Math
398 -- Math in the City

Spring 2006

Spring 2006

Section 003

Instructor: Petronela Radu

Office: AVH 239

Phone: 472-9130

E-mail: pradu@math.unl.edu

Office Hours: 2:30 - 4:00 pm Mondays and Wednesdays or by appointment

Graduate Teaching Assistant:

Sawanya Sakuntasathien

e:mail: s-ssakunt1@math.unl.edu

Office Hours: TuTh 10:00 -- 12:00 or by appointment

Nebraska Research Expo (Cornhusker Marriott, March 2006)

Poster: Tell-Tale Heart Attack photo 1 - Nikki, Jackie, Tigh, Julianne

photo 2 - Nikki, Jackie, Tigh, Sawanya, Petronela

Poster: Lake McConaughy, Is Your Water Gonna Stay?

photo 1 - Caleb, Eric, Melissa

photo 2 - Caleb, Eric, Melissa, Petronela

Schedule of classes: MWF 12:30 -- 1:20 Avery Hall 110

Syllabus (tentative):

Week 01/09 - 01/13 Project descriptions; Introduction to Linear Algebra

01/16 - 01/20 Linear Algebra: matrices, linear systems

01/23 -01/27 Statistics: Random variables, expected value, variance, special distributions, Introduction to Maple

01/30 - 02/03 Statistics: The t and chi-square distributions, confidence intervals

02/06 - 02/10 Statistics: Hypothesis testing, Linear regression

02/13 - 02/17 Multiple Linear Regression, Multiple Logistic Regression

02/20 - 02/24 DE: Substitution Methods in DE, Modelling with DE

02/27 - 03/03 Existence and Uniqueness Issues for DEs, Euler's Method

03/06 - 03/10 Qualitative Methods for DE and for systems of DEs

03/13 - 03/17 Spring Break - No classes!

03/20 - 03/24 Nonlinear DE

03/27 - 03/31 DE: Fourier Transform

04/03 - 04/07 Review for Exam

04/10 - 04/14 Review for Exam (Exam is on 04/12)

04/17 - 04/21 Mathematics for your future

04/24 - 04/28 Poster presentations and discussions

Project: As part of the coursework in this class groups of 3-4 students will work on a project designed

in collaboration with a local bussiness or research center. You may design your own project, however you need

to get the instructor's approval for your choice before starting any work on it. Some possible choices are:

-- Medical Trial Analysis -- in collaboration with Professor Jane Meza from Nebraska Medical Center, Omaha

Project Description

Data for the project

with Dr. Shuhai Zheng from the Department of Natural Resources

Data Set 1 (Elevation/Storage/Surface Area)

Data Set 2 (Date/Elevation/Storage)

Guidelines for grading the project:

30 points for the mathematical content - correct formulas and arguments, complete explanations

15 points for esthetical aspect (use of graphs, diagrams, colors) and organization

5 points for presenting the novelty and the significance of the work (any research that was done on the subject,

new methods, programming skills that you learnt while working on the project, emphasize the importance of

the work).

Each project should have 3 parts. The Introduction will contain a project description, an outline of the methods

used, and the significance of the work. In the Main Body you will include the work: a set-up of the problem,

the hypothesis, the arguments, and the steps taken to solve the problem. The conclusions will contain the final

results and their interpretation.

On a separate piece of paper, each student should summarize the work that he/she did on the project.

References: For the material taught in class you may use as additional references besides the notes given in class,

any textbook in Linear Algebra, Differential Equations, and Statistics. You may have to find and read references

for the project that you will chose to work on during the semester.

Homework: The homework will be announced in class and posted on the web. You are encouraged to discuss

the problems with your colleagues, but you have to write your own solutions.

Homework 1 (due 01/30)

Homework 2 (due 02/10)

Homework 3 (due 02/20) - Data file. Description of the data

Homework 4 (due 03/01) - Data file 1(.dat) Data file 1 (.xls). Description of the data 1.

Data file 2 (.dat) Data file 2 (.xls). Description of the data 2

Homework 5 (due 03/08)

Homework 6 (due 03/22)

Homework 7 (due 04/03)

Homework 8 (due 04/11)

Exam: There will be a two-hour exam for this course covering the topics discussed in class.

Assessment: Your final grade will be computed based on the follwing scheme.

