Weds office hours and z-alpha values

I will have office hours from 1-3pm on Weds.

There has been some confusion about what z values to use when applying a hypothesis test for a mean with a known variance. In this situation, the hypothesis is rejected if the test statistic satisfies
|z_0| > z(alpha/2)
where z(alpha/2) is given in the table below for the most common significance levels (alpha).

alpha       z(alpha/2)
0.10         1.645
0.05         1.96
0.01         2.58
0.005       2.81
0.002       3.08

This information will not be included on the statistics tables that will be handed out as part of the fnial exam, but you may choose to include it on your one page formula sheet.

Final exam info and Monday exercise

For the final exam, you may bring a formula sheet written in hand on one side of a standard sheet of paper. This is the same format as the earlier exams in this course.

Today's exercise continues the baseball theme from last week:
To date, the Atlanta Braves record at home this year is 27 wins and 24 losses. For away games, their record is 30 wins and 20 losses. Test the hypothesis that the Braves winning percentage for home and away games is identical.

Thursday exercise

Tha Atlanta Braves have (so far) won 54 games and lost 44 games in the 2012 baseball season. Treat each game as a data point and determine an interval estimate for the fraction of their games that the Braves will win this season.
In a similar vein, use a hypothesis test to assess whether the winning percentages of the Braves and their division rivals the Washington Nationals are statistically different. To date, the Nationals have won 58 games and lost 39.
More information on MLB win/loss records is here:
http://mlb.mlb.com/mlb/standings/index.jsp?tcid=mm_mlb_standings

Days until final exam: 7

Instructor and TA surveys

Please take a few minutes to complete the course survey and TA survey. Access to the GT survey system is available here: http://www.cetl.gatech.edu/cios

Information from these surveys is very helpful to improve future versions of the course. Your feedback on positive aspects of the course and areas that you think could be improved is welcome.

Summary of activities remaining in the class

Here is a summary of the activities left in the remainder of the semester:

Tuesday 7/24 and Thursday 7/26: Final week of class meetings. Kelly will be giving these lectures. Prof. Sholl will not have office hours because he will be attending a conference.

Reading material for these lectures:

All readings for these lectures are from Chapra and Canale

Pt 6.1 and Pt. 6.2 Motivation and Mathematical Background
Chapter 21, skipping 21.2.3 to the end of the chapter
22.2.1 Richardson’s Extrapolation
22.4.1 and 22.4.2 Gauss Quadrature
4.1.3 Numerical Differentiation
23.1 High-accuracy Differentiation Formulae

Thursday 7/26: Homework 8 due by 5pm

Review Session: Monday 7/30 10am in EST L1255. This is an optional activity. Prof. Sholl will answer questions about the sample exam problems that will be distributed next week.

FINAL EXAM: Thursday 8/2m 2:50-5:40pm

Wednesday exercise

The equipment cost estimates given in Seider, Seader, and Lewin are not given in 2012 dollars. Give an example of adjusting a cost estimate from this source to today's values.

Days until exam 3: 1
Days until final exam: 15

Tuesday exercise

Approximate exp(1.8) in four different ways:
(a) Using the first three terms of a Taylor series expanded around 1;
(b) Using the first three terms of a Taylor series expanded around 2;
(c) Using linear interpolation with data at 1 and 2;
(d) Using linear regression with data at 0, 0.5, 1, 1.5, 2, and 2.5.
Before you do any calculations, predict which method you think will be the most accurate.

Days until exam 3: 2
Days until final exam: 16

Office hours and review session for next week and exam week

I will not be able to hold office hours during the week of July 23 (the last week of lectures) because I will be travelling to give a keynote lecture to a conference in Oregon.

During exam week, the following activities will be scheduled:
Monday July 30 - 10-11am, Review session in EST L1255 (review solutions to the sample exam problems that will be distributed in the last week of class and any other questions)
Tuesday July 31 - 10-11am, Office hour
Wednesday, August 1 - 1-3pm Office hours
Other meeting times on Mon-Weds of exam are possible by appointment.

Monday exercise

Describe how to use the Newton-Raphson method to solve the following problems:
(a) solve f(x) = 0;
(b) solve f(x) = c;
(c) find a maximum of f(x);
(d) find a minimum of f(x).
Define a simple polynomial as an example and do a sample calculation for each problem.

Days until exam 3: 3
Days until final exam: 17
Reminder: We will go over the sample exam problems for exam 3 in class on Tuesday.

Reading for week of July 17

All readings for these lectures come from the text by Spiegel and Stephens assigned in the course syllabus. Only the chapter sections listed below will be covered.

Chapter 3: Arithmetic mean, Root square mean.

Chapter 4: Standard deviation, Variance, Properties of Standard Deviation.

