ACMS 20750, Spring 2011

Geddes Hall B034; MWF 10:40-11:30AM

The famous Lorenz butterfly. In 1963, Edward Lorenz’s article, Deterministic Nonperiodic Flow (Journal of Atmospheric Sciences 20 (1963)), caught scientists by surprise.  Even the toy model of the atmosphere he used had unexpectedly sensitive dependence on initial conditions: a trivial perturbation, e.g., the proverbial butterfly flapping its wings in Tasmania, will change the weather a week from now dramatically.  Such an onset of chaos is a common feature of many real-world systems such as weather.

 
(Tutorial: Pasquerilla Center 114; Tuesday 11-11:50AM)

butterfly

 

 


Course Syllabus

Course Organization


Instructor: Andrew Sommese (Hurley 291).

Email: sommese@nd.edu

Office Hours: after class and by appointment.


Exam Schedule

Exam 1: Tuesday, March 1.

Exam 2: Tuesday, April 12.

Final: Wednesday, May 11, 4:15 to 6:15PM in 231 Hayes-Healy

 


Handouts

Gibbs Phenomena


Homework

Homework 1 (due Tuesday, January 25 in class)

Start reading Chapter 7.  Problems

   § 7.2: 1, 2, 3;

   § 7.3: 1, 2, 4;

   § 7.4: 1, 3, 4, 14, 15;

   § 7.5: 1, 5, 7, 10.

 

Homework 2 (due Tuesday, February 1 in class)

Read Chap. 7 (excluding 7.10 and 7.12).  Problems

   § 7.6: 1, 15;

   § 7.7: 1, 13;

   § 7.8: 11;

   § 7.9: 7, 12, 14;

   § 7.11: 5, 6;

   § 7.13: 5, 8.

 

Homework 3 (due Tuesday, February 8 in class)

Read Chap. 8.  Problems (you can ignore the statements

about using a computer and comparing to your solutions):

   § 8.1: 1, 3;

   § 8.2: 1,  5, 32, 34;

   § 8.3: 1, 2, 11;

   § 8.4: 1, 7, 9;

   § 8.5: 1, 3, 5, 21, 27, 31.

 

Homework 4 (due Tuesday, February 15 in class)

Read Chap. 8.  Problems (you can ignore the statements

about using a computer and comparing to your solutions):

   § 8.6: 1, 2, 4, 21, 30, 31, 34, 41;

   § 8.7: 1a,  2, 5, 17,25;

   § 8.8: 2, 8, 9, 17, 21;

   § 8.9: 2, 9, 27, 39, 42;

   § 8.10: 14.

 

Homework 5 (due Wednesday, March 2 in class)

Problems (you can ignore the statements

about using a computer and comparing to your solutions):

   § 8.10: 17;

   § 8.11: 10, 11, 18;

   § 8.12: 3;

   § 8.13: 40, 42;

   § 9.2: 5.

 

Homework 6 (due Tuesday, March 22 in class)

Problems (you can ignore the statements

about using a computer and comparing to your solutions):

   § 12.1: 3, 4;

   § 12.3: 2, 3, 4, 5;

   § 12.5: 1, 2, 3;

   § 12.8: 1, 2, 3;

   § 12.9: 1.

 

Homework 7 (due Tuesday, March 29 in class)

Read Chap 11.1 to 11.5.

Problems (you can ignore the statements

about using a computer and comparing to your solutions):

   § 12.9: 3 (use formulae 12.5.8b,c from page 570);

   § 11.3: 2, 3, 5, 9, 17;

   § 11.5: 6.

 

Homework 8 (due Tuesday, April 5 in class)

Read Chap 14.1 to 14.7.

Problems (you can ignore the statements

about using a computer and comparing to your solutions):

   § 14.1: 6, 11, 14, 15, 21;

   § 14.2: 11, 14, 15, 21;

   § 14.3: 1, 2, 3, 12, 14, 17, 18, 21, 22, 23.

 

Homework 9 (due Wednesday, April 13 in class)

Read Chap 14.1 to 14.7.

Problems (you can ignore the statements

about using a computer and comparing to your solutions):

   § 14.4: 3;

   § 14.6: 1, 6, 9, 24;

   § 14.7: 1, 2.

 

Homework 10 (due Tuesday, April 19 in class)

Read Chap 14.

Problems (you can ignore the statements

about using a computer and comparing to your solutions):

   § 14.6: 20, 31, 33;

   § 14.7: 9, 10, 11, 16, 17, 20, 22, 29, 33, 42, 43.

 

Homework 11 (due Tuesday, April 26 in class)

Read Chap 14.

Problems (you can ignore the statements

about using a computer and comparing to your solutions):

   § 14.8: 3, 5, 6, 9, 11.


Click here to go to the Society for Industrial and Applied Mathematics (SIAM) webpage: SIAM is the main professional organization for applied mathematicians.  The site has many interesting illustrations of applied mathematics in practice.

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