Math 232: Mathematical Models with Technology - Spring 2012
Instructor Information
- Instructor:
Doreen De Leon
- Office: PB 381A
- Office telephone: (559) 278-3090
- Office hours: M 4-5, W 3-4, or by appointment
Course Information
Announcements
- 01-20-12: Office hours for Monday, 01-23-12 are rescheduled for 3-4 p.m. I apologize for any inconvenience.
- 02-06-12: Office hours for this week are cancelled.
- 03-16-12: Office hours for 03-19-12 are cancelled due to other academic commitments.
- 04-18-12: Revised notes of modeling with linear algebra have been posted, correcting the error in the circuit example. The Maple worksheet (and the .pdf version of it) have also been fixed and re-posted.
Exam Information
- Midterm I
- Midterm I will have two parts: an in-class portion, which will be taken
in class on 02-23-12, and a take-home portion, which will be handed
out on 02-23-12 and due on 02-28-12.
- The midterm will cover:
- The 5-step modeling process (Chapter 2 of text and class notes)
- Discrete dynamical systems (Chapter 3 of text and class notes)
- Least-squares model fitting (both linear and nonlinear) (Chapter 4 of text and class notes)
- Multiple regression (Class notes)
- Modeling using proportionality (Chapter 5 of text and class notes)
- Modeling using geometric similarity (Chapter 5 of text and class notes)
- Dimensional analysis and Buckingham's Pi Theorem (Class notes)
- Similitude (Class notes)
- The midterm shall represent your own individual work.
- External resources may be used in completing the take-home portion of
the exam, like other books and Maple.
- Extra office hours: Wedneesday, 02-22-12, 4-5 p.m.
- Midterm I, Part II solutions - revised 02-29-2012:
- Midterm II
- Midterm II will be a take-home exam, handed out on Tuesday, March 27, 2012 and due Monday, April 9, 2012, by 6:00 p.m.
- The exam will cover the following topics:
- one-variable optimization (Chapter 8 and class notes and examples)
- analytic optimization
- numerical optimization -- Newton's method
- sensitivity analysis (class notes and examples only)
- multivariable optimization (Chapter 9 and class notes)
- analytic optimization
- numerical optimization -- Newton's method
- sensitivity analysis (class notes and examples only)
- constrained optimization (class notes and examples)
- The midterm shall represent your own individual work.
- Midterm II solutions:
- Midterm III
- Midterm III will be given in two parts. Part A will be an in-class
exam given on 05-03-12. Part B
will consist of two problems that you will take home. Part B will be
due on Tuenday, 05-08-12.
- Midterm III topics - posted
04-26-12.
- Midterm II solutions:
Reading Assignments
- 01-17-12: Read Chapter 1
- 01-19-12: Read Chapter 2
- 01-24-12: Read Sections 3.1-3.4
- 01-31-12: Read Section 3.5; Chapter 4
- 02-02-12: Read Chapter 5
- 02-28-12: Read Sections 8.1-8.3
- 03-01-12: Finish reading Chapter 8
- 03-06-12: Read Sections 9.1-9.3
- 03-27-12: Read Sections 12.1-12.3
- 04-10-12: Read Chapter 11
- 04-17-12: Read Sections 13.1
Handouts
Examples
- 01-24-12: Drug dosage example
- 01-26-12: Graphical equilibrium
- 01-26-12: Stability and long-term behavior
- 01-26-12: Growth of a yeast culture
- 01-31-12: Nonlinear Systems of Discreate Dynamical Systems
- Example 1: SIR
- Example 2: Battle between two Forces
- 02-02-12: Model Fitting
- 03-01-12: Singe Variable Optimization
- 03-06-12: Multivariable Optimization
- 03-15-12: Constrained Optimization
- 04-10-12: Modeling with First-Order Differential Equations
- 04-13-12: Modeling with Systems of Equations
- 04-17-12: Modeling with Systems of Differential Equations
- Stability using Linearization -- revised 04-18-12
- Stability via Phase Portraits
- Bonus example: Mathematical Epidemiology (Maple worksheet)
- 05-08-12: Modeling with Discrete Probability
Homework Assignments
- Homework #0, due Friday, January 27, 2012, by 4 p.m.
- Homework #1, due Friday, February 10, 2012, by 4 p.m.
- Homework #2, due Monday, February 20, 2012, by 6 p.m.
- Homework #2 - Note that you should only use Maple for the first 2-3 problems.
- Solutions
- Homework #3, due Tuesday, March 13, 2012, by 6 p.m.
- Homework #4, due Tuesday, March 20, 2012, by 6 p.m.
- Homework #4 -- Problems 1 and 3 are required; problem 2 is extra credit
- Solutions
- Homework #5, due Wednesday, March 28, 2012, by 6 p.m.
- Homework #6, due Friday, April 20, 2012, by 6 p.m.
- Homework #7, due Thursday, April 26, 2012, by 4:30 p.m.
- Homework #8, due Wednesday, May 2, 2012, by 4:30 p.m.