The web pages on special topics

Branko Ćurgus

Below is a list of webpages that I wrote about special mathematical topics, somewhat random, whatever attracted my attention strong enough to convert my thinking into html. Each time that I converted my thinking into html I was happy I did. Writing is magic as it interacts with learning. The integration of teaching and writing enriches both. Over the years of teaching and writing, I learned to appreciate the Latin saying,

Verba volant,
scripta manent.
 

In free translation to my mother tongue, it is: Rečeno nestaje, napisano ostaje. To celebrate thinking, writing, and teaching, I created my own saying

I came,   I thought,    I wrote,
I taught, I thought more,
I rewrote.
 

The above words are inspired by the Latin phrase "veni, vidi, vici" which is in the list of Latin phrases very close to the first phrase that I cited:

Verba volant,
scripta manent.
 

1. Brief Review of Mathematical Logic.
2. Families of ellipses and elliptic integrals
3. Limits
4. Lambert W functions
5. Higher order approximations
6. Functions
7. Orthogonal families of curves
8. Rigor in the context of quadratic functions
9. An Ode to Row Reduction
10. Chebyshev polynomials
11. Law of cosines
12. Linear independence of eigenvectors version 1
13. Linear independence of eigenvectors version 2
14. Linear independence of monomials
15. 3119 pages of $3\!\!\times\!\!3$ unimodular matrices
16. The Book of Beautiful $2\!\!\times\!\!2$ matrices, Vol. 1
17. The Book of Beautiful $2\!\!\times\!\!2$ matrices, Vol. 2
18. The Book of Beautiful $2\!\!\times\!\!2$ matrices, Vol. 3
19. Axioms for the Integers
20. Basic Properties of Integers
21. Dirichlet's Approximation Theorem
22. The Method of Characteristics
23. A Derivation of the Diffusion Equation
24. A Derivation of the Heat Equation
25. Laplacian in Polar Coordinates
26. Solving Laplace's Equation on a Rectangle
27. Fourier Periodic Extension
28. Burgers' Equation
29. Symmetry of Sturm-Liouville Problems
30. Cauchy-Bunyakovsky-Schwarz inequality
31. Completion of a normed space
32. My favorite application of vectors: COLORS. I love this application so much that I wrote a webpage to celebrate it: Color Cube.
33. Getting started with Wolfram Mathematica 12
34. Vibrations of a Membrane in a shape of an Equilateral Triangle. This is a joint project with my student Darmon Ghanbari. There are a lot of beautiful pictures and animations. The necessary theory is being added.
35. My version of power reduction and Multiple-angle formulas