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.