diff --git a/General/Projectile-Motion.ipynb b/General/Projectile-Motion.ipynb index 82e80c9..25bfdb5 100644 --- a/General/Projectile-Motion.ipynb +++ b/General/Projectile-Motion.ipynb @@ -22,7 +22,7 @@ "source": [ "# Intro to Jupyter Notebooks\n", "\n", - "Currently, we are using a jupyter notebook. This format can support either Julia, Python, or R. The setup is quite similar to that present in the propriety software Mathematica. \n", + "Currently, we are using a Jupyter notebook. This format can support either Julia, Python, or R. The setup is quite similar to that present in the propriety software Mathematica. \n", "\n", "We have two types of cells:\n", "* Markdown cells\n", @@ -113,7 +113,7 @@ "\\frac{d v_x}{dt} = 0 \\;\\;\\;\\; \\frac{d v_y}{dt}= g\n", "\\end{equation}\n", "\n", - "To put this into an equation, we take the derivative and break it into a courser-grained version\n", + "To put this into an equation, we take the derivative and break it into a coarser-grained version\n", "\\begin{equation}\n", "\\frac{dx}{dt} \\approx \\frac{ \\Delta x}{\\Delta t}.\n", "\\end{equation}\n", @@ -124,7 +124,7 @@ "y(t_{n+1})= y(t_n)+ v_y(t_n) \\Delta t\n", "\\end{equation}\n", "\n", - "We can also think of this as finding a small enough interval such that we can treat the y-velocity as if it's constant.\n", + "We can also think of this as finding a small enough interval such that we can treat the $y$-velocity as if it's constant.\n", "\n", "\n", "Bonus note: Different types of algorithms, like symplectic, evaluate the velocity at different time points. " @@ -280,7 +280,7 @@ "\n", "We use [Plots.jl](http://docs.juliaplots.org/latest/) to display our results here.\n", "\n", - "Tips from Expierence: Always include x and y labels, title, legends, and relevant units on the graph. \n", + "Tips from Experience: Always include $x$ and $y$ labels, title, legends, and relevant units on the graph. \n", "\n", "The graph might seem obvious to you now, but the labeling might not seem obvious to you next week, next month, or next year. And it probably won't seem obvious to someone else looking at your work.\n", "\n", @@ -3245,7 +3245,7 @@ } ], "source": [ - "# Lets choose our step sizes\n", + "# Let's choose our step sizes\n", "dta=[.001,.01,.1,.2]" ] }, @@ -4156,7 +4156,7 @@ "\n", "Real objects encounter air resistance proportional to velocity. That effect can't be solved analytically, but our code can handle it easily.\n", "\n", - "We include air resistence by adding a force against the direction motion and proportional to the velocity squared in strength. We then have to project it along the x and y directions.\n", + "We include air resistence by adding a force against the direction motion and proportional to the velocity squared in strength. We then have to project it along the $x$ and $y$ directions.\n", "\\begin{equation}\n", "\\vec{F}=-\\text{sign}(\\vec{v}) \\frac{1}{2}\\rho C_d A v^2 = -\\text{sign}( \\vec{v}) R v^2,\n", "\\end{equation}\n", diff --git a/Graduate/1D-Spin-Chain-Prerequisites.ipynb b/Graduate/1D-Spin-Chain-Prerequisites.ipynb index c1f0d0b..de04c9c 100644 --- a/Graduate/1D-Spin-Chain-Prerequisites.ipynb +++ b/Graduate/1D-Spin-Chain-Prerequisites.ipynb @@ -203,7 +203,7 @@ "# psi is an array of all our wavefunctions\n", "psi=convert.