ACMS 20550, Fall 2011
Hurley
154; 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 156A).
Email: sommese@nd.edu
Office Hours: after class and
by appointment.
Exam Schedule
Exam
1: Tuesday, September 27.
Exam
2: Tuesday, November 8.
Final:
Thursday, December 15, 4:15 to 6:15 PM in DeBartolo room 131
Handouts
Taylor.pdf: A
Maple worksheet with some useful commands.
SomeMatrixCommands.pdf: A Maple worksheet with some
useful Matrix/Vector commands.
Homework
Homework 12 (due Tuesday, December 6 in
class)
Read
Chapter 15.
Do
Problems
§ 15.5: 1, 2, 5, 13;
§ 15.6: 15;
§ 15.8: 1, 5, 6, 11, 12, 13, 14;
§ 15.9: 4;
§ 15.10: 2, 3, 4;
§ 15.11: 9, 10.
Homework 11 (due Tuesday, November 29 in
class)
Read
Chapter 15.
Do
Problems
§ 15.3: 19;
§ 15.4: 1, 4, 7, 8.
Homework 10 (due Tuesday, November 22 in
class)
Read
Chapter 15.
Do
Problems
§ 15.1: 1, 2, 3, 4, 5, 6, 7;
§ 15.2: 1, 2, 5, 15, 17;
§ 15.3: 1, 6, 8, 12, 15.
Homework 9 (due Tuesday, November 15 in
class)
Read
through Chapter 6 & start reading Chapter 15.
Do
Problems
§ 6.7: 1, 2, 4, 6, 14, 15, 18;
§ 6.8: 1ab, 2ab;
§ 6.9: 2, 6, 7,10;
§ 6.10: 3, 4, 5, 9;
§ 6.11: 2, 3, 7, 8, 9, 13.
Homework 8 (due Tuesday, November 1 in
class)
Read
through Chapter 6.
Do
Problems
§ 5.4: 7a, 10a, 15, 16, 31, 37, 39;
§ 5.5: 1, 2, 4, 5, 7, 9, 10;
§ 5.6: 1, 6a, 25, 26, 27;
§ 6.3: 1, 12;
§ 6.4: 2, 4.
§ 6.6: 1, 2, 3, 4, 5, 6.
Homework 7 (due Tuesday, October 25 in
class)
Read
through Chapter 5.
Do
Problems
§ 5.2: 1, 7, 10, 14, 29, 31, 37, 39;
§ 5.3: 17, 18, 19;
§ 5.4: 1a, 2ab, 5, 14.
Homework 6 (due Tuesday, October 11 in
class)
Read
through Chapter 5.3.
Do
Problems
§ 4.7: 3, 8, 23;
§ 4.8: 1, 2, 3, 12;
§ 4.9: 4, 5, 6;
§ 4.10: 1, 10;
§ 4.11: 1, 2, 3;
§ 4.12: 4, 7, 12, 13, 14, 16;
§ 4.13: 3, 27, 30.
Homework 5 (due Tuesday, October 4 in
class)
Read
through Chapter 4.9. Skip Chapter
3.12.
Do
Problems
§ 3.8: 6, 13;
§ 3.10: 1, 2c, 4;
§ 3.11: 12, 13, 27, 28, 29;
§ 4.1: 1, 2, 6, 7;
§ 4.2: 4, 5;
§ 4.4: 1, 14;
§ 4.5: 1, 5;
§ 4.6: 1, 2, 3, 4;
§ 4.7: 4, 16.
Homework 4 (due Tuesday, September 20 in
class)
Finish
reading Chapter 3.
Do
Problems
§ 3.4: 2, 3, 9, 10, 12, 13, 14, 18,
20, 21, 22;
§ 3.5: 3, 5, 7, 11, 20, 21, 23, 28,
32, 36;
§ 3.6: 1, 3, 4, 7, 9, 13, 15, 19,
31, 32;
§ 3.7: 7, 15, 16, 17, 22.
Homework 3 (due Tuesday, September 13 in
class)
Read
Chapter 2 (skip section 16) and Chapter 3.1 to 3.5.
Do
Problems
§ 2.7: 1, 2, 13, 14, 16, 17;
§ 2.8: 2;
§ 2.9: 1, 4, 6, 10, 16, 18, 19, 35,
37, 38;
§ 2.10: 2, 12, 16, 24, 26, 30;
§ 2.11: 11, 12;
§ 2.12: 3, 12, 27, 28, 37;
§ 2.13: 1, 4, 8, 9;
§ 3.2: 1, 8, 14, 15, 16;
§ 3.3: 1, 4, 6, 11, 12, 18.
Homework 2 (due Tuesday, September 6 in
class)
Read
Chapter 2. Problems
§ 1.10: 17, 18;
§ 1.13: 5, 9, 36, 37;
§ 1.14: 8, 14;
§ 1.15: 24;
§ 2.4: 1, 2, 5, 15, 18;
§ 2.5: 1, 6, 24, 31, 33, 34, 35, 37,
39, 43, 52, 54, 64;
§ 2.6: 2, 3, 13;
§ 2.6: 15.
Homework 1 (due Tuesday, August 30 in
class)
Read
Chapter 1. Problems
§ 1.1: 3, 6;
§ 1.2: 2, 3, 4, 7, 8;
§ 1.4: 1, 3, 5;
§ 1.5: 4, 6;
§ 1.6: 4, 11, 18, 20, 26, 27;
§ 1.7: 4, 5, 6;
§ 1.9: 4, 5, 8;
§ 1.10: 2, 16.
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.