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#calculus

2 posts2 participants0 posts today

@yongzs1218

Bob Miller's Calc for the Clueless: Calc I & II, 1997

The first calc study guides that really give students a clue. Bob Miller's student-friendly Calc for the Clueless features quickly-absorbed, fun-to-use information and help. Students will snap up Calc for the Clueless as they discover: Bob Miller's painless and proven techniques to learning Calculus Bob Miller's way of anticipating problems.

@bookstodon
#books
#nonfiction
#maths
#calculus

《大學入門微積分》筆記
Introduction to University Calculus Notes
吾習單維彰教授《大學入門微積分》之課,謹將筆記照片上傳於網路。感謝單教授與國立中央大學之辛勤教誨與付出!
I have studied Professor Shann Wei-chang’s course
Introduction to University Calculus and hereby upload photos of my notes to the internet. I sincerely thank Professor Shann and National Central University for their dedicated teaching and efforts!

如欲下載原圖,請訪問吾之網誌:
《大學入門微積分》筆記
If you want to download the original image, please visit my weblog:
Introduction to University Calculus Notes

原影片課程:
YouTube原版 bilibili搬運

#筆記 #數學 #基礎 #微積分 #入門 #單維彰 #大學 #大學入門微積分 #中央大學 #笔记 #数学 #基础 #微积分 #入门级r #单维彰 #大学 #大学入门微积分 #中央大学 #note #math #mathematics #basic #calculus #introduction #Shann_Wei-chang #university #college #NCU

This is called "A Gentle Introduction to the Hessian Matrix"

Hessians are somewhere between #linearalgebra #calculus and #rstats but still a core aspect of #datascience

All in all, building and deriving things like these are probably only useful when developing a unique solution. For the vast majority of cases, having a general understanding is enough.

... actually, I am pretty sure that there is a #python library for just such an occasion (I have never looked though so ymmv)

How much total drag does my truck create while moving down the highway?

Measure it indirectly!

Run cellphone GPS logger at 1-second interval. Get truck up to speed on flat section of highway, put transmission in neutral, foot off the gas. Let the truck slow down 30 - 45 seconds to get a decent number of data points. Make another data run on same section, but opposite direction to average out effects of wind and any slope.

Import GPS log into spreadsheet.

A linear fit gives you a straight line slope...good enough to determine deceleration...then apply that to F = m * a (you need to know truck's weight) Now you know total drag force at one speed.

Total drag is air resistance (varies with square of speed) plus rolling friction (assume it's constant). OK, do a quadratic/polynomial fit. Now you know rolling friction. Subtract from total drag, and you can determine area-drag (Cd * frontal area) of your truck.

(1 of 2)

My graph of the day. Inspired by the fact that
\[ \sum_{k=1}^{\infty}{\sin k} \]
is bounded but diverges, I've been exploring other similar sums. Here's the start of
\[ \sum_{k=1}^{\infty}{\tan k} \]
It's not shocking that it looks like \(y = \ln(\|\cos x\| ) \), but I definitely wonder if at some point it blows up down the line!

A few weeks back I was complaining about this meme and we had a good discussion about it on here. I ended up making a lesson plan about taxes and my students really liked it so I will share it. (It is for students with a basic understanding of integration. But, you could probably rework it to skip that bit.)

drive.google.com/file/d/14xaQ1

(And if you have feedback let me know!)

#tax#taxes#math