Numerical_InquiryNotes.log

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**Numerical_InquiryNotes
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              \section{Floating Point Arithmetic} [5]
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[24]
Chapter 2.
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[46]
Chapter 3.
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\OT1/jkp/m/n/12 2\OML/jkp/m/it/12 :\OT1/jkp/m/n/12 5\OML/jkp/m/it/12 x[] \OT1/j
kp/m/n/12 + 2\OML/jkp/m/it/12 x \OT1/jkp/m/n/12 + 0\OML/jkp/m/it/12 :\OT1/jkp/m
/n/12 7$ is a pretty good ap-prox-i-ma-tion of the data $\OML/jkp/m/it/12 S \OT
1/jkp/m/n/12 = \OMS/jkp/m/n/12 f\OT1/jkp/m/n/12 (0\OML/jkp/m/it/12 ; \OT1/jkp/m
/n/12 1\OML/jkp/m/it/12 :\OT1/jkp/m/n/12 07)\OML/jkp/m/it/12 ;  \OT1/jkp/m/n/12
 (1\OML/jkp/m/it/12 ; \OT1/jkp/m/n/12 3\OML/jkp/m/it/12 :\OT1/jkp/m/n/12 9)\OML
/jkp/m/it/12 ;  \OT1/jkp/m/n/12 (2\OML/jkp/m/it/12 ; \OT1/jkp/m/n/12 14\OML/jkp
/m/it/12 :\OT1/jkp/m/n/12 8)\OML/jkp/m/it/12 ;  \OT1/jkp/m/n/12 (3\OML/jkp/m/it
/12 ; \OT1/jkp/m/n/12 26\OML/jkp/m/it/12 :\OT1/jkp/m/n/12 8)\OMS/jkp/m/n/12 g\O
ML/jkp/m/it/12 :$
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[][]\OT1/jkp/b/n/12 Problem 3.87. []\OT1/jkp/m/n/12 Ex-plain in clear lan-guage
 how the Monte Carlo search op-ti-miza-tion method
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Chapter 4.
[90

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[][]\OT1/jkp/b/n/12 Technique 4.13 \OT1/jkp/m/n/12 (Back-ward Sub-sti-tu-tion: 
\OT1/jkptt/m/n/12 USolve\OT1/jkp/m/n/12 )\OT1/jkp/b/n/12 . []\OT1/jkp/m/n/12 Th
e fol-low-ing code solves the prob-
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\OT1/jkp/m/n/12 Our over-ar-ch-ing goal of this sec-tion is to dis-cuss an ana-
logue to the eigenvalue-eigenvector
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[][][][][][]\OT1/jkp/m/n/10 The idea of SVD for Rec-om-mender Sys-tems: http://
www.cs.carleton.edu/cs[]comps/0607/recommend/recommender/svd.html[][]| 
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[][][][][][]\OT1/jkp/m/n/10 Paper about Rec-om-mender Sys-tems: http://robotics
.stanford.edu/ ron-nyk/WE-
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[][]\OT1/jkp/b/n/12 Theorem 4.72. []\OT1/jkp/m/n/12 If $\OML/jkp/m/it/12 A$ \OT
1/jkp/m/n/12 is an $\OML/jkp/m/it/12 n \OMS/jkp/m/n/12 ^^B \OML/jkp/m/it/12 n$ 
\OT1/jkp/m/n/12 ma-trix with $\OML/jkp/m/it/12 n$ \OT1/jkp/m/n/12 lin-early in-
de-pen-dent eigen-vec-tors $\OT1/jkp/b/n/12 v[]\OML/jkp/m/it/12 ; \OT1/jkp/b/n/
12 v[]\OML/jkp/m/it/12 ; \OT1/jkp/b/n/12 v[]\OML/jkp/m/it/12 ;$
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Chapter 5.

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[]\OT1/jkp/b/n/17.28 Recalling the Ba-sics of Or-di-nary Dif-fer-en-tial Equa-t
ions 
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[][]\OT1/jkp/b/n/12 Technique 5.14 \OT1/jkp/m/n/12 (Eu-ler's Method)\OT1/jkp/b/
n/12 . []\OT1/jkp/m/n/12 You're prob-a-bly al-ready fa-mil-iar with Eu-ler's me
thod
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[]\OT1/jkp/m/n/12 Your an-swers to the pre-vi-ous bul-lets should be: $\OML/jkp
/m/it/12 y[]\OT1/jkp/m/n/12 (0) = \OMS/jkp/m/n/12 ^^@\OT1/jkp/m/n/12 3$, $\OML/
jkp/m/it/12 y\OT1/jkp/m/n/12 (0\OML/jkp/m/it/12 :\OT1/jkp/m/n/12 5) \OMS/jkp/m/
n/12 ^^Y \OT1/jkp/m/n/12 4\OML/jkp/m/it/12 :\OT1/jkp/m/n/12 5$, $\OML/jkp/m/it/
12 y[]\OT1/jkp/m/n/12 (0\OML/jkp/m/it/12 :\OT1/jkp/m/n/12 5) =
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[153]
Chapter 6.
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[]\OT1/jkp/m/n/12 What if we take the ini-tial con-di-tion for the 1D wave equa
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[][]\OT1/jkp/b/n/12 Problem 6.49. []\OT1/jkp/m/n/12 Three ways to fix the is-su
es seen in the pre-vi-ous prob-lem are the ``Leapfrog''
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[]\OT1/jkp/b/n/17.28 The Laplace and Pois-son Equa-tions -- Steady State PDEs 
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\OT1/jkp/m/n/12 In this project you will be ex-plor-ing a par-tic-u-lar Par-tia
l Dif-fer-en-tial Equa-tion: the Advection-
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Appendix A.
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[][]\OT1/jkp/b/n/12 Example A.54 \OT1/jkp/m/n/12 (El-e-men-t--wise Ma-trix-Vec-
tor Mul-ti-pli-ca-tion)\OT1/jkp/b/n/12 . []\OT1/jkp/m/n/12 If we write \OT1/jkp
tt/m/n/12 A * v \OT1/jkp/m/n/12 Python
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[][]\OT1/jkp/b/n/12 Example A.55 \OT1/jkp/m/n/12 (Ma-trix--Ma-trix and Ma-trix-
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numpy
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Appendix B.
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Appendix C.

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\OT1/jkp/m/n/12 When work-ing with equa-tions is it of-ten times con-ve-nient a
nd nec-es-sary to cross-reference
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 []                \OT1/jkptt/m/n/12 \sin \left( \frac{\pi}{6} \right) &=& \fra
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[]\OT1/jkptt/m/n/12 (\ref{eqn:sample_equation}) \OT1/jkp/m/n/12 or, more sim-pl
y, [] us-ing []\OT1/jkptt/m/n/12 \eqref{eqn:sample_equation}\OT1/jkp/m/n/12 .
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[]\OT1/jkptt/m/n/12 (\eqref{eqn:cosine})\OT1/jkp/m/n/12 , are grouped to-gether
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Appendix D.
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