From 026159005302a5d96237c5bf5b1122bd3a8bb3b9 Mon Sep 17 00:00:00 2001 From: S-Blaha Date: Mon, 2 Jun 2025 13:02:57 -0400 Subject: [PATCH 01/39] Added preamble for worksheets as well as model and experiment worksheet --- worksheets/include/beamerworksheet.tex | 56 ++++++++++++++++++ worksheets/include/figures/bmdwlogo.pdf | Bin 0 -> 117308 bytes .../model and experiment.pdf | Bin 0 -> 181988 bytes .../model and experiment.tex | 24 ++++++++ 4 files changed, 80 insertions(+) create mode 100644 worksheets/include/beamerworksheet.tex create mode 100644 worksheets/include/figures/bmdwlogo.pdf create mode 100644 worksheets/model and experiment/model and experiment.pdf create mode 100644 worksheets/model and experiment/model and experiment.tex diff --git a/worksheets/include/beamerworksheet.tex b/worksheets/include/beamerworksheet.tex new file mode 100644 index 0000000..ae892fd --- /dev/null +++ b/worksheets/include/beamerworksheet.tex @@ -0,0 +1,56 @@ +\usepackage[a4paper, margin=1in]{geometry} +\usepackage{graphicx} +\usepackage[absolute, overlay]{textpos} +\usepackage{fancyhdr} + +\newcommand{\customsubject}{} +\newcommand{\customtitle}{} +\pagestyle{empty} + +\newenvironment{worksheet}[2] +{ + + \renewcommand{\customtitle}{#1} + \renewcommand{\customsubject}{#2} + \begin{textblock*}{5cm}(0.4cm,0.4cm) + \includegraphics[width=4cm]{../include/figures/bmdwlogo} +\end{textblock*} + + \vspace*{-1cm} + + {\large\textbf{\begin{center}\customtitle\end{center}}} + + \begin{center}\customsubject\end{center} + + \vspace{0.3cm} + + \hspace*{-1.5cm}\textbf{Name:\ \rule{4cm}{0.4pt}}\; + \textbf{Student \#: \ \rule{3cm}{0.4pt}}\; + \textbf{Student Email \#: \ \rule{1.53cm}{0.4pt}} + + \vspace{0.5cm} + + + \begin{enumerate} +} +{ + \end{enumerate} + + \begin{textblock*}{10cm}(1cm, 28cm) {\footnotesize \scriptsize \customsubject} + + +\end{textblock*} +} + + + +\newcommand{\question}[2][5cm]{% + \item + #2 + \vspace{#1} +} + +\newcommand{\questionpart}[2][5cm]{% + #2 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@@ +\documentclass[12pt]{article} + +\include{../include/beamerworksheet} + + +\begin{document} + +\begin{worksheet}{Phys 101 Worksheet}{Comparing Model and Experiment} + +\question[3cm]{\textbf{Thinking Like a Physicist}\\ Suppose there's a theory "Dogs cannot be born with naturally blue fur." Can this theory be proven to be true? \textbf{Explain} why or why not.} + +\question[0.1cm]{\textbf{Dimensional Analysis}\\ Suppose you're a butterfly researcher. You find that rarer butterflies appear to be faster, and flutter their wings at a higher rate than more common butterflies. You invent a new unit, a "Whimsy" (denoted as $W$), which is the \textbf{product} the maximum velocity of a given species of butterfly, $v$, and the frequency at which it flaps its wings $f$.} + +\questionpart[2cm]{\textbf{(a)} Explicitly write out the formula to calculate Whimsiness. What are it's dimensions?} + +\questionpart[3cm]{\textbf{(b)} Suppose now you want to create a formula that could predict the most whimsical butterfly any given butterfly catcher could catch knowing only their mass, $m$ and the maximum force the can swing with $F_s$. Write a possible solution (within a constant) that could be a solution to the problem.