ACMS 20550, Fall 2010
DeBartolo
209; 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: Jordan Hall of Science
101; 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, September 28.
Exam
2: Tuesday, November 9.
Final:
Wednesday, December 15, 4:15 to 6:15PM
Handouts
Homework
Homework 0 (this assignment will not be
collected or graded)
Review
Chapter 1. Problems § 1.1: 11; § 1.2: 1, 2, 9; §
1.4: 6; § 1.5: 1, 3, 10;
§ 1.6: 4, 5, 8, 12; §
1.9: 5, 8; § 1.10: 1, 4, 5,
7, 23 ; § 1.13: 7, 20.
Homework 1 (due Tuesday, August 31 at
the start of class)
Start
reading Chapter 2. Problems
§ 2.4: 1, 5, 15;
§ 2.5: 1, 7, 28, 30, 34, 35, 48, 50, 51, 62, 64;
§ 2.8: 2;
§ 2.9: 1, 13, 15, 21,
37.
Homework 2 (due Tuesday, September 7 at
the start of class)
Read
Chapter 2: § 1 to 14. Problems
§ 2.10: 21, 24;
§ 2.11: 11, 12, 17, 18;
§ 2.14: 1, 4, 8, 9 (ignore the part about using a computer on
these problems);
§ 2.17: 1, 2, 7, 25, 32.
Start
Reading Chapter 3. Problems § 3.2: 3, 10, 16.
Homework 3 (due Tuesday, September 14 at
the start of class)
Read
Chapter 2: § 1 to 14. Problems
§ 3.3: 1, 2;
§ 3.4: 2a, 2b, 10, 13, 15, 18, 20, 23;
§ 3.5: 5, 7, 11, 20, 21, 27, 32;
§ 3.6: 1, 3, 4, 13, 19.
§ 3.7: 1, 2.
Read
up to § 3.7.
Homework 4 (due Tuesday, September 21 at
the start of class)
Read
up to the bottom of page 164 on §
3.12.
Problems;
§ 3.7: 11, 12, 15, 22;
§ 3.9: 3, 6, 11, 13;
§ 3.10: 1, 2, 4, 5;
§ 3.11: 12, 15, 18.
§ 3.12: 2.
Read
§ 4.1 and 4.2.
Homework 5 (due Tuesday, October 5 in
class)
Read
§ 4.3–4.9.
Problems;
§ 4.2: 4;
§ 4.4: 1, 11, 14;
§ 4.5: 1, 3, 5;
§ 4.6: 2, 3, 4, 8.
§ 4.7: 1, 4, 15, 22, 23.
§ 4.8: 3, 5, 12, 15.
Homework 6 (due Tuesday, October 12 in
class)
Read
§ 4.10 to § 5.4.
Problems;
§ 4.9: 4, 5;
§ 4.11: 3;
§ 4.12: 1, 4, 7, 8, 12;
§ 5.2: 1, 3, 4, 9, 24.
§ 5.3: 6, 17, 18, 19, 20.
Homework 7 (due Tuesday, October 26 in
class)
Read
through § 6.6.
Problems;
§ 5.4: 1a, 2abc,
5, 14, 19;
§ 5.5: 1, 2, 3, 9;
§ 5.6: 1, 13, 25, 26, 27;
§ 6.3: 1.
Homework 8 (due Tuesday, November 2 in
class)
Read
through the end of Chapter 6.
Problems;
§ 6.3: 12a;
§ 6.4: 3, 4, 10;
§ 6.6: 1, 6, 9;
§ 6.7: 1, 7, 10, 18, 19;
§ 6.8: 2, 3;
§ 6.9: 2, 6, 7;
§ 6.10: 2;
§ 6.11: 7, 12.
Homework 9 (due Tuesday, November 16 in
class)
Read
Chapter 15.1 to 15.4
Problems;
§ 15.1: 1, 2, 3, 4, 5, 7, 8;
§ 15.2: 5, 7, 8, 17;
§ 15.3: 6, 8, 12a, 12b, 15, 19.
Homework 10 (due Tuesday, November 23 in
class)
Read
through Chapter 15.5 to 15.7.
Problems;
§ 15.4: 1, 2, 7, 8, 12, 22;
§ 15.5: 1, 2, 5, 13, 16;
§ 15.6: 5, 13, 16.
Homework 11 (due Monday, December 6 in
class)
Finish
reading Chapter 15.
Problems;
§ 15.8: 11, 12, 13;
§ 15.9: 4, 8;
§ 15.10: 4;
§ 15.11: 3, 4, 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.