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calculus's Introduction

Compiling the textbooks using Xake (and LaTeX)

Compiling these documents is a bit tricky.

First install SAGE: http://www.sagemath.org/ This should install SageTeX.

Now if you are planning to use Xake to compile this repository, you first need to compile:

frontCover.tex spine.tex backCover.tex

for every subdirectory of coverArt, for example:

pdflatex coverArt/calculus1Cover/frontCover.tex
pdflatex coverArt/calculus1Cover/spine.tex
pdflatex coverArt/calculus1Cover/backCover.tex

After this, you should be able to compile the .tex files and PDFlatex.

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License. To view a copy of this license, visit

http://creativecommons.org/licenses/by-nc-sa/4.0/

or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA. If you distribute this work or a derivative, include the history of the document.

The source code is available at

https://github.com/mooculus/calculus

This text contains source material from several other open-source texts:

  • Single and Multivariable Calculus: Early Transcendentals. Guichard. Copyright 2015 Guichard, Creative Commons Attribution-NonCommercial-ShareAlike License 3.0.

    http://communitycalculus.org/

  • APEX Calculus. Hartman, Heinold, Siemers, Chalishajar, Bowen (Ed.). Copyright 2014 Hartman, Creative Commons Attribution-Noncommercial 3.0.

    http://www.apexcalculus.com/

  • Elementary Calculus: An Infinitesimal Approach. Keisler. Copyright 2015 Keisler, Creative Commons Attribution-NonCommercial-ShareAlike License 3.0.

    http://www.math.wisc.edu/~keisler/calc.html

We will be glad to receive corrections and suggestions for improvement at [email protected]

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calculus's Issues

More than one rate

See moreThanOneRate/digInMoreThanOneRate.tex

First Example under section header "Formulas": Change "perimeteter" to "perimeter"

First Example under section header "Right triangles": Change "accomidate" to "accommodate"

First Example under section header "Angular rates": Change "accomidate" to "accommodate" and also change "the angle attached to the fixed leg" to "the angle opposite the fixed leg"

The derivative as a function

See derivativeAsAFunction/digInTheDerivativeAsAFunction.tex

Second line of text: varible --> variable
First Question Answer: cooresponds --> corresponds
Second Question Answers: negtive --> negative

In the last Example on the page, in the first part of the problem we are making f continuous at x = 3. I understand the choice to use evaluation notation for this, but it might be nice to include the left- and right-hand limit notation in there as well to emphasize the continuity [[[[[ack]]]]] of the concepts.

\hdotsfor

in logarithmicDifferentiation/digInLogarithmicDifferentiation

I'd like to use \hdotsfor{11} (but cannot!)

The Inverse Function Theorem

See derivativesOfInverseFunctions/digInInverseFunctionTheorem.tex

  1. In the first paragraph, just after the display equation:
    "All we have shown is that if it has a derivative then that derivative must be 1/x."
    Maybe I'm just tired, but I'm not seeing what this has to do with the display equation.

  2. This may be one of the issues that they haven't resolved yet, but there's random partial code displayed in the Inverse Function Theorem box.

The limit laws (little typos)

See limitLaws/digInLimitLaws.tex

The fourth Question under "A list of questions" says "We suspect that the limit on on the denominator." Fix as desired.

The sixth Question under "A list of questions" says "The limit in the numerator definitely exists, so lets check..." Fix as desired.

Calculus 1 - Maximums and Minimums

https://ximera.osu.edu/course/mooculus/mooculus/master/textbook/maximumsAndMinimums/digInMaximumsAndMinimums

For the Maximums and Minimums exercise, in the section "First Derivative Test", there is a sketch under the sentence "From this we can make a sign table:". The lines/arrows in the sign table seem to be doing the opposite of the labels. The labels and the function graph below the table are correct. Just the lines in the "sign table" seem off. Or maybe I am reading the table wrong.

The chain rule

See chainRule/digInChainRule.tex

In the box towards the bottom where we compute the derivative of e^(sin(x^2)), there are two issues. Capitalize the first word "set" in the box. More importantly, the end of the first sentence should read "so that f(g(h(x))) = e^(sin(x^2))."