} + +\questionpart[0cm]{\textbf{(c)} Does the formula you've devised make sense? Explain wy or why not. (Hint: When you increase certain variables, does whimsiness increase or decrease as you would expect?)} + + +\end{worksheet} + + +\end{document} \ No newline at end of file From 718add375b11c75ebf7df0ba4e85f905a98ada76 Mon Sep 17 00:00:00 2001 From: S-Blaha Date: Mon, 2 Jun 2025 14:30:44 -0400 Subject: [PATCH 02/39] Added more functionality and automation to preamble, reformated modela dn experiment worksheet to adjust and added empty derivatives worksheet --- worksheets/Math/Derivatives.pdf | Bin 0 -> 155402 bytes worksheets/Math/Derivatives.tex | 18 +++++++++++ .../ModelAndExperiment.pdf} | Bin 181988 -> 181515 bytes .../ModelAndExperiment/ModelAndExperiment.tex | 24 ++++++++++++++ ...merworksheet.tex => preambleworksheet.tex} | 30 ++++++++++++++---- .../model and experiment.tex | 24 -------------- 6 files changed, 66 insertions(+), 30 deletions(-) create mode 100644 worksheets/Math/Derivatives.pdf create mode 100644 worksheets/Math/Derivatives.tex rename worksheets/{model and 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+ + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/model and experiment/model and experiment.pdf b/worksheets/ModelAndExperiment/ModelAndExperiment.pdf similarity index 91% rename from worksheets/model and experiment/model and experiment.pdf rename to worksheets/ModelAndExperiment/ModelAndExperiment.pdf index 6cf4a75b717bcd4e6c06cfd5505bcda56420114d..b26061ec7ece9b274fdaa16280f0cec22ae16f75 100644 GIT binary patch delta 15461 zcmajGQe zImWuk!x-48NZ9yaAWW=jcXS|B01cVAO-{Jp6Ai4UFmAyj=|UBkFl8+V=c`D`pL+O}@v?M!Zx5hn*l6eCUCD0PE9?x-bh> zqa_)ejI-R#PV>`@du<0K1#^@@vy9^CMdP22Si2_j;msSKIw~HGv}qLaMVz-IoD4%| znL@S1#%vkwLkFEShI!w+XY)HdViE)aWb8rFREZ1--ipXb@4GjexRrb#LZ<-B!k)Hj zqmW=S@*pR4KW$&#?p$FvfVP(NbaMPo7LbGgUxmSTh-Rc(;JGs1Z##(4C9V%PEOIkE z^)Kj1QI}MlF9FJ(l@&Ekw59+wpb4*MnsBrsF#%v#r&DqhXh>d1yb5Sfuq+;K$u3^D zy~)ijTfGNCE8vc&G#|lNvT52cIj>Wg)md`9Fjqy{3ff?!EhU5&03WxsDzEKit?$Yr zSPwb$#KyH?Vb#Smza{J@>y;q6$KJ3fqY(&wSLo%l{n|o#!{FL_B{x`?HC&bbNUYxc 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Experiment} + +\question[3cm]{Thinking Like a Physicist}{Suppose there's a theory "Dogs cannot be born with naturally blue fur." Can this theory be proven to be true? \textbf{Explain} why or why not.} + +\question[0.1cm]{Dimensional Analysis}{Suppose you're a butterfly researcher. You find that rarer butterflies appear to be faster, and flutter their wings at a higher rate than more common butterflies. You invent a new unit, a "Whimsy" (denoted as $W$), which is the \textbf{product} the maximum velocity of a given species of butterfly, $v$, and the frequency at which it flaps its wings $f$.} + +\questionpart[2cm]{Explicitly write out the formula to calculate Whimsiness. What are it's dimensions?} + +\questionpart[3cm]{ Suppose now you want to create a formula that could predict the most whimsical butterfly any given butterfly catcher could catch knowing only their mass, $m$ and the maximum force the can swing with $F_s$. Write a possible solution (within a constant) that could be a solution to the problem.} + +\questionpart[0cm]{Does the formula you've devised make sense? Explain wy or why not. (Hint: When you increase certain variables, does whimsiness increase or decrease as you would expect?)} + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/include/beamerworksheet.tex b/worksheets/include/preambleworksheet.tex similarity index 53% rename from worksheets/include/beamerworksheet.tex rename to worksheets/include/preambleworksheet.tex index ae892fd..f74598a 100644 --- a/worksheets/include/beamerworksheet.tex +++ b/worksheets/include/preambleworksheet.tex @@ -3,10 +3,18 @@ \usepackage[absolute, overlay]{textpos} \usepackage{fancyhdr} -\newcommand{\customsubject}{} +\newcommand{\customsubject}{} \newcommand{\customtitle}{} \pagestyle{empty} +\newcounter{questionpartcounter} %Setup for question part counter for a,b,c listing +\renewcommand{\thequestionpartcounter} +{\alph{questionpartcounter}} + +\newcounter{questionpartpartcounter} %Setup for question part partcounter for a,b,c listing +\renewcommand{\thequestionpartpartcounter} +{\roman{questionpartcounter}} + \newenvironment{worksheet}[2] { @@ -44,13 +52,23 @@ -\newcommand{\question}[2][5cm]{% +\newcommand{\question}[3][1cm]{% \item - #2 + \setcounter{questionpartcounter}{0} + \setcounter{questionpartpartcounter}{0} + \textbf{#2} \\#3 \vspace{#1} } -\newcommand{\questionpart}[2][5cm]{% - #2 +\newcommand{\questionpart}[2][1cm]{% + \setcounter{questionpartpartcounter}{0} + \stepcounter{questionpartcounter} + (\thequestionpartcounter)~#2 \vspace{#1} -} \ No newline at end of file +} + +\newcommand{\questionpartpart}[2][1cm]{% + \stepcounter{questionpartpartcounter} + \thequestionpartpartcounter.~#2 + \vspace{#1} +} diff --git a/worksheets/model and experiment/model and experiment.tex b/worksheets/model and experiment/model and experiment.tex deleted file mode 100644 index a91472a..0000000 --- a/worksheets/model and experiment/model and experiment.tex +++ /dev/null @@ -1,24 +0,0 @@ -\documentclass[12pt]{article} - -\include{../include/beamerworksheet} - - -\begin{document} - -\begin{worksheet}{Phys 101 Worksheet}{Comparing Model and Experiment} - -\question[3cm]{\textbf{Thinking Like a Physicist}\\ Suppose there's a theory "Dogs cannot be born with naturally blue fur." Can this theory be proven to be true? \textbf{Explain} why or why not.} - -\question[0.1cm]{\textbf{Dimensional Analysis}\\ Suppose you're a butterfly researcher. You find that rarer butterflies appear to be faster, and flutter their wings at a higher rate than more common butterflies. You invent a new unit, a "Whimsy" (denoted as $W$), which is the \textbf{product} the maximum velocity of a given species of butterfly, $v$, and the frequency at which it flaps its wings $f$.} - -\questionpart[2cm]{\textbf{(a)} Explicitly write out the formula to calculate Whimsiness. What are it's dimensions?} - -\questionpart[3cm]{\textbf{(b)} Suppose now you want to create a formula that could predict the most whimsical butterfly any given butterfly catcher could catch knowing only their mass, $m$ and the maximum force the can swing with $F_s$. Write a possible solution (within a constant) that could be a solution to the problem.} - -\questionpart[0cm]{\textbf{(c)} Does the formula you've devised make sense? Explain wy or why not. (Hint: When you increase certain variables, does whimsiness increase or decrease as you would expect?)