ACMS 20750, Spring 2012
DeBartolo Hall 318; 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:
Hayes-Healy 229; 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 156).
Email: sommese@nd.edu
Office Hours: After class and
by appointment.
TA: Amy
Buchmann (Hurley 163).
Email: abuchman@nd.edu
Office
Hours: Monday 3:00 - 4:00 and by appointment.
Exam Schedule
Exam
1: Tuesday, February 21 at Tuesday
11-11:50AM in Hayes-Healy 229.
Exam
2: Tuesday, April 3 at Tuesday
11-11:50AM in Hayes-Healy 229.
Final:
Thursday, May 10, 4:15 to 6:15PM in 318 DeBartolo Hall (where our class
met MWF).
Handouts
Legendre Polynomial Expansions
Homework
Homework 12 (due Tuesday, May 1 in class)
Read
Chapter 14.
Problems:
§ 14.8: 3, 4, 6, 7, 14;
§ 14.9: 9, 10, 11;
§ 14.11: 15, 17, 29.
Homework 11 (due Tuesday, April 24 in
class)
Read
Chapter 14.
Problems:
§ 14.5: 3;
§ 14.6: 1, 5, 9, 14, 17, 19, 24,
26, 27, 33, 34, 37;
§ 14.7: 1, 2, 6, 9, 10, 11, 16,
20, 21, 22, 28, 29, 33, 37, 38, 42, 45, 51, 53.
Homework 10 (due Tuesday, April 17 in
class)
Read
Chapter 14.
Problems:
§ 14.2: 31, 32, 46, 47, 51, 52,
55, 59;
§ 14.3: 1, 2, 3, 11, 12, 16, 17,
18, 21, 22, 23;
§ 14.4: 3, 7, 8, 9, 11;
§ 14.5: 1.
Homework 9 (due Tuesday, April 10 in
class)
Start
reading Chapter 14.
Problems:
§ 14.1: 1, 2, 3, 4, 11, 12, 13,
14, 15, 17, 19, 21;
§ 14.2: 1, 3, 4, 19, 29.
Homework 8 (due Tuesday, March 27 in
class)
Read
Chap. 12.1 to 12.12 plus Chap. 13.1 an 13.2.
Problems:
§ 12.6: 1, 2, 5; § 12.7: 2;
§ 12.8: 1, 2, 4; § 12.9: 2, 3;
§ 12.10: 1, 2, 3; § 13.1: 2.
Homework 7 (due Tuesday, March 20 in
class)
Read
Chap. 12. Problems:
§ 11.5: 3, 5;
§ 11.7: 1, 7;
§ 11.9: 4;
§ 11.11: 4, 5;
§ 12.1: 1;
§ 12.2: 2;
§ 12.3: 2, 4, 5; § 12.4: 2;
§ 12.5: 3, 7, 13.
Homework 6 (due Tuesday, March 6 in
class)
Read
Chap. 9.1 to 9.3 and 9.5 to 9.6 plus
Chap.
11.1 to 11.5. Problems:
§ 9.2: 1, 2, 4, 5, 9;
§ 9.3: 1, 4, 5,9;
§ 9.6: 1, 7;
§ 11.3: 2, 3, 7, 8, 10, 13, 15, 17.
Homework 5 (due Tuesday, February 28 in
class)
Read
Chap. 8 and Chap. 9.1 to 9.4. Problems:
§ 8.11: 1, 2, 3, 7, 9, 11, 15, 21;
§ 8.12: 1, 2, 8;
§ 8.13: 37, 40, 41, 42, 43;
§ 9.1: 1, 2.
Homework 4 (due Tuesday, February 14 in class)
Read
Chap. 8. Problems:
§ 8.7: 1b,d, 3, 5, 16, 18, 26;
§ 8.8: 3, 4, 8, 10, 18, 22;
§ 8.9: 3, 8, 15, 29, 37, 41;
§ 8.10: 3, 11, 15, 17.
Homework 3 (due Tuesday, February 7 in
class)
Read
Chap. 8. Problems (you can ignore
the statements
about
using a computer and comparing to your solutions):
§ 8.2: 3, 8, 21, 22, 32;
§ 8.3: 1, 3, 13;
§ 8.4: 3, 5, 14, 21;
§ 8.5: 2, 4, 12, 25, 31.
§ 8.6: 2, 3, 22,
26, 31a, 34, 42.
Homework 2 (due Tuesday, January 31 in
class)
Read
Chap. 7 (excluding 7.10 and 7.12). Problems
§ 7.6: 2, 12;
§ 7.7: 2, 12;
§ 7.8: 12;
§ 7.9: 8, 14, 27;
§ 7.11: 7;
§ 7.13: 8, 9;
§ 8.1: 1, 2.
Homework 1 (due Tuesday, January 24 in
class)
Start
reading Chapter 7. Problems
§ 7.2: 1, 3, 4, 5;
§ 7.3: 3, 4, 6;
§ 7.4: 1, 2, 5, 7, 13, 14;
§ 7.5: 1, 2, 8, 9.
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.