I really should study manifolds. I feel like I'd unlock so much intuition behind 2d and 3d calculus if I got to understand them. Anyone got any textbook recommendations?
#Calculus
Ordinary Differential Equations (Dover Books on Mathematics) by Edward L. Ince (PDF)
Author: Edward L. Ince
File Type: PDF
Download at https://sci-books.com/ordinary-differential-equations-dover-books-on-mathematics-b00ezdhv9q/
#Calculus, #EdwardL.Ince
Sometimes, you just gotta break out the #algebra and a touch of #calculus for a particular #led #circuit
At least, when you want to make sure you don't let out the magic smoke.
Calculus: A Modern Approach (Dover Books on Mathematics) by Karl Menger (PDF)
Author: Karl Menger
File Type: PDF
Download at https://sci-books.com/calculus-a-modern-approach-dover-books-on-mathematics-b00ms49n5y/
#Calculus, #KarlMenger
USM really does slash the rote burden, chiefly because one handful of exponential/hyperbolic identities replaces a patchwork of separate trig, inverse-trig, radical and Euler recipes.
Article (draft): https://arxiv.org/abs/2505.03754
#math #calculus #integral #new #euler #arxiv #halfangleapproach #symmetrymatters
Integrals of inverse functions!
Proof without words (see image; credit: Jonathan Steinbuch, CC BY-SA 3.0, via Wikimedia Commons)...
For any montonic and invertible function \(f(x)\) in the interval \([a,b]\):
\[\displaystyle\int_a^bf(x)~ \mathrm dx+\int_{f(a)=c}^{f(b)=d}f^{-1}(x)~\mathrm dx=b\cdot f(b)-a\cdot f(a)=bd-ac\]
If \(F\) is an antiderivative of \(f\), then the antiderivatives of \(f^{-1}\) are:
\[\boxed{\displaystyle\int f^{-1}(y)~\mathrm dy=yf^{-1}(y)-F\circ f^{-1}(y)+C}\]
where \(C\) is an arbitrary constant (of integration), and \(\circ\) is the composition operator (function composition).
For example:
\[\begin{align*}\displaystyle\int \sin^{-1}(y) \, \mathrm dy &= y\sin^{-1}(y) - (-\cos(\sin^{-1}(y)))+C\\ &=y\sin^{-1}(y)+\sqrt{1-y^2}+C\end{align*}\]
\[\displaystyle\int \ln(y) \, dy = y\ln(y)-\exp(\ln(y)) + C= y\ln(y)-y + C.\]
#Function #InverseFunction #InverseFunctions #Functions #Integral #Integrals #Antiderivative #Integration #Calculus #FunctionComposition #CompositeFunction)
Lo, a problem in a business calculus textbook:
"Sarah is paid $500 for working up to 40 hours per week. For work beyond 40 hours per week she is paid $18/hour."
The neurotypical interpretation of the above specification results in Sarah *owing* the company money if she works less than 12.222... hours in a week.
I shit you not. The equation describing the specification above is:
Pay=18*(hrs-40)+500
:headache:
If you're a business calculus teacher, and you want to be taken seriously by your colleagues, you gotta do better than this.
Abstract Convex Analysis (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts) 1st Edition by Ivan Singer (PDF)
Author: Ivan Singer
File Type: PDF
Download at https://sci-books.com/abstract-convex-analysis-wiley-interscience-and-canadian-mathematics-series-of-monographs-and-texts-1st-edition-0471160156/
#Calculus, #IvanSinger
Geometrically understanding calculus of inverse functions (2023)
https://tobylam.xyz/2023/11/27/inverse-functions-legendre-part-1
#HackerNews #Geometrically #understanding #calculus #of #inverse #functions #inverse #functions #calculus #mathematics #geometry
Differential Forms: A Complement to Vector Calculus 1st Edition by Steven H. Weintraub (PDF)
Author: Steven H. Weintraub
File Type: PDF
Download at https://sci-books.com/differential-forms-a-complement-to-vector-calculus-1st-edition-0127425101/
#Calculus, #StevenH.Weintraub
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)
#Math #Engineering #Science #Data #Calculus #EV #Drag #Trailer
Additional ISBNs for A First Course in Differential Equations with Modeling Applications 12th Edition: 9780357760192, 9780357760338, 9780357760208, 9780357760321, 978-0357760345, 9798214406718, 979-8214406718
Download 👉 https://lttr.ai/AeKuM
Integral Equations by Harry Hochstadt (PDF)
Author: Harry Hochstadt
File Type: PDF
Download at https://sci-books.com/integral-equations-0471504041/
#Calculus, #HarryHochstadt
Finding Values on the Unit Circle! (Sine, cosine) #maths #calculus #unitcircle #trigonometry
A quick way to find values on the unit circle in the first quadrant!In this video I show how to sketch the values corresponding to 0, pi/6, pi/4, pi/3, and pi/2 on the unit circle.Using those values I show how to evaluate sine and cosine.This is useful info for those of you in precalculus or calculus!
Differential Calculus in Topological Linear Spaces (Lecture Notes in Mathematics, 374) 1974th Edition by S. Yamamuro (PDF)
Author: S. Yamamuro
File Type: PDF
Download at https://sci-books.com/differential-calculus-in-topological-linear-spaces-lecture-notes-in-mathematics-374-1974th-edition-3540067094/
#Calculus, #S.Yamamuro
The Stanford Mathematics Problem Book: With Hints and Solutions (Dover Books on Mathematics) by George Polya (PDF)
Author: George Polya
File Type: PDF
Download at https://sci-books.com/the-stanford-mathematics-problem-book-with-hints-and-solutions-dover-books-on-mathematics-b00cwr50ou/
#Calculus, #GeorgePolya
Mathematical Analysis For School Students by Lev Pontryagin
A book for school students, and not only for them!
Released under Creative Commons by Share Alike 4.0
#mathematics #books #soviet #calculus #integration #highschool #oer
https://archive.org/details/lev-pontryagin-mathematical-analysis-for-school-students-mir-titles-2025
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