} - - -\end{worksheet} - - -\end{document} \ No newline at end of file From 927e6c65029faa40891ef00f576901520822b0ab Mon Sep 17 00:00:00 2001 From: S-Blaha Date: Mon, 2 Jun 2025 15:50:24 -0400 Subject: [PATCH 03/39] Made derivatives worksheet, added \operation as anew function which simply resizes equations and removes some formatting clutter --- worksheets/Math/Derivatives.pdf | Bin 155402 -> 196503 bytes worksheets/Math/Derivatives.tex | 7 ++++++- .../ModelAndExperiment/ModelAndExperiment.pdf | Bin 181515 -> 181515 bytes worksheets/include/preambleworksheet.tex | 6 ++++++ 4 files changed, 12 insertions(+), 1 deletion(-) diff --git a/worksheets/Math/Derivatives.pdf b/worksheets/Math/Derivatives.pdf index 6ce8ad3685322c570f07566733bb93d18c4ad5aa..87c93a087030e513f872ff73ce3b2d3452e21302 100644 GIT binary patch delta 63178 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100644 index 0000000..a3cec60 --- /dev/null +++ b/worksheets/Math/Integrals.tex @@ -0,0 +1,22 @@ +\documentclass[12pt]{article} + +\include{../include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Integral Practice} + +\question[4cm]{Integration}{Compute: \operation{\int 3x^2[x^3 + 5]^4 dx}} + +\question[0.1cm]{Modelling and Integrating}{Alex is a long distance crawler. Their coach, James, who happens to be a physicist is attempting to model their crawling as a function of time. He to finds that their jerk ($\frac{d^3}{dt^3}x$) is $j = t e^{-t} $ in $km \slash h^3$ based on data from their races.} + +\questionpart[4cm]{Using this, find $v(t)$ in $km \slash h$.} + +\questionpart[3cm]{How far can alex crawl in 3 hours? Assume initial velocity, acceleration, and jerk are all 0.} + +\questionpart[3cm]{James wants to find the point where Alex runs out of energy and stops crawling. How long can Alex crawl for until they stop making substantial progress?} + + +\end{worksheet} + +\end{document} \ No newline at end of file From 399a6fea41320eecc58e581dcbe363d3d1aecaee Mon Sep 17 00:00:00 2001 From: S-Blaha Date: Tue, 3 Jun 2025 16:42:08 -0400 Subject: [PATCH 05/39] Added most of vector worksheet, changed formatting of integrals and derivatives worksheet and added tikz capabilites to preamble. --- Latex conventions and formatting.pdf | Bin 0 -> 84347 bytes worksheets/Math/Derivatives.pdf | Bin 193775 -> 179483 bytes worksheets/Math/Derivatives.tex | 9 +++--- worksheets/Math/Integrals.pdf | Bin 216183 -> 206359 bytes worksheets/Math/Integrals.tex | 8 ++--- worksheets/Math/Vectors.pdf | Bin 0 -> 198592 bytes worksheets/Math/Vectors.tex | 37 +++++++++++++++++++++++ worksheets/include/preambleworksheet.tex | 4 +++ 8 files changed, 49 insertions(+), 9 deletions(-) create mode 100644 Latex conventions and formatting.pdf create mode 100644 worksheets/Math/Vectors.pdf create 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Their coach, James, who happens to be a physicist is attempting to model their crawling as a function of time. He to finds that their jerk ($\frac{d^3}{dt^3}x$) is $j = t e^{-t} $ in $km \slash h^3$ based on data from their races.} +\question[-.5cm]{Modelling and Integrating}{Alex is a long distance crawler. Their coach, James, who happens to be a physicist is attempting to model their crawling as a function of time. He finds that their jerk($\frac{d^3}{dt^3}x$) can be modelled as $j(t) = t e^{-t}$ in \si{\kilo\metre\per\hour\cubed} based on data from their races.