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.

Reading for week of July 2

Reading for Lecture 15-16: (Tuesday July 3 and Thursday July 5)

CC Chapter 14 Multidimensional Unconstrained Optimization (skip 14.2.3)

Reminders of upcoming deadlines:
Computer lab exam - second half of class on Tuesday July 3
Project interim report 2 due on Thursday July 5
Homework 6 due on Tuesday July 10

Tour de France bonus quiz problems

The 2012 Tour de France begins on July 1 and end on July 22. Since last year's winner, Cadel Evans, grew up in my hometown, we will celebrate his successes in this year's Tour with the following scheme:

Cadel Evans places first in overall standings (yellow jersey): 1 free quiz
Cadel Evans places second in overall standings: 2 free problems on a quiz
Cadel Evans places third in overall standings: 1 free problem on a quiz

If these quiz bonuses are needed, they will be given for a quiz in the final week of class (after the Tour finishes). You will need to be present in class to benefit from a bonus quiz.

You can follow the daily progress of the Tour here: http://www.letour.fr/le-tour/2012/us/

Prof. Sholl

Thursday MATLAB exercise

Learn how to make two dimensional contour plots using ezcontour and ezcontourf. Use these to make plots of Z = (cos x)*(cos y)*exp(-sqrt((x^2+y^2)/4).

Wednesday MATLAB exercise

Plot the parametric curve x(t) = t, y(t) = exp(-t/2) for 0 < t < pi/2 using ezplot (after looking at the help file for ezplot).

Tuesday MATLAB exercise

Make an equivalent plot to the one from yesterday's exercise using ezplot.

Reminders of upcoming deadlines:
Thursday June 28 - Homework 5 due
Tuesday July 3 - Lab exam
Thursday July 5 - Project Interim Report 2 due
Tuesday July 10 - Homework 6 due (**this is later than indicated on original class syllabus)

Monday MATLAB exercise

Make a plot of a function of a single variable using fplot by executing fplot(‘exp(-0.1*x).*sin(x)’,[0,20]). Note the use of an array operator in this command. Add labels and title using xlabel(‘x’), ylabel(‘f(x) = e^[x/10]sin(x)’), title(‘A function plotted with fplot’).

Reading for next week's classes

Reading for Lecture 13: (Tuesday June 26)

CC 6.6 Multidimensional Newton-Raphson method

Reading for Lecture 14: (Thursday June 28)

CC Chapter 13 1D unconstrained optimization (skip 13.2 and 13.4)

Thursday exercises

In designing a materials handling system for a mining operation, you decide to use a ball mill to reduce the particle size of a solid ore. Estimate the cost (in current $) of a ball mill to handle 3 ton solids/hr.

The cost estimation table in Seider/Seader/Lewin Ch. 16 lists seveal types of screens. What are these devices used for?

Wednesday exercise and Lecture reading

Please take a few minutes to complete the midsemester survey announced in a previous blog post.

Exercise: Use a Taylor series to expand sin(2x) around pi/4. Also determine the Taylor series expansion of sin(x) and cos(x) around pi/4. Use your results to check the trigonometric identity sin(2x) = 2 sin(x) cos (x).

Reading for Lecture 12: (Thursday June 21)

CC 5.2 Bisection method
CC 5.4 Incremental searches
CC 6.2 Newton-Raphson method
CC 6.3 Secant method

Tuesday MATLAB exercise

 The eval function evaluates text strings if they contain valid MATLAB commands. Compare the results from x = 12*pi/exp(-0.5) and eval(‘x = 12*pi/exp(-0.5)’).

Reading for lecture 11 and Monday MATLAB exercise

Reading for Lecture 11: (Tuesday June 19)

Alternative Equipment Purchases (Seader/Seider/Lewin 17.4)
Cost Indexes, Commodity Chemicals, Economies of Scale (Seader/Seider/Lewin 16.2)

MATLAB exercise:

Text strings in MATLAB are defined using single quotes. For example, define message = ‘2120 is fun’.