The limit laws

See limitLaws/digInLimitLaws.tex

Under the Example where we compute $\lim_{x \to 0} \sqrt{\cos(x)}$, the second display line is not maximally clear. Maybe add $\lim_{x \to 0} \sqrt{\cos(x)} = $ to the front of it.

error in "what is a limit"

there's an error the question f(0)on the second graph in the what is a limit section, it returns false when the answer is DNE.

I'm an idiot and got the wrong answer, there is no error.

Missing parentheses

See indeterminateForms/digInLimitsOfTheFormZeroOverZero.tex

There should be parentheses around the answer box for the example involving (x^2-3x+2)/(x-2).

31f99b

If the record is rotating in the clockwise direction there should be a negative sign for the y-coordinate to account for it.

Expected answer for y-coordinate: \answer{(-t/4)\sin((33+1/3) 2\pi t/60) or \answer{(t/4)\sin(-(33+1/3) 2\pi t/60) (Sin is an odd function)
Accepted answer for y-coordinate: \answer{(t/4)\sin((33+1/3) 2\pi t/60)

See normalVectors/exercisesParametricPlots/record.tex

development vs master

development and master are diverging

Currently (as of oct 18, 2015) Tikz images do not render online in breakground.tex (probably related to the input, or tikzexport issues)

Hence each of the breakgrounds are distinct in development and master.

The work-around was as follows,

use includegraphics in master

and tikz in development.

This allowed us to produce the PDF with development and the online version with master

However, content edits have been master, which have not been merged to development (when this is done, images in development breakground will break in the PDF and need to be fixed)

Compiling for the first time

Cover art needs to be compiled, as theCover.tex relies on PDF's created by frontCover.tex, spine.tex and backCover.tex

Also

calculus3 needs to be compiled with write18 enabled.

pdflatex --enable-write18 calculus3.tex

Limits and velocity

See anApplicationOfLimits/breakGround.tex

  1. Columbus Ohio to Urbana-Champaign Illinois --> Columbus, Ohio to Urbana-Champaign, Illinois

  2. There is no Answer field for the first problem. There's also no step to plug in t=5 and realize the final position is 300 miles west of Columbus.

  3. I'm not sure how one is supposed to do the second problem, but this page is now giving me the impression that you're still working on it, so maybe this comment is useless.

The limit laws

See limitLaws/digInLimitLaws.tex

Under "Composition Limit Law," I think it might be helpful not to write $x = \lim_{x \to a} g(x)$ using $x$ as both a dummy variable and an in context non-dummy variable.

Product Rule Text Fields - Wrong Answers

It replaced all my fields that I previously filled in with 5 and even before that it checked it off as being correct before I was even done writing the answer.

image

The chain rule

This dig in states towards the end:
Note how our solution for $\dd[y]{x}$ above is just the partial derivative of $z$, with respect to $x$, divided by the partial derivative of $z$ with respect to $y$. We state the above as a theorem.

While this clearly points out the relationship between the partial derivatives, it is slightly misleading in that it leaves out the negative multiplier in front. I wonder if there is a way to word this that includes the negative, without sacrificing clarity.
See chainRuleForFunctionsOfSeveralVariables/digInChainRule.tex

Continuity

See limitLaws/digInContinuity.tex

The last sentence in the Example should read something like "Hence $\lim_{x \to 6} f(x) \neq f(6)$, and so $f$ is not continuous at $x = 6$." Two sentences before that, it should read something like "Hence $\lim_{x \to 4} f(x) does not exist, so $f$ is not continuous at $x = 4$."

Basic rules of differentiation

In the Sum Rule proper theorem statement box's Explanation near "We only prove part (a) above; the rest are similar," the explanation box has two "Givens" appearing in strange places and also the box is unexpectedly zoom-in-able.

The Dot Product Underbraces

See dotProducts/digInDotProducts.tex

In the section about Orthogonal Decomposition a few underbraces are too large and need to be made to fit the vector notation they are under. See linked picture.

Bracket Issue

Quick update- This seems to be happening in all cases of orthogonal decomposition problems (maybe just a copy paste issue?). The second picture demonstrates it in HW 3.

Bracket Issue in Homework

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