} -\questionpart[4cm]{Using this, find $v(t)$ in $km \slash h$.} +\questionpart[3.5cm]{Using this, find $v(t)$in \si{\kilo\metre\per\hour}.} \questionpart[3cm]{How far can alex crawl in 3 hours? Assume initial velocity, acceleration, and jerk are all 0.} -\questionpart[3cm]{James wants to find the point where Alex runs out of energy and stops crawling. How long can Alex crawl for until they stop making substantial progress?} +\questionpart[0cm]{James wants to find the point where Alex runs out of energy and stops crawling. How long can Alex crawl for until they stop making substantial progress?} \end{worksheet} diff --git a/worksheets/Math/Vectors.pdf b/worksheets/Math/Vectors.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a22c8f00f7a9bc07f4846d0369979ca4fbf0906b GIT binary patch literal 198592 zcma&MbyQs4vnGrOhY$z>f;+*Xad&rjYaAMPcXxMpcbDKE+}%BB(D3#9{_edqYt5`R zU;lCXbRXHZpQ_sRRMjR|5D}weq6Z+7|5_MYL1ZUlBmx;(BJ%JcGROdJ&791Mm^hi4 ziT?c{GKg7NI{_Vt7{sg%oq!@hV~`0Dk&h42(a8a5XoKjs)~qQF!V|~nxl?DY3nfRJ zKm9}6Pck}xPNX5yf=*~n_{~8CRV1ECQgoEyZN0UEaNufJA)yF5K>=LF?3nED9CV)Ayqgw}ceC6=*LUxJPy!zGEz zQjn>htn2IgK!;6i~gs76g#=@CBfPT6>4Ez!}5E!ig)Lu!6x1BuCLH%VKrHL z7Qe73cr1!a2)qy(-pzcLeQ;#{+VMU!?ixgYmdh&Ka5JJkS&pE+q5y5PGz6LPe}<#L zcZW}KH4s!fMUG-WcsMx23`zv{_i57yu%WI6>@JVI0y~EUzMDn=vVMvE%pUY`?{3Q> zi=*K^h-87YIL)^^gywo@8z{_o76%o|!!mOtA*f@0tq>hglR6C{(#IeX=`zM3_v0J# zG8FvXT7MzY+mz|z-OKI{2m`?(%4)ei)UvMtu^1Fv<(cqw=De z1dZ$s!U7`_g)a1W0$t}_Wg3f?R2Vn}I%me*N50`HpO^pcjw8^HDnb25D(M9@`_epeDqOs0x8lxN+~X 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z|84e$24_ztL;#0xYJ&z>fuvypu(JY~IOv&JDVdlkso@yq985)xT+N86M7f!nnAw=v znf_muR8BP(?5&Io(S%rPXK_674UzNvHVNM#Ka6>=KQa{01mGIlzr(j z0oYTCk-*7-Oq?A5vho!G2lH3s{-5%V1eoGkw(W9Q=duf42a z!mqu+|8T+qU}pPIgI}Stas12RmyDB@wNod1TOi-VbkHPs3goZnDXR76-vj78`R)vsa@ z6#}rZvxu?^i?gwRHPl7Kg!qYg|9@5Vi1_*8TwINuT|J%6%;5lB9IR}taOC7-3gU48 E54qi}Qvd(} diff --git a/worksheets/Math/Vectors.tex b/worksheets/Math/Vectors.tex index 80b3ec0..8390dd3 100644 --- a/worksheets/Math/Vectors.tex +++ b/worksheets/Math/Vectors.tex @@ -8,9 +8,9 @@ \question[2cm]{Algebra With Vectors}{A boat is traveling across a river. It's going south east with a velocity of: \\ $\vec{v_B} = (-5,-4) \si{\kilo\metre\per\hour}$. The river is flowing with a velocity of $\vec{v_w} = (2,1) \si{\kilo\metre\per\hour}$. With what velocity is the boat crossing the river?} -\question[2cm]{Scalar Product}{Aki and Luke go running off in different directions. $\vec{v_A}= (\frac{1}{3},2) \si{\metre\per\second}, \\ \vec{v_L}= (-1,\frac{3}{4})\si{\metre\per\second}$. What is the angle between their velocity vectors?} +\question[2.5cm]{Scalar Product}{Aki and Luke go running off in different directions. $\vec{v_A}= (\frac{1}{3},2) \si{\metre\per\second}, \\ \vec{v_L}= (-1,\frac{3}{4})\si{\metre\per\second}$. What is the angle between their velocity vectors?