PME3210
Linear Algebra and Linear Dynamical System Synthesis

(線性代數與線性動態系統分析)

(Autumn 2008)

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Course Information

Instructor:       Liu, Cheng-Hsien           chhsliu@mx.nthu.edu.tw
            Office:                                      Room 517, Engineering Building #1
                        Phone:                          (03) 5715131 ext.3706
                        Office hours:                 made by appointment

Lectures:        Time     Tuesday 8:35am~9:50am; Friday. 8:35am~9:50am  (First meeting is 8:00am on Sep.16)
Location            Room 215, Engineering Building #1

Course Web site: http://mx.nthu.edu.tw/~chhsliu/linear/PME3210_Liu.html　  

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Course Objectives

The goals of the course are to introduce undergraduate to use/ manipulate matrices, understand/get physical intuition of matrices and apply linear algebra to synthesize linear dynamical systems. The emphasizing topics in this course are useful in other disciplines, including circuitry analysis, signal processing, communication, control systems, Robotics, networks, image display, system dynamics and vibration.

本課程為一新的課程，企圖跨越整合線性代數理論及線性動態系統分析的教學，目的在針對大學部大二及大三學生，介紹矩陣的運算、瞭解矩陣及向量的物理直觀內涵、運用線性代數理論以分析動態系統。本課程所強調的主題介紹將極有助於提供諸如電路分析、訊號處理、通訊系統、控制系統、機器人學、影像處理、機器視覺、系統振動分析等領域的數學基礎及物理掌握與瞭解。下圖為目前動力機械系後續應用之相關課程例舉-

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General Info

§         Final exam:  30%

§         Policy for Exam Cheating/Project Copy- Exam cheating/Project Copy will make you fail for this class.

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Topics included in this course(tentative syllabus)

Topics

Reading

Lecture(scheduled)

Lecture(updated)

Practice Problems

Introduction to this course and Dynamic Systems

Reader Ch. 1;

09/16, 09/19

09/16, 09/19

 

Linear Dynamical Systems

Reader Ch. 2, Ch. 3;

09/23, (No Lecture on 09/26) 09/30, 10/3(Quiz1)

09/23, (No Lecture on 09/26) 09/30, 10/3, 10/7

Reader Practice pp. 1-16 (no state space model)  (Quiz1)

Matlab/Simulink

Reader Ch. 3;

 

10/3

 

 

Reader Practice pp. 1-16 (including state space model)  (Quiz2)

Matlab/Simulink

(Competition Project

Due: 11/7)

Class Room 434

Reader Ch. 3,

Matlab notes, Simulink notes,

 

10/7, 10/14, 10/17(Quiz2),

 

10/14 (Quiz1), 10/17, 10/21 (Quiz2),

 

Matlab/Simulink files downloadable from our class website (Quiz2)

The Geometry of Linear Equations

Meyer Ch1.1

 

10/17, 10/21

 

(No Lecture on 10/24& 10/28) , 10/31

 

Elimination with Matrices

Meyer Ch1.2; 1.3; 2.1; 2.2; 2.4

Ref1. pp-2-26~2-38

10/21,(No Lecture on 10/24& 10/28) , 10/31, 11/04

11/04, 11/7

Ex3(p. 2-30), Ex10(p2-34), Ex 13(p2-37) (Quiz3)

Matrix Operations and Inverses

Meyer3.2; 3.3; 3.5; 3.6, 3.7, 6.2

Ref1. pp-2-1~2-25, Ref1. pp2-39~2-66

11/04, 11/7(Quiz3),

 

11/11(Quiz3), 11/14

 

Ex9(p.2-65), Ex4(p.2-22), Ex5(p.2-42), Ex11(p.2-44), Ex16(p.2-50), Ex4(p.2-62) (Quiz4)

LU and LDU Factorization

Meyer3.9; 3.10

Ref1. pp-2-67~2-79

11/11

 

11/18(Quiz4), 11/21

Ex2(p.2-69), Ex8(p.2-75), Ex14(p.2-79)

Vector Spaces and Subspaces

Meyer4.1

Ref1. pp5-1~5-39

11/14 (Quiz4)

 

11/25, (No Lecture on 11/28 )

Ex7(p.5-8), Ex18(p.5-13), Ex7(p.5-23) (Quiz5)

Linear Independence

Meyer4.3

11/18

12/2 (Quiz5)

 

Basis and Dimension

Meyer4.4

Ref1. pp5-40~5-56

11/18

 

12/2, 12/5

Ex24(p.5-32), Ex27(p.5-35), Ex11(p.5-45),

The Four Fundamental Subspaces

Meyer4.2; 4.4; 4.5

Ref1. pp5-40~5-56

11/21, 11/25,

(No Lecture on 11/28 ), 12/2 (Quiz5)

12/5, 12/9, 12/16

 

Vector Norm and Orthogonality

Meyer5.1; 5.4

 

12/5

 

12/16 (Competition Project due), 12/19

 

Projections and Gram-Schmidt

Meyer5.5; 5.6; 5.13; 5.14

Ref1. pp 1-26

12/9, 12/12

 

12/23, 12/26(Competition demo)

Ex17(p.1-26), Ex18(p.1-26), Ex1(p.10-38), Ex21(p.10-60), Ex48(p.10-78), Ex63(p.10-88) (Quiz6)

Determinants

Meyer Ch 6 (ref)

Ref1. pp3-1~3-27

Ref1. pp3-35~3-69

 

12/16 (Quiz6)

 

12/30

Ex9(p.3-13), Ex12(p.3-15), Ex14(p.3-16), Ex15(p.3-16), Ex23(p.3-52), Ex26(p.3-54), Ex36(p.3-59), Ex1(p.3-68), (Quiz7)

Eigenvalues and Eigenvectors

Meyer Ch 7.1; 5.2(ref)

Ref1. pp7-1~7-77

Ref1. pp7-87~7-91

(Quiz7)

 

1/6, (Quiz7), 1/9

Ex14(p.7-17), Ex22(p.7-22), Ex8(p.7-49), Ex11(p.7-51)

Diagonalization

Meyer Ch 7.2; 7.3

Ref1. Pp8-1~8-79

(Quiz8)

 

1/9

Ex8(p.8-20), Ex15(p.8-26), Ex13(p.8-56), Ex27(p.8-64), Ex43(p.8-77)

Differential Equations

Meyer Ch 7.4

Ref1. pp8-80~8-102

 

1/9

Ex1(p.8-87), Ex5(p.8-93),    Ex9(p.8-96), Ex11(p.8-99), Ex13(p.8-100)

Singular Value Decomposition

Meyer Ch 5.12

 

 

skip

 

Competition Project Demo (Tentative)

 

12/26

 

 

More practice problems-

Ex25(p.4-27), Ex12(p.6-62), Ex27(p.6-75), Ex28(p.6-76)

Final Exam

 

01/13 (8:00am~10:10pm)

Close book/notes

Q&A Office hours :9:30am-12:00 , 01/10 at my office.

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Announcements

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Handouts

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Links to Other Sites

    http://mx.nthu.edu.tw/~chhsliu/
    http://memsliu.pme.nthu.edu.tw/index.html

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Last updated: Sep. 18, 2008 by Cheng-Hsien Liu