| ME504ST: Nonlinear Modeling and Analysis, Fall 2006 | |||||||
| Class No. | Description | Date | Read Assn | Prob. | Campus Due | Outreach Due | S |
| INTRODUCTION | |||||||
| 1 | Information about the course and the instructor. | 21-Aug | |||||
| DESIGN PROCESS | |||||||
| 2 | Mathematics as a language, numbers, process. History of mathematics. | 23-Aug | 1-13 | ||||
| 3 | Math as the basis for modeling. Definition of a nonlinear equation and its special behavioral character. | 25-Aug | |||||
| MODELING BASICS | |||||||
| 4 | Mathematics as a language. Modeling basics, examples of nonlinear systems. Basics of differential eqns, classification, modeling, normalization of variables & their domains. | 28-Aug | 13-25 | 3.1 | Aug.31 | Sep.14 | |
| 5 | Examples of Normalization | 30-Aug | 41-60 | 2.9 | 1-Sep | Sep.16 | |
| 6 | Understanding differential equations. Comparison of model and experiment. | 1-Sep | |||||
| Labor Day Holiday | 4-Sep | ||||||
| EXACT SOLUTION METHODS | |||||||
| 7 | A. Technique of Linearization, linearization errors | 6-Sep | 68-72 | ||||
| 8 | B. Direct Integration, C. Variation of Parameters, D. Elliptic Integrals. | 8-Sep | 72-83 | 2.1 | 11-Sep | 22-Sep | |
| 9 | E. Power Series Method | 11-Sep | 87-96 | ||||
| 10 | F. Picard's Method | 13-Sep | |||||
| 11 | G. Reversion of Power Series | 15-Sep | 96-101 | 3.2 | 18-Sep | 29-Sep | |
| 12 | H. In-Class Examples of Exact Solution Techniques | 18-Sep | 101-103 | ||||
| 13 | Continuation | 20-Sep | 103-114 | 3.10 | 20-Sep | 2-Oct | |
| NUMERICAL SOLUTION METHODS | |||||||
| 14 | Taylor's Series, Eulers Method | 22-Sep | 118-123 | 3.11 | 22-Sep | 3-Oct | |
| 15 | Exam Review | 25-Sep | 4.2 | 27-Sep | 8-Oct | ||
| 16 | EXAMINATION I | 27-Sep | Oct.4 | Oct.14 | |||
| Class No. | Description | Date | Read Assn | Prob. | Campus Due | Outreach Due | |
| 17 | No Class (Take-Home Exam) | 29-Sep | |||||
| 18 | Runge-Kutta, Multi-Step Methods | 2-Oct | 123-130 | ||||
| 19 | Example Problems | 4-Oct | |||||
| GRAPHICAL SOLUTION METHODS | |||||||
| 20 | Method of Isoclines, Phase Plane Analysis | 6-Oct | 133-136 | 5.3 | 9-Oct | 20-Oct | |
| 21 | Recovery of the Independent Variable, 2nd Order Systems | 9-Oct | 136-142 | 5.4 | 11-Oct | 23-Oct | |
| 22 | Lienard's, Pell's Method | 11-Oct | 142-144 | 5.2 | 13-Oct | 25-Oct | |
| 23 | In-class examples | 13-Oct | |||||
| APPROXIMATE SOLUTION METHODS | |||||||
| 24 | Method of Perturbation | 16-Oct | 148-155 | 6.1 | 18-Oct | 27-Oct | |
| 25 | Iteration Technique, Power Series Method | 18-Oct | 155-162 | 6.2 | 20-Oct | 31-Oct | |
| 26 | Orthogonal Functions | 20-Oct | 163-168 | ||||
| 27 | Method of Harmonic Balance | 23-Oct | 168-181 | 6.4 | 25-Oct | 6-Nov | |
| 28 | Galerkin's Method, Project Proposal Due Date | 25-Oct | 25-Oct | 6-Nov | |||
| 29 | No class | 27-Oct | |||||
| 30 | Example Problems | 30-Oct | 6.10 | 30-Oct | 10-Nov | ||
| STABILITY OF NONLINEAR SYSTEMS | |||||||
| 31 | Introduction to Stability | 1-Nov | 184-187 | Balloon | 1-Nov | 13-Nov | |
| 32 | Singular Point Analysis | 3-Nov | 187-216 | ||||
| 33 | Singular Point Examples | 6-Nov | 7.6 | 6-Nov | 17-Nov | ||
| 34 | Student Lectures | 8-Nov | 217-220 | ||||
| CASE STUDIES | |||||||
| 35 | Poincare Index | 10-Nov | 7.14 | ||||
| 36 | Chaotic Systems | 13-Nov | 226-247 | ||||
| 37 | Pre-Exam Review | 15-Nov | |||||
| 38 | Student Lectures | 17-Nov | |||||
| FALL BREAK | Nov.20-4 | ||||||
| 39 | EXAMINATION II | 27-Nov | 27-Nov | 7-Dec | |||
| 40 | Project Assignment | 29-Nov | |||||
| 41 | Project Assignment | 1-Dec | |||||
| 42 | PROJECT DUE DATE | 4-Dec | 4-Dec | 15-Dec | |||
| 43 | No class | 6-Dec | |||||
| 44 | No class | 8-Dec | |||||
| Class No. | Description | Date | Read Assn | Prob. | Campus Due | Outreach Due | S |