} -\question[3cm]{Cross Product}{A force $\vec{F} = (6,3)$ is applied to the edge of a disc centered at the origin at $\vec{r} = (1,2)$. What is the magnitude and direction of the angular acceleration? +\question[2cm]{Cross Product}{A force $\vec{F} = (6,2)$ is applied to the edge of a disc centered at the origin at $\vec{r} = (1,1)$. What is the magnitude and direction of the angular acceleration? \\ \begin{tikzpicture}[scale=1] \tikzmath{ @@ -23,13 +23,39 @@ \draw[-latex, line width = 2pt] (0,0) -- (45:\R) node[midway, below]{$\vec r$}; \draw[dashed, line width = 2pt] (45:\R) -- + (45:\R); -\draw ($(45:\R)+(0.5,0)$) arc (0:45:0.5) node[midway, right]{$\theta$}; -\draw[-latex, line width = 1pt] (45:\R) -- + (1.75*\R,0) node[midway, below]{$\vec F$}; +\draw ($(45:\R)+(0.5,0.18)$) arc (25:50:0.5) node[midway, above right, yshift=-3pt]{$\theta$}; +\draw[-latex, line width = 1pt] (45:\R) -- + (3*\R,1*\R) node[midway, below]{$\vec F$}; } \end{tikzpicture}} -\question{Right Hand Rule}{Insert questions and tikz drawings here} +\question[0cm]{Right Hand Rule}{Use the right hand rule to find the direction $\vec{a} \times \vec{b}$ for the first two sets of vectors, and find the rotation vector of the third figure.} +\\ +\begin{tikzpicture}[scale=1] +\scalebox{1.0}{ +\draw[-latex,line width = 2pt] (0,0) -- (3,0)node[midway, below]{$\vec b$}; +\draw[-latex,line width = 2pt] (0,0) -- (0,3)node[midway, left]{$\vec a$}; +} +\end{tikzpicture} +\noindent +\hspace{3cm} +\noindent +\begin{tikzpicture}[scale=1] +\scalebox{1.0}{ +\draw[line width = 2pt] (-0.3,-0.3) -- (0.3,0.3)node[midway, below]{$\vec a$}; +\draw[line width = 2pt] (0.3,-0.3) -- (-0.3,0.3); +\draw[-latex,line width = 2pt] (0,0) -- (0,3)node[midway, left]{$\vec b$}; +} +\end{tikzpicture} +\noindent +\hspace{3cm} +\begin{tikzpicture}[scale=1] +\scalebox{1.0}{ +\draw[line width = 0pt] (0,0) -- (0,0); +\draw[->, line width = 2pt] (2,1.5) arc[start angle=0, end angle=-270, radius=1cm]node[pos=0.33, below]{$\vec a$}; +} +\end{tikzpicture} + \end{worksheet} From 60918d9f90f2677ecf209e90ef487f4ef339bdd0 Mon Sep 17 00:00:00 2001 From: S-Blaha Date: Wed, 4 Jun 2025 14:25:45 -0400 Subject: [PATCH 07/39] Small Fixes --- worksheets/Math/Derivatives.pdf | Bin 179483 -> 179694 bytes worksheets/Math/Integrals.pdf | Bin 206359 -> 206570 bytes 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worksheets/{Math => }/Integrals.pdf | Bin 206570 -> 208919 bytes worksheets/Integrals.tex | 105 ++++++++++++++++++ .../{Math/Derivatives.pdf => Kinematics.pdf} | Bin 179694 -> 143304 bytes worksheets/Kinematics.synctex(busy) | 0 worksheets/Kinematics.tex | 13 +++ worksheets/Math/Derivatives.tex | 22 ---- worksheets/Math/Integrals.tex | 22 ---- .../ModelAndExperiment.pdf | Bin .../ModelAndExperiment.tex | 0 worksheets/{Math => }/Vectors.pdf | Bin 201140 -> 198567 bytes worksheets/{Math => }/Vectors.tex | 23 +++- worksheets/include/preambleworksheet.tex | 9 +- 14 files changed, 223 insertions(+), 52 deletions(-) create mode 100644 worksheets/Derivatives.pdf create mode 100644 worksheets/Derivatives.tex rename worksheets/{Math => }/Integrals.pdf (67%) create mode 100644 worksheets/Integrals.tex rename worksheets/{Math/Derivatives.pdf => Kinematics.pdf} (67%) create mode 100644 worksheets/Kinematics.synctex(busy) create mode 100644 worksheets/Kinematics.tex delete mode 100644 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+ +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Derivative Practice} + +%Polynomial +\question[4.75cm]{Compute: \vspace{-1cm}\begin{eqnarray*}\frac{d}{dx} (x^{5} + 3x^3 + \frac{1}{x}) \end{eqnarray*}} + +%Quotient rule +\question[4.75cm]{Compute: \vspace{-1cm}\begin{eqnarray*}\frac{d}{dx} (\frac{\cos{x}}{\sin{x}} ) \end{eqnarray*}} + +%Chain