Midsemester class survey

At the end of Tuesday's class, we will be half way through the semester. It would be helpful if you could spend a few minutes and complete the following survey to give Prof. Sholl some feedback on the course so far:
http://www.surveymonkey.com/s/DZVWNXB
Your responses to this survey are anonymous and the only aim is to gather feedback to potentially make adjustments in the second half of the semester to improve the course.

Friday exercise

Today's exercise is a recap of a problem that confused many people on yesterday's exam.

Write down the first several terms in the Taylor series expansion for ln(y), expanding around 1, and use these terms to estimate ln(2).
On the exam, you were asked about the same expansion, which was described as ln(1+x).
[Hint: define y = y0 +x with y0 = 1]

What is the difference between a chemist and a chemical engineer?

Each year, the American Chemical Society does a salary survey. The results of this year's survey were published in the June 4 edition of Chemical and Engineering News. Here is their data for the median annual salary of people who graduated in 2011 with full time employment with several levels of education:

B.S./B.A.: Chemists $36,000, Chemical Engineers $65,000

M.S.: Chemists $51,800, Chemical Engineers $77,000

Ph.D.: Chemists $75,000, Chemical Engineers $92,800

Quick review questions for ODEs

Give an example of a nonlinear, third order ODE and define appropriate initial conditions for this equation.

Give an example of a stiff ODE.

Give an example of a separable ODE and solve the ODE exactly.

Solve the following ODE exactly: 2y'' + y' - 2y = 0.

Reading for Tuesday lecture and Tuesday MATLAB exercise

MATLAB exercise: Remind yourself how to use the eig function to find the eigenvalues and eigenvectors of a matrix. What is the eigenvector that corresponds to the largest eigenvalue of A = [1 2 3; 4 5 6; 7 8 8]? Without looking up the answer, explain what it means for a vector to be an eigenvalue of A.

Reading:

Seader/Seider/Lewin Ch. 17: Section 17.4 (all). We will focus on the following sections:

Compound Interest

Annuities (discrete compounding)

Present Worth of Annuity

Alternative Equipment Purchases

Reading for Thursday lecture

CC 26.1 Stiff ODEs

CC 26.2 Multistep methods (up to end of 26.2.2 only)

Sample exam problems and Weds. MATLAB exercise

Sample exam problems to help you prepare for Exam 2 have been posted on T-Square. We will discuss the solutions of these problems in class next Tuesday.

MATLAB exercise: Learn how to use the rounding functions fix, floor, mod, and sign.

Tuesday MATLAB exercise

Learn how to rapidly create special matrices using the commands eye(m,n), zeros(m,n), one(m,n) and diag(v). For each command, try an example or two.

Reading and Monday MATLAB exercise

Reading for Lecture 7: (Tuesday, June 5):

CC 25.4 Systems of ODEs
CC 26.1 Stiff ODEs


MATLAB exercise: The transpose of a matrix A is defined in MATLAB using A’ (i.e. the matrix name followed by a single right quote). Try this operation on a square matrix, a non-square matrix, and a row vector.

Friday MATLAB exercise

Create a 3x3 square matrix A = [1 2 3; 4 5 6; 7 8 8]. Output the value of matrix element in the lower right corner using A(3,3). It is possible to update a matrix one element at a time. Try this by inputting A(3,3) = 9.

Wednesday MATLAB exercise and reminder about Thursday's class

MATLAB exercise: Use the zeros and ones commands to make a vector containing 100 zeros and another vector containing 50 ones. 

Reminder: On Thursday, class will first meet in the classroom in the M Building, then later move to the computer lab.

Friday MATLAB exercise

Define A to be a 10x10 identity matrix. Find the eigenvalues of A, 2*A, and A^2. Explain what you see.

