{"id":877,"date":"2016-07-15T12:53:22","date_gmt":"2016-07-15T16:53:22","guid":{"rendered":"https:\/\/minireference.com\/blog\/?p=877"},"modified":"2020-11-20T08:18:49","modified_gmt":"2020-11-20T13:18:49","slug":"no-bs-math-and-physics-v51-update","status":"publish","type":"post","link":"https:\/\/minireference.com\/blog\/no-bs-math-and-physics-v51-update\/","title":{"rendered":"No BS math and physics v5.1 update"},"content":{"rendered":"<p>Over the last years, several readers uncovered\u00a0mistakes\u00a0in the <em>No bullshit guide to math\u00a0&amp; physics<\/em>, which I immediately fixed in the source. The\u00a0errors were mostly\u00a0minor, so they didn&#8217;t warrant a new edition, but\u00a0once I reached a threshold of six\u00a0errata, I decided it&#8217;s time\u00a0to release a\u00a0v5.1 update.\u00a0With this bugfix\u00a0update, I took the time to make some other minor improvements\u00a0described below.<\/p>\n<p><!--more--><\/p>\n<h3>Errata<\/h3>\n<p>Most of the mistakes in\u00a0v5 of the book\u00a0were in the exercises and problems. I&#8217;m happy to announce there are\u00a0no major conceptual problems, or mistakes in any of the core equations. Here are the mistakes in v5.0 (Aug 2014) of the book:<\/p>\n<ul>\n<li><strong>P1.41<\/strong>: Both calculations should use the radius instead of the diameter. The change in height is $h_2 &#8211; h_1 = 5.47 &#8211; 4.41 = 1.06$ cm.<\/li>\n<li><strong>P1.44<\/strong>: Answer should be 8.42m = $4\\sin 40 + \\frac{1}{4}(2\\pi(0.5)) + 4\\cos 40 + 2$.<\/li>\n<li><strong>P1.47<\/strong>: Answer should be 180 degrees &#8211; 40 degrees = 140 degrees.<\/li>\n<li><strong>P1.51<\/strong>: Question describes the water tank as $12 \\times 6 \\times 3$, but solution uses $12 \\times 6 \\times 5$.\u00a0The question was changed to match the existing solution: the tank now has height $5$[m].<\/li>\n<li><strong>P2.9<\/strong> part (3) $v_f$ should be 6 [m\/s], not 10 [m\/s].<\/li>\n<li><strong>P2.10<\/strong>, part 4. Distance should be 13[m] not 14[m].<\/li>\n<li>page 202: Revolution of the Earth example: $v_t$ should be 328.32 m\/s not 464.32 m\/s, giving a final answer of 1181.95km\/h not 1671.56 km\/h.<\/li>\n<li>5.5 Limit formulas, page 264 at the bottom: removed\u00a0formulas $\\lim_{x\\rightarrow0}\\frac{\\ln(x+a)}{x}=a$ and $\\lim_{x\\rightarrow0}\\left(a^{1\/x}-1\\right)=\\ln(a)$.\u00a0First formula is wrong, second is not useful.<\/li>\n<li>page 286: &#8220;Consider the point $P=(x_P,y_P)$ that lies on the circle $x^2+y^2=R$.&#8221; should be &#8220;Consider the point $P=(x_P,y_P)$ that lies on the circle $x^2+y^2=R^2$.&#8221;<\/li>\n<li>page 401: the correct conversion formula for inch is 1[in] = 2.54[cm] and not 1[T] = 1000[kg].<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>New math exercises<\/h3>\n<p>Several readers complained about the math fundamentals chapter being too &#8220;rough&#8221; for complete beginners. To fix this, I did a critical rereading of the material and\u00a0corrected some mistakes of continuity (there was crazy rough patch in Section 1.2\u00a0where I suddenly jump into\u00a0negative and\u00a0fractional exponents that\u2014not surprisingly\u2014<a href=\"https:\/\/www.amazon.com\/gp\/customer-reviews\/R2BQ8IRBU9I0TD\/ref=cm_cr_getr_d_rvw_ttl?ie=UTF8&amp;ASIN=0992001005\">some readers found\u00a0confusing<\/a>). I also interspersed exercises throughout Chapter 1 so readers can now test their understanding as they progress through the chapter.<\/p>\n<p>&nbsp;<\/p>\n<h3>Index<\/h3>\n<p>Thanks to the suggestion in a\u00a0<a href=\"https:\/\/www.amazon.com\/gp\/customer-reviews\/R3901UN1IBYSQU\/ref=cm_cr_arp_d_rvw_ttl?ie=UTF8&amp;ASIN=0992001005\">comment on amazon<\/a>, I decided it the book should have an <a href=\"https:\/\/minireference.com\/static\/excerpts\/noBSguideMathMechCalc_index.pdf\">index<\/a>. It turned out creating an index was a very time-consuming task, but it was very\u00a0totally worth it since it allowed me to standardize certain terminology (e.g. <em>function\u00a0range<\/em> vs <em>function image<\/em>) and weed out certain inconsistencies. \u00a0The exercise of cataloguing every concept used in the book will help with\u00a0<a href=\"https:\/\/github.com\/minireference\/structure-api\">STRUCTURE<\/a> project too.