diff --git a/pisne/IWillDerive.tex b/pisne/IWillDerive.tex index e8f909a..efd6147 100644 --- a/pisne/IWillDerive.tex +++ b/pisne/IWillDerive.tex @@ -20,8 +20,8 @@ \end{refren} \begin{refren} And so now ^I, I will de^rive. \\ - Find the ^derivative of x position ^with respect to time. \\ - It's as ^easy as can be, just have to ^take dx/dt. \\ + Find the ^derivative of $x$ position ^with respect to time. \\ + It's as ^easy as can be, just have to ^take $dx/dt$. \\ I will de^rive, I will de^rive. Hey, hey! \end{refren} @@ -48,8 +48,8 @@ \end{refren} \begin{refren} And so now ^I, I will de^rive. \\ - Find the ^derivative of velocity ^with respect to time. \\ - It's as ^easy as can be, just have to ^take dv/dt. \\ + Find the ^derivative of $v$ position ^with respect to time. \\ + It's as ^easy as can be, just have to ^take $dv/dt$. \\ I will de^rive, I will de^rive. \end{refren} \begin{refren} @@ -61,8 +61,8 @@ \end{refren} \begin{refren} And so now ^I, I will de^rive. \\ - Find the ^derivative of x position ^with respect to time. \\ - It's as ^easy as can be, just have to ^take dx/dt. \\ + Find the ^derivative of $x$ position ^with respect to time. \\ + It's as ^easy as can be, just have to ^take $dx/dt$. \\ I will de^rive, I will de^rive, I will derive! \end{refren} \end{song} diff --git a/pisne/calculusRhapsody.tex b/pisne/calculusRhapsody.tex index daf189f..948155c 100644 --- a/pisne/calculusRhapsody.tex +++ b/pisne/calculusRhapsody.tex @@ -1,9 +1,9 @@ \begin{song}[remember-chords=false]{title={Calculus Rhapsody}, music={Queen}, lyrics={Phil Kirk \& Mike Gospel}} \begin{verse} - ^{G7}Is this x defined? ^{C7}Is f ^*{Gm7}con ^*{C7}ti ^*{Gm7}nu ^{C7}ous? \\ + ^{G7}Is this $x$ defined? ^{C7}Is $f$ ^*{Gm7}con ^*{C7}ti ^*{Gm7}nu ^{C7}ous? \\ ^{F7}How do you ^{Cm7}find ^{F7}out? You can ^{B}use the ^*{Cm7} li^{B}mit ^*{F7} pro^{B}cess. \\ ^{Gm7}Approach from both sides, The ^{B7}left and the right and ^{Eb}meet. \\ - ^{Cm7}Im a just a limit, ^{F7}defined analytically. Functions \\ + ^{Cm7}I'm a just a limit, ^{F7}defined analytically. Functions \\ ^*{H}continu ^{B}ous, ^{A}Theres no ^{B}holes, ^{H}No sharp ^{B}points, ^{A}Or asymp^{B}totes. \\ ^{Eb}Any way this ^{B}graph goes. ^{C#dim7}It is diffe^{F7}rentiable for me for ^{B}me. \end{verse} @@ -14,46 +14,49 @@ And ^{Cm}the area en^{Eb}closed bet^{Eb}ween ^{Am7}two curves. \end{verse} \begin{verse} - ^{Eb}Y prime ^{H}oooh^{Cm}\_\_\_ Is the ^{Fm}derivative ^{E5+}of ^{Ab}y \\ - Y ^{B7}equals x to the n, dy/^{Eb}dx \\ - ^{B}Equals ^{Cm}n times ^{Abm}x To the ^{Eb}n-1. \\ + ^{Eb}$y$ prime ^{H}oooh^{Cm}\_\_\_ Is the ^{Fm}derivative ^{E5+}of ^{Ab}$y$ \\ + $y$ ^{B7}equals $x$ to the $n$, $dy/dx$ \\ + ^{B}Equals ^{Cm}$n$ times ^{Abm}$x$ To the ^{Eb}$n-1$. \\ \end{verse} \begin{verse} - Other applications Of derivatives apply \\ - If y is divided or multiplied \\ - You use the quotient And product rules \\ - And dont you forget To do the dance \\ - Also oooh (dont forget the chain rule) \\ - Before you are done, \\ - You gotta remember to multiply by the chain \\ + ^{B}Other a^{Gm}pplications Of de^{Cm}rivatives apply \\ + If $y$ is di^{Cm7}vided or multi^{F7}plied \\ + ^{B}You use the quotient And ^{Gm}product rules \\ + And ^{Cm}dont you for^{Eb}get To ^{B}do ^{Ab}the dance ^{Eb} \\ + \end{verse} + \begin{verse} + ^{Eb}Also ^{B}oooh^{Cm}\_\_\_ (dont forget the chain rule) \\ + ^{Fm}Before you are ^*{Ab}done ^{Dm7}, You ^{B7}gotta remember to multiply by the chain \\ \end{verse} - (Instrumental solo) + Mezihra, crazy kytarové sólo \begin{verse} - I need to find the area under a curve \\ - Integrate! Integrate! You can use the integration \\ - Raise exponent by one multiply the reciprocal \\ - Plus a constant Plus a constant \\ + ^{A} ^{D}I ^{A}need to ^{Adim}find ^{A}the ^{D}area ^{A}under a ^{Adim}curve \\ + ^*{A}Inte ^{D}grate! ^*{A}Inte ^{D}grate! ^{A}You can ^{Adim}use the ^*{A}inte ^*{D}gra ^{A}tion \\ + ^{Db}Raise exponent ^{Ab7}by one ^{C}multiply the ^*{E7}recipro ^{A}cal \\ Add a constant Add a constant \\ - Add a constant labeled C \\ - (Labeled C-ee-ee-ee-ee) \\ - Im just a constant \\ - Nobody loves me. \\ - Hes just a constant \\ - Might as well just call it C \\ - Never forget to add the constant C \\ - Can you find the area between f and g \\ - In-te-grate f and then integrate g \\ + Add a constant Add a constant \\ + Add a constant labeled $C$ \\ + (Labeled $C$-ee-ee-ee-ee) \\ + \end{verse} + \begin{verse} + ^{H}Im ^{B}just a ^*{A}cons ^{B}tant ^*{H}No ^{B}body ^{A}loves ^{B}me. \\ + ^{Ab}He's ^{Eb}just a ^*{Ebdim}cons ^{Eb}tant ^{Ab}Might as ^{Eb}well just ^{Ebdim}call it ^{Eb}$C$ \\ + ^{Ab}Never for^{Eb}get to add ^{F7}the constant ^{B}$C$ \\ + \end{verse} + \begin{verse} + Can you find the area between $f$ and $g$ \\ + In-te-grate $f$ and then integrate $g$ \\ (then subtract) \\ To revolve around the y-axis \\ (integrate) \\ outer radius squared minus inner radius squared \\ (multiplied) \\ - multiplied by pi \\ + multiplied by $\pi$ \\ (multiply) \\ - Multiply the integral by pi! \\ - Pi tastes real good with whipped cream! \\ + Multiply the integral by $\pi$! \\ + $\pi$ tastes real good with whipped cream! \\ Mama-Mia, Mama-Mia \\ Mama-Mia let me go. \\ Pre-calculus did not help me to prepare for Calculus, for Calculus, help me! \\ @@ -62,7 +65,7 @@ (Interlude) \begin{verse} - So you think you can find out the limit of y? \\ + So you think you can find out the limit of $y$? \\ So you think youll find zero and have it defined \\ Oh baby cant define that point baby \\ Its undefined Goes to positive and negative infinity \\ diff --git a/zpevnik.pdf b/zpevnik.pdf index 87b3ece..54cdca6 100644 Binary files a/zpevnik.pdf and b/zpevnik.pdf differ