(Int8,collect(0:(nstates-1)) )\n", "\n", - "# Lets look at each state both in binary and base 10\n", + "# Let's look at each state both in binary and base 10\n", "println(\"binary form \\t integer\")\n", "for p in psi\n", " println(bitstring(p)[end-n:end],\"\\t\\t \",p)\n", @@ -401,7 +401,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So now lets test how the first of our three masks behaves:\n", + "So now let's test how the first of our three masks behaves:\n", "We know that if the mask changes a 01 for a 10 (or vice versa) that the overall magnetization will not be changed. So, we test is our mask is successful by comparing the remaining magnetization. The rows offset by two spaces have matching magnetizations." ] }, diff --git a/Graduate/Winding-Number.ipynb b/Graduate/Winding-Number.ipynb index 8f2b8a7..3476cbf 100644 --- a/Graduate/Winding-Number.ipynb +++ b/Graduate/Winding-Number.ipynb @@ -6,7 +6,7 @@ "source": [ "# The Winding Number and the SSH model\n", "\n", - "The Chern number isn't the only topological invariant. We have multiple invariants, each convenient in their own situations. The Chern number just happened to appear one of the biggest, early examples, the Integer Quantum Hall Effect, but the winding number actually occurs much more often in a wider variety of circumstances.\n", + "The Chern number isn't the only topological invariant. We have multiple invariants, each convenient in their own situations. The Chern number just happened to appear in one of the biggest, early examples, the Integer Quantum Hall Effect, but the winding number actually occurs much more often in a wider variety of circumstances.\n", "\n", "How many times does the phase wrap as we transverse a closed loop?\n", "$$\n", @@ -219,7 +219,7 @@ "$$\n", "U H U^{-1} = -H \\qquad \\qquad U U^{\\dagger} =\\mathbb{1}.\n", "$$\n", - "Finding $U$ if even exists and determining its form if it exists is a problem for another time. Today, multiple places said that $\\sigma_z$ works for the SSH model, and we can confirm that it does. \n", + "Finding if $U$ even exists and determining its form if it exists is a problem for another time. Today, multiple places said that $\\sigma_z$ works for the SSH model, and we can confirm that it does. \n", "\n", "A little less intellectually satisfying (at least for me), but it works.\n", "\n", @@ -284,7 +284,7 @@ "=\\pm \\sqrt{v^2+w^2 \\cos^2 k -2 vw \\cos k + w^2 \\sin^2 k} \n", "= \\pm \\sqrt{v^2 - 2 vw \\cos k + w^2}\n", "$$\n", - "The difference between the upper and lower band will be at it's minimum when $\\cos k$ is greatest,$k=0$.\n", + "The difference between the upper and lower band will be at its minimum when $\\cos k$ is greatest, $k=0$.\n", "$$\n", "=\\pm \\sqrt{(v-w)^2}\n", "$$\n", @@ -1059,7 +1059,7 @@ "$$\n", "Here we have a 1-1 correspondence between the Hamiltonian and a geometric object, this $\\vec{R}$ vector. When we look at how it depends on $k$, we get insight into how $\\mathcal{H}$ depends on $k$ as well.\n", "\n", - "The two different groups, purple and turquoise, will have two different behaviors. $\\vec{R}(k)$ for purple will circle the origin like $S^1$ the unit circle, whereas $\\vec{R}(k)$ for turquoise not circle the origin and will not be like $S^1$." + "The two different groups, purple and turquoise, will have two different behaviors. $\\vec{R}(k)$ for purple will circle the origin like $S^1$ the unit circle, whereas $\\vec{R}(k)$ for turquoise will not circle the origin and will not be like $S^1$." ] }, { diff --git a/Numerics_Prog/Jacobi-Transformation.ipynb b/Numerics_Prog/Jacobi-Transformation.ipynb index 841f0a0..b66e12d 100644 --- a/Numerics_Prog/Jacobi-Transformation.ipynb +++ b/Numerics_Prog/Jacobi-Transformation.ipynb @@ -41,7 +41,7 @@ "\\begin{equation}\n", "A^{\\prime}= P^{T}_{pq} \\cdot A \\cdot P_{pq}\n", "\\end{equation}\n", - "where each iteration brings A closer to diagonal form. Thus in our implementing our algorithm, we need to determine two things\n", + "where each iteration brings A closer to diagonal form. Thus in implementing our algorithm, we need to determine two things\n", "