Chapter 9: Unbiased estimates, Point estimates, Confidence-interval estimates.

Chapter 10: Statistical hypotheses, Tests for hypotheses, Type I and II errors, Level of significance, Tests for normal distributions, Two-tailed and One-tailed tests, Tests involving sample differences (means)

Chapter 11: t-distribution, Confidence intervals, Chi-square distribution, Confidence intervals for sigma, Degrees of freedom.

Friday exercise

Todays exercise: Explore an example of least squares fitting using polynomials in MATLAB using the polyfit command

Tour de France news: Cadel Evans has dropped out of the top 3 - he is currently in 4th place. But there is still a long way to go until the riders reach Paris...

Days until exam 3: 6
Days until final exam: 20
Reminder: We will go over the sample exam problems for exam 3 in class on Tuesday. You will get far more out of this activity if you have completed the problems on your own before then.

Thursday exercise

Sketch a contour plot of a 2D function that has multiple minima and maxima. Choose two different initial positions and sketch the first three iterates of the steepest ascent method and the univariate search method to approximate a maxium of the function.

Days until exam 3: 7
Days until final exam: 21

Resources to help prepare for exam 3

Homework 7 is now available from T-Square. Because of the proximity of this homework to exam 3, this homework will not be graded. Please note that this doesn't mean the homework is unimportant! If you do not spend time solving problems such as those given on the homework assignment, you will not be able to master the material we have covered in class.

A set of sample exam problems for exam 3 is also now available from T-Square (in the Resources folder). We will discuss the solutions to these sample problems in class next Tuesday.

Days until exam 3: 8
Days until final exam: 22

Comments on finalizing project

In class tomorrow, the second half of the class will be left open for project teams to finalize any remaining details from your project.

In preparing your report, please remember to produce a single electronic file that clearly identifies your group number and the group members.

Tuesday review exercise

Bessel functions, which we used in the lab exam last week, are solutions of ODEs similar to
x^2 y'' + x y' + (x^2 -4) y = 0.
State the order of this ODE and give a complete set of initial conditions at x = 1. Numerically determine the solution of the ODE from these initial conditions using the midpoint method with a step size of 0.05.

Change to Thursday office hours (and Tour de France update)

On Thursday, I will have an office hour right after class (11:45-12:45) instead of from 9-10. I am unable to hold my regularly scheduled office hour that day because of a teleconference with some collaborators from Dow.

Tour de France update:
After today's time trial, Cadel Evans is in second place, behind Bradley Wiggins. The Tour is now about half complete, with the challenging mountain stages to come in the next week.

Reading for week of July 10

Reading for Lecture 17: (Tuesday July 10)

CC 18.1 Newton’s interpolating polynomials (skip 18.1.5)

CC 18.2 Lagrange interpolating polynomials

Reading for Lecture 18: (Thursday July 12)

CC 17.1 Linear regression

CC 17.2 Polynomial regression

CC 17.3 Multiple linear regression

Days until exam 3: 10
Days until final exam: 24
Sample problems for exam 3 will be distributed later this week and discussed in class on Tuesday July 17.

General comments on project

General guidelines on reports for class project

1. Make sure every document has a title and lists the names and group number of the group.

2. Make sure the name of the file include your group number.

3. A detailed economic analysis (i.e. costing for each piece of equipment) of each process is not required. You should, however, think carefully about what factors will dominate costs for your process and discuss this in your final report.

If you have questions as your project proceeds, the best way to contact me is by email. I will be out of town from Sunday to Wednesday at a DOE conference in Pittsburgh - Prof. Sholl


Days until exam 3: 13
Days until final exam: 27
Regular time spent studying each day now has much greater value than time spent cramming in the last days before an exam.

Thursday review exercise

Most (although not all) of the blog posts for the rest of the semester will give exercises to help you review material we have covered during the semester.

Define a 4x4 triangular matrix, A. Without doing any calculations, state what it means for a vector to be an eigenvector of this matrix and how many eigenvectors exist for this matrix. Use MATLAB to calculate the eigenvalues and eigenvectors of your matrix. Without doing further calculations, determine all the eigenvectors of A^2.

Days until exam 3: 14
Days until final exam: 28
Regular time spent studying each day now has much greater value than time spent cramming in the last days before an exam.

Information for Tuesday lab exam

The lab exam on Tuesday will focus on your ability to solve numerical problems using MATLAB. You will be asked to develop MATLAB codes that solve specified problems and turn in these codes using T-Square. During the exam, you may use your notes, the text book, previous MATLAB codes you have developed and static online resources. Use of any resource that involves another person (e.g. email, text message) will not be permitted. Seating in the computer lab will be assigned for the exam.