## Bảng điểm thành phần môn Toán kỹ thuật nhóm 3 và 4, D17

Các bạn vào xem Bảng điểm thành phần môn Toán kỹ thuật nhóm 3 và nhóm 4:

Update:

• 21h50, 09/12: Bổ sung Phạm Đức Duy nhập thiếu bài kiểm tra thứ hai.

DungHP-Diem thanh phan Toan ky thuat Nhom 3+4

Bảng điểm này là bảng điểm đã có cộng trừ: một dấu + thì được cộng 2 điểm, ngược lại một dấu – sẽ bị trừ 2 điểm. Chuyên cần vắng 1 buổi trừ 2, 5 buổi là 0 điểm.

Một số bạn lên bảng nhiều (khoảng 4 lần trở lên) thì được cộng full.

Mọi thắc mắc gửi về mail hpdung83@gmail.com – hạn cuối: trước 24h00 ngày 10/12/2018. Sau thời gian trên, bảng điểm sẽ được gửi lên trường.

Best.

# Introduction to Time Series

https://www.stat.berkeley.edu/~bartlett/courses/153-fall2010/

### People

 Office hours Instructor Peter Bartlett bartlett@stat Evans 399, Tue 11-12, Thu 10-11. GSI Joe Neeman jneeman@stat Evans 387, Mon 3-4, Wed 5-6.

### Course Outline:

An introduction to time series analysis in the time domain and frequency domain. Topics will include: Stationarity, autocorrelation functions, autoregressive moving average models, partial autocorrelation functions, forecasting, seasonal ARIMA models, power spectra, discrete Fourier transform, parametric spectral estimation, nonparametric spectral estimation.

### Text:

Time Series Analysis and its Applications. With R Examples., by Robert H. Shumway and David S. Stoffer. Springer. 2nd Edition. 2006. web site.

### Prerequisites:

101, 134 or consent of instructor.

### Assessment:

Lab/Homework Assignments (25%): posted every one to two weeks, and due on Fridays at 9 (at the start of the section). The grade will be the average of all homework grades except the worst.
Midterm Exams (30%): scheduled for October 7 and November 9, at the usual lecture time and place. Midterm 1: pdf Solutions: pdf. Midterm 2: pdf Solutions: pdf.
Project (10%).
Final Exam (35%): scheduled for Friday 12/17/10.

### Lectures:

Chapter/section references are to Shumway and Stoffer.

• Thu, Aug 26. Overview, Chapter 1 (+2.3). slides: pdf.
• Tue, Aug 31. Section 1.5. slides: pdf.
• Thu, Sep 2. Section 1.6. slides: pdf.
• Tue, Sep 7. Section 1.6 (+A.1,A.2). slides: pdf.
• Thu, Sep 9. Section 3.2. slides: pdf.
• Tue, Sep 14. Section 3.2, 3.3, 3.4. slides: pdf.
• Thu, Sep 16. Section 3.3, 3.4, 3.5. slides: pdf.
• Tue, Sep 21. Section 3.4, 3.5. slides: pdf.
• Thu, Sep 23. Section 3.4, 3.5. slides: pdf.
• Tue, Sep 28. Section 3.5. slides: pdf.
• Thu, Sep 30. Section 3.6. slides: pdf.
• Tue, Oct 5. Review. [Joe Neeman]
• Thu, Oct 7. Midterm Exam 1.
• Tue, Oct 12. Section 3.6. slides: pdf.
• Thu, Oct 14. Section 3.6-3.9. slides: pdf.
• Tue, Oct 19. Section 3.9. slides: pdf.
• Thu, Oct 21. Section 4.1-4.3. slides: pdf.
• Tue, Oct 26. Section 4.3. slides: pdf.
• Thu, Oct 28. Section 4.3, 4.7. slides: pdf. (This book attributes the name `pole’ to the shape of the graph of a rational function.)
• Tue, Nov 2. Section 4.7, 4.4. slides: pdf.
• Thu, Nov 4. Section 4.4. slides: pdf.
• Tue, Nov 9. Midterm Exam 2.
• Thu, Nov 11. UC Holiday.
• Tue, Nov 16. Section 4.4, 4.5. slides: pdf.
• Thu, Nov 18. Section 4.5 slides: pdf.
• Tue, Nov 23. Section 4.5, 4.8. slides: pdf.
• Thu, Nov 25. Thanksgiving holiday.
• Tue, Nov 30. Section 1.5, 1.6, 5.6, 4.6, 4.10. slides: pdf.
• Thu, Dec 2. Review. slides: pdf.

