工程數學 - 微分方程
( Enginnering Mathematics - Differential Equations )
Electrical Engineering Department, National Taiwan University
108-1 (Sep 19 - Jan 20)
----- News & Actions -----

----- Lecture Notes -----
Wk Date Subject Lecture PDF HW Note
18 1/8 Exam: Final
-
- Covered Range:
- 4.6, 4.7
- 5.1
- 7.1, 7.2, 7.3, 7.4, 7.5, 7.6
- 11.1, 11.2, 11.3
- 12.1
-
17 1/1 Holiday
-
- Problems on 101 Firework Show - - - (生活應用題:加分題)

- Use DE to find the dropping distance of the firework
...... both vertical z(t), & horizontal (x(t), y(t))
...... Projectile Motion
...... Projectile on Chap7_Problem-51

- Use DE to find the number of people who watch the filework
...... p(t), t = 6pm to 2pm
...... 人數 vs 時間:台北101/世貿站
-
16 12/25 Fourier Series
PDE

-
- 11.3_CosSinSeries ---------- 筆記
-
- 12.1_SeparablePDE -------- 筆記
-
HW, (不用交)
-(12.1) 6, 11 18 25

Sol-
12.1
15 12/18 Fourier Series
-
- Story of Fourier Series
------ Pages 3-9
- 11.1_OrthogonalFunctions - 筆記
- 11.2_FourierSeries ---------- 筆記
-
HW-8, by 12/31
-(11.1) 5, 8, 14 17
-(11.2) 5, 10 19
-(11.3) 14 21 37 45

Sol-
14 12/11 Laplace TFM


Fourier Series

-
- 07.4_OperationProperty2 -- 筆記
- 07.5_DiracDeltaFunction -- 筆記
- 07.6_SysLinearDE ---------- 筆記
-
HW-7, by 12/25
-(7.5) 5 12
-(7.6) 11 15

Sol-
7.5
7.6
13 12/4 Laplace TFM
-
- 07.3_OperationProperty1 -- 筆記
- 07.4_OperationProperty2 -- 筆記
-
HW-6, by 12/18
-(7.3)
...10 16 25 44 59 73
-(7.4) 8 13 29 47 56

Sol-
7.3
7.4
12 11/27 Laplace TFM
-
- 07.0_IntroLT.pdf
- 07.1_LaplaceTransform -- 筆記
- 07.2_InverseLT.pdf -------- 筆記
-
HW-5, by 12/11
-(7.1) 5, 9, 32 41
-(7.2) 27 37 51

Sol-
7.1
7.2
11 11/20 Higher-Order
Models

Laplace TFM

-
- 05.1_Models_IVP ----------- 筆記
..... Damped Oscillatory Motion
..... Damped Harmonic Oscillator
..... Forced Oscillation Resonance
-
- 07.0_IntroLT.pdf
- 07.1_LaplaceTransform -- 筆記
-
HW-4, by 11/27
-(4.6) (4.7) (5.1)

Sol-
4.6
4.7
5.1

HW4
10 11/13 Higher-Order
DE

Models

-
- 04.6_VariationParameters - 筆記
- 04.7_CauchyEulerEqn ------ 筆記
-
HW-4, by 11/27
-(4.6) 5, 14 21 29
-(4.7) 11 21 32 39
-(5.1) Problems
09 11/6 Exam: Midterm
-
- Covered Range:
- 2.2, 2.3, 2.4, 2.5,
- 3.1, 3.2,
- 4.1, 4.2, 4.3, 4.4, 4.5
-
08 10/30

1st Quiz



Higher-Order
DE
-
- Covered Range:
- 2.2, 2.3, 2.4, 2.5,
- 3.1, 3.2,
- 4.1, 4.2, 4.3
-
- 04.4_UC-Superposition -- 筆記
- 04.5_UC-Annihilator ------ 筆記
-



HW, (不用交)
-(4.4) 7, 18 33 39
- 4.5) 7, 13 18 31
........... & 45 69
Sol-
Quiz 1

Sol-
4.4
4.5
07 10/23 Higher-Order
DE
-
- 04.2_ReductionOfOrder -- 筆記
- 04.3_CCHomoLE ---------- 筆記
-
HW-3, by 10/30
Sol-
4.1
4.2
4.3
06 10/16 Higher-Order
DE

-
- 04.0_Model-EE-ME -------- 筆記
- 04.1_PreliminaryTheory -- 筆記
HW-3, by 10/30
-(4.1) 3, 7, 30 33 36
-(4.2) 5, 13, 19
-(4.3) 7, 25, 39, 41
05 10/9 Models 0f
1st-Order DE

Higher-Order
DE

-
- 03.2_NonlinearModels ----- 筆記
- 03.3_SystemsDEsModels - 筆記
-
- 04.1_PreliminaryTheory --- 筆記
-
HW-2, by 10/16 Sol-
HW 2
04 10/2 Models of
1st-Order DE

