Publications by Donny Lofland
DATA605 Homework 15 - Multivariate Calc
knitr::opts_chunk$set(echo = TRUE) library(tinytex) library(Deriv) library(reticulate) ## Warning: package 'reticulate' was built under R version 3.6.2 Sys.setenv(RETICULATE_PYTHON = "/Users/dlofland/anaconda3/bin/python") Source files: [https://github.com/djlofland/DATA605_S2020/tree/master/] Problem 1 Find the equation of the regression line f...
4820 sym R (2962 sym/48 pcs) 1 img
Data605 Discussion 16 - Problem 12.5.26 (p728)
knitr::opts_chunk$set(echo = TRUE) library(tinytex) library(Deriv) library(symengine) ## Warning: package 'symengine' was built under R version 3.6.2 ## SymEngine Version: 0.6.0 ## _____ _____ _ ## | __|_ _ _____| __|___ ___|_|___ ___ ## |__ | | | | __| | . | | | -_| ## |_____|_ |_|_|_|_____|_|_|_ |_...
2852 sym R (917 sym/13 pcs)
Data605 Discussion 15 - Problem 8.8.18
knitr::opts_chunk$set(echo = TRUE) library(tinytex) library(ggplot2) Source files: [https://github.com/djlofland/DATA605_S2020/tree/master/] Problem 8.8.18 Use the Taylor Series in 8.8.1 to verify: \[sin(-x) = -sin(x)\] Analytics Solution Definition 8.7.1 Taylor Polynomial of degree \(n\) of \(f\) at \(x=c\): \[p_n(x) = f(c) + f'(c)(x-c) + \fra...
1195 sym R (2152 sym/6 pcs) 1 img
DATA605 Homework 14
knitr::opts_chunk$set(echo = TRUE) library(tinytex) Source files: [https://github.com/djlofland/DATA605_S2020/tree/master/] Taylor Expansions This week, we’ll work out some Taylor Series expansions of popular functions. For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansio...
2405 sym R (51 sym/1 pcs)
DATA605 Homework 13
knitr::opts_chunk$set(echo = TRUE) library(tinytex) Source files: [https://github.com/djlofland/DATA605_S2020/tree/master/] Problem 1 Use integration by substitution to solve the integral below. \[\int{4e^{-7x}}dx\] \[u=-7x,\text{ }u'=-7x\ dx = -\frac{1}{7}\\ \int{4e^{-7x}}dx = 4 \int{e^u} du * u'\\ -\frac{4}{7}\int{e^u du}\\ -\frac{4}{7} e^u...
4035 sym R (51 sym/1 pcs)
DATA605 Homework 11
knitr::opts_chunk$set(echo = TRUE) library(tinytex) Source files: [https://github.com/djlofland/DATA605_S2020/tree/master/] CARS Analysis Using the cars dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residua...
1454 sym R (1004 sym/9 pcs) 4 img
DATA605 Homework 10
knitr::opts_chunk$set(echo = TRUE) library(tinytex) Source files: [https://github.com/djlofland/DATA605_S2020/tree/master/] Smith in Jail Smith is in jail and has 1 dollar; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars with probability .4 and loses A dolla...
1095 sym R (2597 sym/13 pcs)
DATA605 Homework 9
knitr::opts_chunk$set(echo = TRUE) library(tinytex) Source files: [https://github.com/djlofland/DATA605_S2020/tree/master/] Problem 11 (p 363) The price of one share of stock in the Pilsdorff Beer Company (see Exercise 8.2.12) is given by \(Y_n\) on the \(n\)th day of the year. Finn observes that the differences \(X_n = Y_{n+1} − Y_n\) appear ...
2102 sym R (360 sym/8 pcs)
DATA605 - Homework 5
knitr::opts_chunk$set(echo = TRUE) library(tinytex) library(Matrix) library(pracma) ## ## Attaching package: 'pracma' ## The following objects are masked from 'package:Matrix': ## ## expm, lu, tril, triu Source files: [https://github.com/djlofland/DATA605_S2020/tree/master/] Problem Set 1 Choose independently two numbers B and C at random ...
1208 sym R (681 sym/18 pcs) 2 img
DATA605 - Discussion Problem 4 (LT C16 p443)
LT C16 (p443) Find the matrix representation of: \[\begin{align} T: C^{3} \xrightarrow[]{} C^{4}, T\left(\left[\begin{array}\\x\\y\\z\\\end{array}\right]\right) = \left[\begin{array}\\3x+2y+z\\x+y+z\\x-3y\\2x+3y+z\\\end{array}\right]\\ =x\left[\begin{array}\\3\\1\\1\\2\\\end{array}\right] + y\left[\begin{array}\\2\\1\\-3\\3\\\end{array}\right...
572 sym