rule +\question[0cm]{Compute: \vspace{-1cm}\begin{eqnarray*}\frac{d}{dx} \: \ln(\cos (x))\end{eqnarray*}} + +\newpage + +%limit method +\question[7cm]{Compute $\frac{d}{dx} x^3$ using the limit definition of the derivative} + + +%Partial Derrivatives +\question[7cm]{You are standing on a mountain who's shape can be modelled as $z = 7 - \frac{1}{3}x^2 - 2y^4$. You are at the point of $(2, 1, \frac{13}{3})$ and wish to descend the mountain as quikcly as possible. What direction (in unit vector form) should you go in?} + + +%Plotting derrivatives +\question[1cm]{Below is a plot of the function $y = x^2$, compute and plot on the following two empty graphs the derrivatives: $\frac{d}{dx} (x^2)$ and $\frac{d^2}{dx^2}(x^2)$} + +\hspace{-3.5cm} +\begin{tikzpicture}[scale=0.9] + \begin{axis}[ + axis lines = middle, + xlabel = $x$, + ylabel = {\hspace{-1.2cm}$f(x) = x^2$}, + xmin=-4, xmax=4, + ymin=0, ymax=9, + samples=100, + grid=both, + ] + \addplot[blue, thick] {x^2}; + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.9] + \begin{axis}[ + xmin=-4, xmax=4, + ymin=0, ymax=9, + axis lines=middle, + xlabel=$x$, ylabel={\hspace{-2.5cm}$f(x) = \frac{d}{dx}(x^2)$}, + xtick={-4,-2,0,2,4}, + ytick={0,2,4,6,8}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.9] + \begin{axis}[ + xmin=-4, xmax=4, + ymin=0, ymax=9, + axis lines=middle, + xlabel=$x$, ylabel={\hspace{-2.5cm}$f(x) = \frac{d^2}{dx^2}(x^2)$}, + xtick={-4,-2,0,2,4}, + ytick={0,2,4,6,8}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/Math/Integrals.pdf b/worksheets/Integrals.pdf similarity index 67% rename from worksheets/Math/Integrals.pdf rename to worksheets/Integrals.pdf index dc9c1829885cfff1e3bf59c322de576ebb5f5608..328a8049e5d1ecf76807e367542c1c7119a56e7b 100644 GIT binary patch delta 67634 zcmZU)bC4%N(=EJXn>)5`+qOMBwmrYGZQDDxZQHhOe*3&%Jomj3_mAq%IC-ivqoSj` zPDb|m6m04)Y#b3NClfP4YE2(71t3{%EM`FfvFn6dYkwZyQT_%7W3U?sF-$@N7ANXp zQe%*95dQaf&N*p#HY2mWWNP-gdd*)w)yx8Fk-5KMU1mP*Iy#-G@Qji{i#W6^VK8E# zN23x_MabrDLaDD`E@YVBTPr5HNBtC^lupQQ8#iArs&H#7M;qF+epZOag8<58`|xGh zqfNv;nINA9)6L!d_H}gZ-XpA@9rPoG)a1~pNjXT)(hv?hMLJXm0Y-yP>Wp(mgIlAv z*ER#hETWJ~QW@?dxFBWZ?g-BOmFhdfB)wSVW0p)o#`x*@)R1nV6 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a/worksheets/include/preambleworksheet.tex b/worksheets/include/preambleworksheet.tex index f74598a..d34b1d9 100644 --- a/worksheets/include/preambleworksheet.tex +++ b/worksheets/include/preambleworksheet.tex @@ -72,3 +72,9 @@ \thequestionpartpartcounter.~#2 \vspace{#1} } + +\newcommand{\operation}[1]{% +{\large $ +#1 +$} +} \ No newline at end of file From 947be56d3005101e613144db60b476be0d324eb2 Mon Sep 17 00:00:00 2001 From: S-Blaha Date: Mon, 2 Jun 2025 16:54:45 -0400 Subject: [PATCH 04/39] Fix spelling + added Integrals Worksheet --- worksheets/Math/Derivatives.pdf | Bin 196503 -> 193775 bytes worksheets/Math/Derivatives.tex | 2 +- worksheets/Math/Integrals.pdf | Bin 0 -> 216183 bytes worksheets/Math/Integrals.tex | 22 ++++++++++++++++++++++ 4 files changed, 23 insertions(+), 1 deletion(-) create mode 100644 worksheets/Math/Integrals.pdf create mode 100644 worksheets/Math/Integrals.tex diff --git a/worksheets/Math/Derivatives.pdf b/worksheets/Math/Derivatives.pdf index 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