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)
|
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. |
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
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.
Click here to go to the
Department of Applied and Computational Mathematics and Statistics (DACMS) home
page.
Click here to go to the
College of Science home page.
Click here to go to the University of
Notre Dame home page.