Final Presentation Order

I have just done a lucky random draw to get the following presentation order.

I have listed only the group number. For groups of a single student, I have put a star next to the group number. The presentation should last for 10-14 mins. For groups of 2 students, the final presentation should take 18-22 mins.

17 Nov (Thursday): 6* --> 3* --> 11 --> 7
22 Nov (Tuesday): 14* --> 8 --> 5 --> 1
24 Nov (Thursday): 2 --> 4 --> 13
29 Nov (Tuesday): 9 --> 10 --> 12

You are expected to show up for all presentations. You will evaluate each others and these peer evaluations will contribute to a part of your final grade. A rubric will be given to you all by Nov 11 (Friday) so you know what we are looking for and how you should prepare your presentation.

Lecture 11 (Oct 11)

How to write an academic paper: [click here]

Other references on writing a paper:

Advice for Undergraduates on Special Aspects of Writing Mathematics - S. Maurer
Writing a Math Phase Two Paper - S. Kleiman

Planning for the rest of the semester

Below is the arrangement for the rest of the lectures.

NOTE:

• All HW/Project due dates are highlighted in red.
• Meeting with individual group: Each group please login to CANVAS and take TWO 10 min slots with one on either OCT 18/20 and another on either NOV 01/03.
• LAB: I will be in the MATH UG lab (where you have your tutorials) and will help you on the code. You can also work on your own HW/project over there. 
• Final Presentation: Each group will present their research finding. For group consists of only 1 student, the time limit is 10-14 mins. For groups with 2 students, the time limit is 18-22 mins.

10/06: Lecture cancelled

10/07: HW3 DUE

10/11: LAB. I will talk about how to write an academic paper and how to do an academic presentation. Please show up.

10/13: LAB

10/14: HW4 DUE

10/18: Meeting with individual group

10/20: Meeting with individual group

10/21: Group member list and Topic for Project 2 DUE

10/25: LAB

10/27: LAB

10/28: Project 1 DUE

11/01: Meeting with individual group

11/03: Meeting with individual group

11/04: HW5 DUE

11/08: LAB

11/10: LAB

11/15: LAB

11/17: Final Presentation

11/22: Final Presentation

11/24: Final Presentation

11/29: Final Presentation

12/02: Project 2 DUE

HW 5

Due: Nov 4 11:59pm

Compute the bifurcation diagram of your nonlinear ODE system or mapping for Project 2.

Project 2

Project 2: [click here]

Due: Dec 2 (Friday) 1159pm

Submission: A zip file of all tex and figures. Make sure the tex is error-free. We will compile all files to create a report for everyone and for future use. Do not change the format of the report including the font size and the margin size.

Lecture 10 (Oct 4)

Logistic map and it's bifurcation diagram.

Other interesting reference for chaos:

• T.-Y. Li and J.A. Yorke, Period Three Implies Chaos, The American Mathematical Monthly, 82(10), 1975, 985-992. [click here]
• E. Sander and J.A. Yorke, The Many Facets of Chaos, Int. J. of Bifurcation and Chaos, 25(4), 2015. [click here]

Project 1

Project 1: [click here]

Due: Oct 28 (Friday) 1159pm

Submit only the final PDF file.

Lecture 9 (Sep 29)

Attractor. Basin of attraction.

Damped-driven pendulum. Poincare section.

Movies:

• Overdamped-undriven: [click here]
• Underdamped-undriven: [click here]
• Damped-driven pendulum for f=1.5, gamma=2/3:
• q=1.24: period-1 motion [click here]
• q=1.36: period-2 motion [click here]
• q=1.3725: period-4 motion [click here]
• q=1.3741: period-8 motion [click here]
• Poincare section for f=1.5, gamma=2/3 and q=4 with solutions at t=[10001:50000]*2pi/gamma: [click here] (computational time is around 2 mins).

Lecture 8 (Sep 27)

Linear stability analysis.

Lecture 7 (Sep 22)

Simplification I: linear damped pendulum. Under-damped, over-damped, critically-damped. Phase diagram.

Simplification II: linear driven pendulum.

Simplification III: linear damped-driven pendulum.

Simplification IV: Nonlinear damped-undriven pendulum.

Lecture 6 (Sep 20)

Model for damped-driven nonlinear pendulum.

Dimensional analysis.

Non-dimensionalization.

Reference
The Physical Basis of dimensional analysis - A.Solin

Lecture 5 (Sep 15)

Lecture cancelled.

Lecture 4 (Sep 13)

Phase diagram or Phase portrait of the linear and nonlinear pendulum.

The forward Euler method and the Runge-Kutta methods for solving an ODE.

MATLAB demonstration for ODE solvers: [click here]

NOTE: In the lecture, I mentioned that HW1 will due Sep 30. But it should be Sep 23 (NEXT FRIDAY) as stated on the blog and the question paper. This leaves you two weeks between the deadlines of HW4 and Project 1 (which will due Oct 28).

HW1-4

HW1: Due 23 Sep
HW2: Due 30 Sep
HW3: Due 7 Oct
HW4: Due 14 Oct

We will have one more set of HW due near the end of the course.

Lecture 3 (Sep 8)

Approximation of the period of the nonlinear undamped-undriven pendulum system.

Phase space. Phase diagram or Phase portrait of the linear and nonlinear pendulum.

Lecture 2 (Sep 6)

Introduction to Mathematical Modeling

4 steps in doing modeling:
1. formulation of a problem: approximations and assumptions to develop, simplify and understanding the mathematical model;
2. solve the equation(s): analytically (usually with some simplification) and numerically;
3. interpretation of the mathematical results in the context of the physical problem;
4. prediction: see the limitation(s) of the mathematical model/theory.

Simple pendulum: derivation of the nonlinear ODE. small angle approximation. period for both the linear and nonlinear pendulum.

Lecture 1 (Sep 1)

Course overview

PPT slides: [click here]

Reference
Scientific computing - J. Chasnov

Welcome

Syllabus: [click here]