MATH 4347 – Introduction to PDE...
12
Transcript of MATH 4347 – Introduction to PDE...
![Page 1: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/1.jpg)
![Page 2: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/2.jpg)
![Page 3: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/3.jpg)
MATH 4347 – Introduction to PDE (Harrell)
11/11/11 Triple prime time for a review
Copyright 2011 by Evans M. Harrell II.
![Page 4: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/4.jpg)
MATH 4347 – Introduction to PDE (Harrell)
11/11/11 Triple prime time for a review
Copyright 2011 by Evans M. Harrell II.
WHAT’S THE TEST ALL ABOUT? • ZT, Chapter 6. • ZT, Chapter 7, §§1-4, 5 (except representation theorem), 6, 7 (except Poisson’s integral), 8. • ZT, Chapter 9, §§1-2. • Related parts of HH.
![Page 5: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/5.jpg)
![Page 6: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/6.jpg)
![Page 7: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/7.jpg)
![Page 8: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/8.jpg)
New harmonic functions from old
reflections rotations similarities (scale by λ) For R2, inversion through the circle rr* = a2.
strange fact: If u(r,θ) is harmonic, then so is u*(r*,θ) = u(a2/r*,θ) (2D) or (a/r*) u(a2/r*,θ) (3D)
![Page 9: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/9.jpg)
![Page 10: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/10.jpg)
Who invented the Dirac Delta function?
![Page 11: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/11.jpg)
![Page 12: MATH 4347 – Introduction to PDE (Harrell)people.math.gatech.edu/~harrell/4347/Lex/L32Math4347F11.pdfGustav Kirchhoff From Wikipedia, the free encyclopedia Gustav Robert Kirchhoff](https://reader030.fdocuments.net/reader030/viewer/2022040301/5e72187179ce131c36503553/html5/thumbnails/12.jpg)