15 % Homeworks

50 % Project

25 % Exam

10 % Quizzes / Oral Presentation

Instructor: Petronela Radu

Office: AVH 239

Phone: 472-9130

E-mail: pradu@math.unl.edu

Office Hours: 2:30 - 4:00 pm Mondays and Wednesdays or by appointment

Graduate Teaching Assistant:

Sawanya Sakuntasathien

e:mail: s-ssakunt1@math.unl.edu

Office Hours: TuTh 10:00 -- 12:00 or by appointment

Nebraska Research Expo (Cornhusker Marriott, March 2006)

Poster: Tell-Tale Heart Attack photo 1 - Nikki, Jackie, Tigh, Julianne

photo 2 - Nikki, Jackie, Tigh, Sawanya, Petronela

Poster: Lake McConaughy, Is Your Water Gonna Stay?

photo 1 - Caleb, Eric, Melissa

photo 2 - Caleb, Eric, Melissa, Petronela

Schedule of classes: MWF 12:30 -- 1:20 Avery Hall 110

Syllabus (tentative):

Week 01/09 - 01/13 Project descriptions; Introduction to Linear Algebra

01/16 - 01/20 Linear Algebra: matrices, linear systems

01/23 -01/27 Statistics: Random variables, expected value, variance, special distributions, Introduction to Maple

01/30 - 02/03 Statistics: The t and chi-square distributions, confidence intervals

02/06 - 02/10 Statistics: Hypothesis testing, Linear regression

02/13 - 02/17 Multiple Linear Regression, Multiple Logistic Regression

02/20 - 02/24 DE: Substitution Methods in DE, Modelling with DE

02/27 - 03/03 Existence and Uniqueness Issues for DEs, Euler's Method

03/06 - 03/10 Qualitative Methods for DE and for systems of DEs

03/13 - 03/17 Spring Break - No classes!

03/20 - 03/24 Nonlinear DE

03/27 - 03/31 DE: Fourier Transform

04/03 - 04/07 Review for Exam

04/10 - 04/14 Review for Exam (Exam is on 04/12)

04/17 - 04/21 Mathematics for your future

04/24 - 04/28 Poster presentations and discussions

Project: As part of the coursework in this class groups of 3-4 students will work on a project designed

in collaboration with a local bussiness or research center. You may design your own project, however you need

to get the instructor's approval for your choice before starting any work on it. Some possible choices are:

-- Medical Trial Analysis -- in collaboration with Professor Jane Meza from Nebraska Medical Center, Omaha

Project Description

Data for the project

with Dr. Shuhai Zheng from the Department of Natural Resources

Data Set 1 (Elevation/Storage/Surface Area)

Data Set 2 (Date/Elevation/Storage)

Guidelines for grading the project:

30 points for the mathematical content - correct formulas and arguments, complete explanations

15 points for esthetical aspect (use of graphs, diagrams, colors) and organization

5 points for presenting the novelty and the significance of the work (any research that was done on the subject,

new methods, programming skills that you learnt while working on the project, emphasize the importance of

the work).

Each project should have 3 parts. The Introduction will contain a project description, an outline of the methods

used, and the significance of the work. In the Main Body you will include the work: a set-up of the problem,

the hypothesis, the arguments, and the steps taken to solve the problem. The conclusions will contain the final

results and their interpretation.

On a separate piece of paper, each student should summarize the work that he/she did on the project.

References: For the material taught in class you may use as additional references besides the notes given in class,

any textbook in Linear Algebra, Differential Equations, and Statistics. You may have to find and read references

for the project that you will chose to work on during the semester.

Homework: The homework will be announced in class and posted on the web. You are encouraged to discuss

the problems with your colleagues, but you have to write your own solutions.

Homework 1 (due 01/30)

Homework 2 (due 02/10)

Homework 3 (due 02/20) - Data file. Description of the data

Homework 4 (due 03/01) - Data file 1(.dat) Data file 1 (.xls). Description of the data 1.

Data file 2 (.dat) Data file 2 (.xls). Description of the data 2

Homework 5 (due 03/08)

Homework 6 (due 03/22)

Homework 7 (due 04/03)

Homework 8 (due 04/11)

Exam: There will be a two-hour exam for this course covering the topics discussed in class.

Assessment: Your final grade will be computed based on the follwing scheme.

15 % Homeworks

50 % Project

25 % Exam

10 % Quizzes / Oral Presentation

If
you have any suggestions, please fell free to bring them up!

Introduction to some Maple commands

The motion of a spring in Maple

Systems of Differential Equations in Maple - exact solutions, plots, eigenvectors and eigenvalues

Euler's Method for DEs and for systems

Nonlinear Systems of Differential Equations

Introduction to some Maple commands

The motion of a spring in Maple

Systems of Differential Equations in Maple - exact solutions, plots, eigenvectors and eigenvalues

Euler's Method for DEs and for systems

Nonlinear Systems of Differential Equations