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Difference between revisions of "Peter Saveliev"
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**Chapter 4 The Derivative [https://www.dropbox.com/s/q7ur2pmy259popd/ch4.pdf?dl=0 pdf] | **Chapter 4 The Derivative [https://www.dropbox.com/s/q7ur2pmy259popd/ch4.pdf?dl=0 pdf] | ||
**Chapter 5 Differentiation and Integration [https://www.dropbox.com/s/zt1n4x1mninvndi/ch5.pdf?dl=0 pdf] | **Chapter 5 Differentiation and Integration [https://www.dropbox.com/s/zt1n4x1mninvndi/ch5.pdf?dl=0 pdf] | ||
+ | **Chapter 6 Applications [https://www.dropbox.com/s/dkj8lkjo9uojawi/ch6.pdf?dl=0 pdf] | ||
These are sold on Amazon: | These are sold on Amazon: |
Revision as of 00:41, 22 April 2022
Hello! My name is Peter Saveliev (rhymes with “leave”). I am a professor of mathematics at Marshall University, Huntington WV, USA.
Books:
- Topology Illustrated (Note: Because of the employment situation, the second edition is postponed until 2024+.)
- Calculus Illustrated
- Volume 1 Precalculus
- Volume 2 Differential Calculus
- Volume 3 Integral Calculus
- Volume 4 Calculus in Higher Dimensions
- Volume 5 Differential Equations
- How Swords Cut
- Linear Algebra Illustrated
- Elementary Discrete Calculus: How far we can go without limits? For now, I just picked enough material for these three chapters from the first 3 volumes of Calculus Illustrated. PDF
$$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$
- One-Semester Calculus (calculus abbreviated, streamlined, simplified), lecture notes.
These are sold on Amazon:
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- Once upon a time, I took a better look at the poster of Drawing Hands by Escher hanging in my office and realized that what is shown isn't symmetric! To fix the problem I made my own picture called Painting Hands:
Such a symmetry is supposed to be an involution of the $3$-space, $A^2=I$; therefore, its diagonalized matrix has only $\pm 1$ on the diagonal. These are the three cases:
- (a) One $\ -1$: mirror symmetry. But then pen draws pen. No!
- (b) Two $\ -1$'s: $180$ degrees rotation. But then we have two right (or two left) hands. No!
- (c) Three $\ -1$'s: central symmetry. Yes!
- - Why is discrete calculus better than infinitesimal calculus? - Why? - Because it can be integer-valued! - And? - And the integer-valued calculus can detect if our universe is non-orientable! Read Integer-valued calculus, an essay that makes a case for discrete calculus by appealing to topology and physics.
- So, what would mathematics look like without fractions?
- - The political “spectrum” might be a circle! - So? - Then there can be no fair decision-making system! Read The political spectrum is a circle, an essay based on the very last section of the topology book.