<\/p>\n<p>&nbsp;<\/p>\n<h3>New\u00a0proof of the chain rule for derivatives<\/h3>\n<p>A mathematician friend of mine pointed out a mistake in the proof of the chain rule for derivatives in the book.\u00a0The hand-wavy argument that I had improvised had possible <span class=\"il\">divide<\/span> <span class=\"il\">by<\/span> zero error: the quantity $\\Delta = g(x+\\delta) &#8211; g(x)$\u00a0can be zero, so it&#8217;s not OK to use it\u00a0in expressions\u00a0where it appears in the denominator. In other words, bullshit had creeped into the book! \u00a0We can&#8217;t have any of that\u00a0in a book\u00a0which claims to be bullshit free! The new\u00a0<a href=\"https:\/\/minireference.com\/static\/excerpts\/proof_of_chain_rule_for_derivatives.pdf\">proof of the chain rule for derivatives<\/a> is longer and more technical, but at least it&#8217;s not wrong. Hopefully I will not\u00a0alienate my readers too much by having such a technical argument in the middle of the calculus chapter, but there\u00a0really wasn&#8217;t any way to make the proof simpler or more intuitive. It&#8217;s just a technical\u00a0argument.<\/p>\n<p>&nbsp;<\/p>\n<h3>More calculus problems<\/h3>\n<p>Upon critical review, I found the section on surface\u00a0and volumes of revolution was a little short. Sure\u00a0all the formulas are introduced, but\u00a0it\u00a0would have been a stretch to assume the average reader will be able to pick up the concepts from these few pages. To remedy this, I added a few more pictures, beefed up the discussion, and added some problems.\u00a0I\u00a0also came up with a &#8220;append only&#8221; policy for adding problems to the book\u2014this way the numbers won&#8217;t change between versions so if \u00a0a prof assigns\u00a0<strong>P5.33<\/strong> to their students, it will be the same problem in v5, v6, or whenever. The new problems added test the student&#8217;s ability to apply the volume of revolution formulas and also the infinite\u00a0Riemann sum formula.<\/p>\n<p>&nbsp;<\/p>\n<h3>The diff<\/h3>\n<p>As with previous updates, I&#8217;ve generated a <a href=\"https:\/\/minireference.com\/static\/diffs\/noBSdiff_v5_v51.pdf\">red-blue diff of all the changes<\/a> between v5.0 (Aug 2014) and v5.1 (July 2016). You can check out\u00a0the diff\u00a0to see the details of all that changed.<\/p>\n<p>&nbsp;<\/p>\n<p>Right now I&#8217;m waiting for the green light from my editor about the changes and the\u00a0next step will be\u00a0to push the updated PDFs\u00a0to all distribution channels. I&#8217;ll also\u00a0send out an update email to all readers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Over the last years, several readers uncovered\u00a0mistakes\u00a0in the No bullshit guide to math\u00a0&amp; physics, which I immediately fixed in the source. The\u00a0errors were mostly\u00a0minor, so they didn&#8217;t warrant a new edition, but\u00a0once I reached a threshold of six\u00a0errata, I decided it&#8217;s time\u00a0to release a\u00a0v5.1 update.\u00a0With this bugfix\u00a0update, I took the time to make some other [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,23,16],"tags":[],"class_list":["post-877","post","type-post","status-publish","format-standard","hentry","category-content","category-structure","category-writing"],"_links":{"self":[{"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/posts\/877","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/comments?post=877"}],"version-history":[{"count":12,"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/posts\/877\/revisions"}],"predecessor-version":[{"id":1474,"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/posts\/877\/revisions\/1474"}],"wp:attachment":[{"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/media?parent=877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/categories?post=877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/minireference.com\/blog\/wp-json\/wp\/v2\/tags?post=877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}