MATH 331, Fall 2017: Introduction to Mathematical Modeling


Text: This course is based on class notes. The chapters are posted below. Download book.
Prerequisites: MATH 161 or concurrent registration; MATH 229 or concurrent registration or MATH 369 or concurrent registration.
Topics  Class Notes 
•
Introduction: The Modeling Process
(Ch.1) 
Chapter
1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Appendix 
Grading: • Homework 40% • Two Midterm exams 15% each • Final Exam 30%
Your grades will be available in CANVAS.Exam Dates:
Exam 1: Friday, October 6 at 1010:50 am in Engr E104
Exam 2: Friday, November 17 at 1010:50 am in Engr E104
FINAL: Thursday, December 14, 4:10pm to 6:10pm Engr E104
Allowed in Midterm Exams: 1 handwritten page (letter size) of notes,
Allowed in Final: 2 handwritten pages (letter size) of notes
Not allowed in all exams: calculators, cell phones, tablets, laptops, books, typed notes!Software used: MATLAB  Labs, Matlab Codes, Matlab Notes, and Links
Lab Sessions: Some of the classes will be held in the Weber 205 computer lab to practice Matlab. See Schedule below.
HW# Schedule and Homework Assignments due Your Grades are available in CANVAS: login with your eID and password.
Homework and Exam Solutions will be posted in the CANVAS "Files" section.1 Chapter 1: #2, 3, 4 Chapter 2: #1, 3, 4, 5, 9, 12
Fri, 09/08 Lab 1: Friday, September 15 in the Weber 205 computer lab Lab 2: Wednesday, September 20 in the Weber 205 computer lab 2 Chapter 2: # 16, 20, 22; Chapter 3: #1, 2, 3, Problem 3.13 Fri, 09/22 Exam 1: Friday, October 6 at 1010:50 am in Engr E104
3 Chapter 3: # 6, 8, 9; Chapter 4: # 1, 2, 3 Fri, 10/06 4 Chapter 4: # 5, 6, 8, 10, 13, 15 Fri, 10/20 Lab 3: Wednesday, October 25 in the Weber 205 computer lab 5 Chapter 4: #16, 23*, 24* << see note below #) ; Chapter 5: 1, 2, 3 Fri, 11/03 Exam 2: Friday, November 17 at 1010:50 am in Engr E104
6 Chapter 5: # 4, 7, 11, Chapter 6: # 1, 2, 4 Fri, 11/17 7 Chapter 6: # 6, 10, 15, 17a, 25, 26 Fri, 12/08 FINAL: Thursday, December 14, 4:10pm to 6:10pm Engr E104
#) note:
*: Use Matlab’s fmincon function for constrained optimization. The objective function and the constraints have to be coded in a separate function file.
Pr. 4.23: Use the gradient option for both objective and constraint functions. This means you have to code and provide as output the gradient in addition to the function.
Pr. 4.24: For finding the maximal area, you minimize –A(s1,s2,s3,s4). Use L as upper bound for all 4 variables, a aslower bound of s1 and s3, and b as lower bounds of s2 and s4. A good starting point for the search is (a+L)/2 for s1 and s3, and (b+L)/2 for s2 and s4. Furthermore:
(1) Use the gradient option only for the objective function (the derivatives of the constraint function are more messy in this case).
(2) Provide plots for each of parts (a), (b), (c) displaying the boundary of the fish farm, the fence, and the boundary of the fish lake (ellipse). If you have computed the optimal solution s1, s2, s3, s4, this plot can be created through the following commands:
t=linspace(0,2*pi,100);xe=a*cos(t);ye=b*sin(t);
plot(xe,ye,'k',[L 0 L 0 L],[0 L 0 L 0],'k',[s1 0 s3 0 s1],[0 s2 0 –s4 0],'k'), title('(a)')
There will be seven homework assignments, due every two weeks. Four selected problems from the homework assignment will be graded. Please formulate your solutions so that one can clearly understand the logic and line of reasoning. Include appropriate explanations and comments and avoid "MathSteno". Please write neatly and state every problem number and the problem itself. Points can be taken away if writing or presentation are not clear. You can discuss your homework solutions with other students, but the homework you turn in should be your own. No late homework assignments will be graded.
And, PLEASE, write your FULL NAME clearly on the top sheet, thank you!