-
- 02.5_Substitution ------ 筆記
-
- 03.1_LinearModels ---- 筆記
-
HW-2, by 10/16
-(2.5) 5, 14, 17, 25
-(3.1) 5, 10, 11, 32
-(3.2) 2, 9, 15
03 9/25 1st-Order DE
-
- 02.3_LinearDE ----- 筆記
- 02.4_ExactDE ------ 筆記
- 02.5_Substitution -- 筆記
-
HW-1, by 10/2
Sol-
HW 1
02 9/18 1st-Order DE
-
- 02.1_SolutionCurve -- 筆記
- 02.6_Numerical ------- 筆記
- 02.2_SeparableDE --- 筆記
- 02.3_LinearDE -------- 筆記
-
HW-1, by 10/2
-(2.2) 7, 25, 32, 38
-(2.3) 9, 22, 27, 37
-(2.4) 3, 17, 25, 29
01 9/11 Introduction
Lecture Outline
Exams & HWs
-
- 00.0_Intro
-
- 01.1_Def-Term
- 01.2_IVP
- 01.3_DEModel
-
Wk Date Subject Lecture PDF Code HW
----- Homeworks -----
  • Homework Assigment (updated on //19)
    • Assigned: /, 2019 , Deadline: /, 2019
    • Topics: DE
      - Problem 1:
      ....... Given the system
    • Actions:
      - Submit it on / in class
      ....... on summarizing the information you catch from each section.

----- Course Information -----
  • What:
    • Topics: Differential Equations
    • Course No: EE2021
    • Credit: 2
  • Who:
    • Students:
      • Undergraduate Students
    • Instructor:
      • Name: Feng-Li Lian (連豊力)
      • Office: EE-MD717,
      • Phone: 02-3366-3606
      • Email: fengli@ntu.edu.tw
  • When:
    • Lectures: 10:20am-12:10pm, Wednesdays (Sep 2019 - Jan 2020)
    • Office Hours: appointment by e-mail
  • Where:
  • Why:
    • Required course for EE students
    • Short-Term Goal:
      - equations: involving derivatives and integrations
      - solutions: qualitative and quantitative
    • Long-Term Goal:
      - languages and tools for the modeling and analysis of engineering problems,
      ---- especially those with changing/varying variable/parameters
  • How:
    • Preview: ~2 hours/per week
    • Lecture: ~2 hours/per week
      • Demonstration, derivation and practice, etc.
    • Review: ~2 hours/per week
    • Homework: ~2 hours/per week
    • Q & A & lecture participation:
      • group discussion
      • lecture questionnaire
      • e-mail
      • website etc.
  • TextBooks:

    • Differential Equations with Boundary-Value Problems (9th Ed., 2018, metric version)
      - by Dennis G. Zill
    • Webpage: 高立圖書
    • Webpage: PDF of 7th Edition (參考用,非本學期使用教科書之版本)

  • Course Outline:

    • ( Introduction ) -------------------------> 1.1, 1.2, 1.3
    • ( First Order DE - Math ) ------------> 2.1, 2.2, 2.3, 2.4, 2.5, 2.6
    • ( First Order DE - Modeling ) -------> 3.1, 3.2, 3.3
    • ( Higher Order DE - Math ) ----------> 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7
    • ( Higher Order DE - Modeling ) -----> 5.1
    • ( Transform – Laplace ) ---------------> 7.1, 7.2, 7.3, 7.4, 7.5, 7.6
    • ( Transform – Fourier ) ----------------> 11.1, 11.2, 11.3
    • ( Partial DE ) -----------------------------> 12.1

  • Grading:
    • Homeworks etc.   15%
    • Exams                   85%

=======================================================================
======================== ----- Old News in 108-1 ------ ========================
=======================================================================

  • 待處理
  • References (updated on 8/8/19)

