IMPORTANT: READ VERY CAREFULLY

Below, you find two different types of an extra project (choose only one of the two):

1. Project Type A: Numerical Approximations using the Euler's Method (Section 2.7)

2. Project Type B: The extended statement of the Existence and Uniqueness Theorem (Section 2.8)

Grading policy (read very carefully):

Upon a successful completion of the extra project, students can upgrade their final grades by one level (e.g., from B+ to A-). Since this is an extra work, the credit will be given in the form of either "successful/complete" or "unsuccessful/incomplete". Only those marked as "successful/complete" will grant you an upgrade of your final grade; otherwise, all unsuccessful/incomplete (or inaccurate) submission of the project will not give you an upgrade. For example, a project that merely shows a good level of (partial) attempts without rigorous mathematical conclusions for ALL problems will not earn you an upgrade.  For this reason, a very strict rule will be applied to grading the extra projects. 

Your decision by 6 pm, 3/15/18:

If you decide to submit your extra project, you should send an email to Prof. Dongwook Lee no later than 6pm, Thur, March 15th. In your email, clearly identify which project you're going to do and you're only allowed to do the project of your choice. An email without identifying your choice will be considered as "unsuccessful/incomplete". Failures of sending out your email notification will not grant you an opportunity to submit your extra project. You can, however, decide not to submit yours later without any penalty.

Project Problems:

Project Type A: 

1. Study 2.7 and study the online material (click here).

2. Submit Matlab code implementations for problems 15, 16, 17, 18, and 19 (one set of code implementations for each problem). Make sure that all code implementations should be self-explanatory with good code documentation.

3. Submit a written report (maximum 5 page). Your written report needs to be cleanly organized (a failure of providing a cleanly organized report will be marked as "unsuccessful/incomplete") and explain your solutions and findings.

4. A complete project (5 Matlab source codes and one written report in pdf) will be submitted to Prof. Dongwook Lee via email by 11:59 pm, Tue, March 20th. No late submission will be accepted.

Project Type B:

1.  Study 2.8 (in particular, pg. 117 -- 119) and realize that what we studied in class was only a very specific case of an IVP (e.g., we assumed the function f and f' in the IVP are continuous). The idea is to generalize the notion of the uniqueness and the existence of the solutions to the first-order ODEs using the so-called "Lipschitz condition". 

2. Solve problems 13 through 19. The rigorousness and the completeness of your solutions are crucial to earn an upgrade of your grade.

3. Submit a written report including a summary of your study of 2.8 (one-page limit) and mathematical proofs and solutions of the problems (15-page limit). Your written report needs to be cleanly organized (a failure of providing a cleanly organized report will be marked as "unsuccessful/incomplete") and explain your solutions and findings.

4. A complete project (one-page of summary and solutions to the problems, all in one pdf) will be submitted to Prof. Dongwook Lee via email by 11:59 pm, Tue, March 20th. No late submission will be accepted.

Academic Honesty

Your report should be of your own work. A work that has solutions copied from any other resources will be marked as incomplete regardless of the quality and the completeness of your report.