### Announcements:

• Thursday, December 2: The final exam will be open book. There will be five questions. You may answer all five if you wish. Your grade will consist of the total from the best four questions.
Here are some review questions from Shumway and Stoffer for the material since the second mid-term: 1.12, 1.13, 4.16, 4.18a, 4.32, 4.33.
Partial solutions (to 1.12-4.18a): pdf
• Tuesday, November 16: Homework 5’s due date has been extended to 11am on Tuesday, November 23, 2010, in 399 Evans.
• Wednesday, November 3: Homework 5 has been posted. It is due at 9am on Friday, November 19, 2010, in 344 Evans.
The second mid-term exam will cover all material up to and including the lecture on Tuesday, November 2. There will be 3 questions. You should answer all questions. Each part of each question will have a percentage written next to it – the percentage of the grade that it constitutes.
Here are some review questions from Shumway and Stoffer for the material since the first mid-term: 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.21, 4.23, 4.24.
• Thursday, October 28: Remember that the second mid-term exam will be in class (12:30-2:00) on Tuesday, November 9. Like the first mid-term, it will be an open-book exam: you can bring any material you like. Exam papers will be handed out at 12:40, the exam will go from 12:45 to 1:55.
• Thursday, October 21: If you are looking for ideas for the project, there is a large collection of time series here.
• Tuesday, October 19: Information about the project has been posted here. A one-paragraph proposal is due on Wednesday, November 3. Please email it to bartlett at stat.
• Thursday, September 30: The first mid-term exam will cover all material up to and including today’s lecture. Here are some review questions from Shumway and Stoffer: 1.4, 1.5, 1.6, 1.9, 1.15, 1.16a, 2.6, 3.1, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.10, 3.11, 3.23a.
• Monday, September 27: Remember that the first mid-term exam will be in class (12:30-2:00) on Thursday, October 7. It will be an open-book exam: you can bring any material you like. Exam papers will be handed out at 12:40, the exam will go from 12:45 to 1:55. There will be 6 questions. You may answer all six if you wish; your grade will consist of the total from the best five questions. Each part will have a percentage written next to it – the percentage of the grade that it constitutes. Please take notice of this. The percentages reflect the relative significance of the relevant material, not how much time it will take to answer the question.
• Monday, August 30: Some R resources referred to in the first computer lab:
• Tuesday, August 24: To sign up for computer accounts, you will need to obtain a form from Joe. At the first lab section, on this Friday, August 27, Joe will have these forms available, and will also present an introduction to R.

### Collaboration:

You are encouraged to work in small groups on homework problems; it’s an excellent way to learn. However, you must write up the solutions on your own, and you must never read or copy the solutions of other students. Similarly, you may use books or online resources to help solve homework problems, but you must credit all such sources in your writeup and you must never copy material verbatim.

Any student found to be cheating risks automatically failing the class and being referred to the Office of Student Conduct. In particular, copying solutions, in whole or in part, from other students in the class or any other source without acknowledgment constitutes cheating.

## Môn Toán kỹ thuật ở MIT

Đây là các phần Toán kỹ thuật được dạy ở Massachusetts Institute of Technology (Học viện Công nghệ Massachusetts).

## Course Textbook

Kreyszig, Erwin. Advanced Engineering Mathematics. 8th ed. New York, NY: J.W. Wiley & Sons, 1999. ISBN: 9780471333753.

# Mathematics for Materials Scientists and Engineers

Parabolic approximation to a surface and local eigenframe. The surface on the left is a second-­order approximation of a surface at the point where the coordinate axes are drawn. The surface has a local normal at that point which is related to the cross product of the two tangents of the coordinate curves that cross at the that point. The three directions define a coordinate system. The coordinate system can be translated so that the origin lies at the point where the surface is expanded and rotated so that the normal n coincides with the z-axis as in the right hand curve. (Image by Prof. W. Craig Carter.)

### Instructor(s)

Prof. W. Craig Carter

3.016

Fall 2005

CITE THIS COURSE

## Course Description

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis.

Users may find additional or updated materials at Professor Carter’s 3.016 course Web site.

Expansion of $\ln(1-z)$
$\sum_{n=1}^{\infty} \frac{z^n}{n}=\ln(1-z)$
Hence, $\sum_{n=1}^{\infty} \frac{\sin(n\theta)}{n} = \sum_{n=1}^{\infty}\frac{e^{in\theta}-e^{-in\theta}}{2in} = \frac{\ln(1-e^{i\theta})-\ln(1-e^{-i\theta})}{2i} = \frac{\pi-\theta}{2}$.
We can apply above formula: $\sum_{n=1}^{\infty} \frac{\sin^3 n}{n} = \sum_{n=1}^{\infty} \frac{3\sin n -\sin(3n)}{4n} = \frac34\cdot\frac{\pi-1}{2} - \frac14\cdot\frac{\pi-3}{2} = \frac{\pi}{4}$.