or the `Julia` documention for the different commands discussed.
+This page  describes the use of symbolic math for some topics of Calculus within `Julia` utilizing the [Giac](http://www-fourier.ujf-grenoble.fr/~parisse/giac.html) library. Giac is accessed through `Giac.jl`. Giac is a computer algebra system (CAS) implemented in C++; `Giac.jl` is an interface. See this [pdf documentation](https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/cascmd_en.pdf) for a comprehensive set of topics or the `Julia` documentation for the different commands discussed.
 
 There are other possible choices for symbolic math within the Julia ecosystem:
 
@@ -1680,7 +1680,7 @@ This new object can be manipulated as any other symbolic expression.
 
 ## Parametric description of functions
 
-Vectors can be used to describe curves parameterically (where the $x$ and $y$ motions are modeled by a third variable, typically $t$ for time). We describe this in a bit more detail later when discussing univariate, vector-valued functions.
+Vectors can be used to describe curves parametrically (where the $x$ and $y$ motions are modeled by a third variable, typically $t$ for time). We describe this in a bit more detail later when discussing univariate, vector-valued functions.
 
 
 Consider a person on an advanced ferris wheel with coordinates $x(t)$ and $y(t)$ describing position. The wheel of radius $r$ is centered $R$ units above and circles at radius $\omega$, the car has radius $r_0$ and rotates $6$ times faster.
@@ -2176,7 +2176,7 @@ integrate.(spiral, t, 0, pi)
 
 ##### Line integrals
 
-A line integral might be generically written over a curve $C$ or with a paramterization, $r(t)$, of $C$, yielding
+A line integral might be generically written over a curve $C$ or with a parameterization, $r(t)$, of $C$, yielding
 
 $$
 I = \int_C f(\vec{x}) ds = \int_a^b f(r(t)) dt
@@ -2379,8 +2379,8 @@ For example, to integrate $F(x,y) = x^2 \cdot y^3$ over the triangular region fo
 ```{julia}
 @giac_var x y
 F = x^2 * y^3
-Iy = integrate(F, y, 0, 1-x)  # integrating int_{x=0}^1 int_{y=0}^{1-x} F(x,y) dy dx
-integrate(Iy, x, 0, 1)
+I_y = integrate(F, y, 0, 1-x)  # integrating int_{x=0}^1 int_{y=0}^{1-x} F(x,y) dy dx
+integrate(I_y, x, 0, 1)
 ```
 
 (Integrating is made easy, but *not* the task of identifying valid endpoints to describe the region integrated over.)

quarto/alternatives/makie_plotting.qmd

@@ -510,7 +510,7 @@ arrows3d!(Point3.(us), Point3.(dus))
 current_figure()
 ```
 
-Plot of tangent lines in both two and three dimenstions
+Plot of tangent lines in both two and three dimensions
 :::
 
 
@@ -851,9 +851,9 @@ The manual construction of a figure and an axis object will be further discussed
 ### Three dimensional contour plots
 
 
-The `contour` function can also plot $3$-dimensional contour plots. Concentric spheres, contours of $x^2 + y^2 + z^2 = c$ for $c > 0$ are presented in @fig-makie-countour-three-d.
+The `contour` function can also plot $3$-dimensional contour plots. Concentric spheres, contours of $x^2 + y^2 + z^2 = c$ for $c > 0$ are presented in @fig-makie-contour-three-d.
 
-::: {#fig-makie-countour-three-d}
+::: {#fig-makie-contour-three-d}
 ```{julia}
 f(x,y,z) = x^2 + y^2 + z^2
 xs = ys = zs = range(-3, 3, length=100)

quarto/alternatives/symbolics.qmd

@@ -762,7 +762,7 @@ Symbolics.jacobian(eqs, [x,y])
 
 ## Integration
 
-The `SymbolicIntegration` package provides two means to integration *univariate* functions using either the Risch alogorithm or a rules-based approach.
+The `SymbolicIntegration` package provides two means to integration *univariate* functions using either the Risch algorithm or a rules-based approach.
 
 ```{julia}
 using SymbolicIntegration, Symbolics