Wednesday MATLAB exercise and reading for lecture 4

Reading for Lecture 4:

CC Pt. 7.1-7.2 (p. 697-703) Ordinary differential equations

CC 4.1 (p. 78-83) Taylor series

CC 25.1 (p. 707-715) Euler’s method

MATLAB exercise: Define x = linspace(0,10,5) and then y = sin(x) and z = sqrt(x) and understand what operations have been used in defining the elements in y and z.

Tuesday MATLAB exercise and sample exam problems

MATLAB exercise: Find out what the linspace command does. Generate a vector with five elements spaced equally between 0 and 10.

Sample exam problems: The first exam in this class is next Tuesday (May 29). A set of sample exam problems has been posted on T-Square. We will discuss these sample problems in class on Thursday. You will get much more out of this discussion if you have worked through the problems on your own before class.

Monday MATLAB exercise and minor homework correction

Correction to HW 1: The file names for the two MATLAB files you turn in should be HW1Prob1LastName.m and HW1Prob2LastName.m. The assignment originally listed these file names as HW2Probx... The homework assignment on T-Square has been updated.

MATLAB exercise: Create two row vectors with three elements by typing x = [1 2 3] and y = [2 1 0]. Evaluate z = x + y and understand what this quantity is.

Reading for lecture 3 and Friday MATLAB exercise

Reading for Lecture 3:

CC 9.1.2 Singular matrices

CC 10.2 Matrix inverse (skip Example 10.3)

CC 10.3 Ill conditioned matrices

Eigenvalues – excerpt from Greenberg available from T-square Resources

MATLAB exercise:
Calculate y = sin^2(x) for x = 30, 60, and 90 degrees. Sketch sin(x) by hand and verify your calculations make sense.

TA office hour schedule

Kelly has scheduled her office hours for the entire semester. These are listed on an updated version of the class schedule in the syllabus available from T-Square. They are also listed below. All of Kelly's office hours will be in the computer lab from 2-3pm on the days listed below:

Th 5/17
T 5/22
Th 5/31
T 6/5
T 6/12
Th 6/21
Th 6/28
T 7/3
Th 7/12
T 7/17
T 7/24

Thursday MATLAB exercise

Access MATLAB’s help files another way by typing helpwin. Find out what the commands clock and date do.

No office hour on Thursday May 17

I will not be able to hold my office hour on Thursday because I am a committee member on a PhD oral exam that was scheduled some time ago. I will be available after class if anyone has questions to they want to discuss.
Prof. Sholl

Wednesday MATLAB exercise

Most days during the semester, I will post a short MATLAB exercise. These exercises are intended to take just a few minutes and to give you ways to broaden you experience with MATLAB.

Today's exercise: Use  MATLAB’s help files to understand how the format command works. Access the help files from the command window by typing help format. Alternatively, access the help files via the dropdown Help menu. Find the 12^th digit of the area of a circle with radius 2.64.

Reading for lecture 2

The reading assignment for lecture will be distributed in class today. Future reading assignments will only be announced via the blog.

Reading for Lecture 2: CC = Chapra and Canale

CC 9.2 Gauss Elimination (skip 9.2.1)

CC 9.3 Pitfalls of Gauss Elimination

CC 9.4.1, 9.4.2 Techniques for Improving Solutions

TA office hours survey

TA OFFICE HOURS SURVEY (open until Tuesday, May 22)
Students, please indicate your preferred meeting time for TA office hours using the survey below. Office hours will be held on Tuesdays, Wednesdays, or Thursdays depending on the class schedule. Often students use office hours to get assistance in completing assignments or to review exam content. Filling out the survey will increase your chances of selecting a time that works for you!

http://www.surveymonkey.com/s/WSDHYKV

 

Welcome to the CHBE 2120 Summer blog

This blog will be used to communicate information related to CHBE 2120 during the GT summer semester. Critical updates will also typically be communicated by email via T-Square. Nevertheless, I highly recommend that you regularly read the contents of this blog during the semester.

Prof. Sholl