AMS504 - Foundations of Applied Mathematics

---

Fall 2009


Instructor: Lingling Wu
TA: Yijie Zhou
Class Time: MW 05:20-6:40PM
Class Location: LGT ENGR 152
Office Hours: Monday 3:00pm-5:00pm
Office Hours by TA: Tuesday 9:00-10:00 am, Wednesday 3:00pm-4:00pm
Office: Math 1125


Lecture Notes and Solutions

No later homework is acceptable. If you have some special reason and cannot come to class, please send completed part of homework by email before due day. We will have 6-7 homework, you may drop 1 grade which you are not satisfied with.

Hw1 due day:Sep 9.
hw1:1,2,5,6,9,12,13,17.
solution for hw1 (PDF)

Hw2 due day:Sep 23.
hw2:(PDF)
solution for hw2 (PDF)

Hw3 due day:Oct 7.
hw3:(PDF)
hw3:3.24 a and b only. No need to prove c,d,e.
solution for hw3 (PDF)

midterm:(PDF)
midterm distribution:
100 2 students
[80,100) 6 students
[60,80) 5 students
[30,60) 4 students
problem 2: hint, closure of E = A U B, and intersection of A and B are empty set. Then define AA = intersection of A and E, BB = intersection of B and E. Follow the definition...

Book Stacking Problem
Some comments by Lingling Wu:
(1) Physical reason of balance is determined by mass and torque.
(2) Don't forget to prove divergence or convergence.
(3) Don't take it for granted that we choose top book has overhang length = 1/2. It is not so simple.
Please read this: http://en.wikipedia.org/wiki/Linear_programming
Here we have a11 = 1, a12 = 0; a21 = 1, a22 = 2;
Then we need to solve matrix to get final result.


Hw4 due day:Oct 28. Extended to Nov 4.
hw4: 3,4,7,9,14,18,20,21
Another proof of "f is continuous on [a,b],then f is uniformly continuous on [a,b]". (PDF)


Hw5 due day:Nov 18.
hw5: 2,9,12,13,15,22.

Hw6 due day: Dec 2.
hw6 :1,2,4,7,8,13.


If you have any question about the credit for homework, you may send email to TA yzhou@ams.sunysb.edu.

About final
Something not required : Perfect set, Rearrangement, Differentiation of Vector-value Function, Integration of Vector-value Function, Rectifiable curved, Equicontinuous Families of functions .

Syllabus

Chapter:
1: The Real and Complex Number Systems (Review)
2: Basic Topology
3: Numerical Sequences and Series
4: Continuity
5: Differentiation
6: The Riemann-Stieltjes Integral
7: Sequences and Series of Functions

Exams: Two closed-book exams. One at midterm on oct 19. Midterm will cover ch1-ch3. One during finals week in Dec. 1 page of cheating sheet is fine.
Grading: The final grade is based upon the following
• Homework assignments 20%
• Midterm : 40%
• Final : 40%

Disability Act: If you have a physical, psychological, medical or learning disability that may impact on your ability to carry out assigned course work, I would urge that you contact the staff in the Disabled Student Services office(DSS), Room 133, Humanities, 632-6748/TDD. DSS will review your concerns and determine with you what accommodations are necessary and approciate. All information and documentation of disability are confidential.