  • Special Lectures (updated on 8/7/15)
    • Month/Day: progress report
      - On the result of experimental tests
      - On the paper reading of related topics
  • Midterm Exam on 11/6
    - 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 4.1, 4.2, 4.3, 4.4, 4.5
    - 120 mins, about 15 questions/sub-questions
  • 1st Quiz on 10/30
    - 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 4.1, 4.2, 4.3
    - 30 mins, 3 questions
  • Final Exam on 1/8
    - 4.6, 4.7, 5.1, 7.1-7.6, 11.1-11.3, 12.1 (13 sections)
    - 110 mins, about 20 questions/sub-questions
  • Homework 1: 2.2, 2.3, 2.4 Due 10/2 (in class)
  • Homework 2: 2.5, 3.1, 3.2, Due 10/16 (in class)
  • Homework 3: 4.1, 4.2, 4.3, Due 10/30 (in class)
  • Homework ... 4.4, 4.5, (不用交)
  • Homework 4: 4.6, 4.7, 5.1, Due 11/27 (in class)
  • Homework 5: 7.1, 7.2 Due 12/11 (in class)
  • Homework 6: 7.3, 7.4, Due 12/18 (in class)
  • Homework 7: 7.5, 7.6, Due 12/25 (in class)
  • Homework 8: 11.1, 11.2, 11.3, Due 12/31 (in mailbox of MD-1F-717)
  • Homework ... 12.1, (不用交)
  • Week 16: (12/25/19)
    • Chapter 11: Fourier Series
      - (11.3) Fourier Cosine and Sine Series
      ............ Even & Odd Functions
      ............ Even-Odd Decomposition
      ............ Fourier Cosine and Sine Series
    • Chapter 12: Boundary-Value Problems in Rectangular Coordinates
      - (12.1) Separable Partial Differential Equations
      ............ Separation of Variables
      ............ Superposition Principle
      ............ Classification of Equations
    • Homework 8: 11.1, 11.2, 11.3, Due 12/31 (in mailbox of MD-1F-717)
    • Homework X: 12.1, (不用交)
  • Week 15: (12/18/19)
    • Chapter 11: Fourier Series
      - (11.1) Orthogonal Functions
      ............ Inner Product
      ............ Orthogonal Functions
      ............ Orthogonal Set
      ............ Orthonormal Set
      ............ Vector Decomposition & Orthogonal Series Expansion
      ............ Orthogonal Set/Weight Functions
      - (11.2) Fourier Series
      ............ Fourier Series
      ............ Sequence of Partial Sums
    • Homework 8: 11.1, 11.2, 11.3, Due 12/31 (in mailbox of MD-1F-717)
  • Week 14: (12/11/19)
    • Chapter 7: Laplace Transform
      - (7.4) Operational Properties II
      ............ Derivatives of a Transform
      ............ Transforms of Integrals
      ............ Transform of a Periodic Function
      - (7.5) Dirac Delta Function
      ............ Unit Impulse Function
      ............ Dirac Delta Function and its Laplace Transform
      - (7.6) Systems of Linear DEs
      ............ Set of Multiple DEs
    • Homework 6: 7.3, 7.4, Due 12/18 (in class)
    • Homework 7: 7.5, 7.6, Due 12/25 (in class)
  • Week 13: (12/4/19)
    • Chapter 7: Laplace Transform
      - (7.3) Operational Properties I
      ............ Translation on the s-Axis
      ............ Translation on the t-Axis
      - (7.4) Operational Properties II
      ............ Derivatives of a Transform
      ............ Transforms of Integrals
      ............ Transform of a Periodic Function
    • Homework 5: 7.1, 7.2 Due 12/11 (in class)
    • Homework 6: 7.3, 7.4 Due 12/18 (in class)
  • Week 12: (11/27/19)
    • Chapter 7: Laplace Transform
      - (7.1) Definition of Laplace Transform
      ............ Defintion
      ............ Some Laplace Transforms
      ............ Sufficient Conditions for Existence
      ............ Behavior of F(s) as s -> infinity
      - (7.2) Inverse Transforms and Transforms of Derivatives
      ............ Some Inverse Transforms
      ............ Transforms of Derivatives
      ............ Solving IVP DE
    • Homework 5: 7.1, 7.2, 7.3, Due 12/11 (in class)
  • Week 11: (11/20/19)
    • Chapter 5: Models of Higher-Order DE
      - (5.1) Linear Models: Initial-Value Problems
      ............ Free Undamped Motion
      ............ Free Damped Motion
      ............ Driven Motion
      ............ Series Circuit Analogue
    • Chapter 7: Laplace Transform
      - (7.1) Definition of Laplace Transform
      ............ Defintion
      ............ Some Laplace Transforms
      ............ Sufficient Conditions for Existence
      ............ Behavior of F(s) as s -> infinity
    • Homework 4: 4.6, 4.7, 5.1, Due 11/27 (in class)
  • Week 10: (11/13/19)
    • Chapter 4: Higher-Order DE
      - (4.6) Variation of Parameters
      ............ 求解:particular solution
      ............ 假設:g(x) 不是特定的函數類型
      ............ 結果:使用 Variation of Parameters
      ............ 特性:Linear Indenpendent Solutions of AHE
      ............ 則:y_p(x) = u1 y1 + u2 y2
      ............ e.g., (2.3) y_c -> y_p
      ............ e.g., (4.2) y_1 -> y_2
      - (4.7) Cauchy-Euler Equations
      ............ 求解:y = x^m
      ............ 技巧:類似 y== e^(mx)
      ............ 特性:相異根,重根,共軛虛根
    • Homework 4: 4.6, 4.7, 5.1, Due 11/27 (in class)
  • Exam on 11/6: (10/30/19)
    • Midterm Exam on 11/6
      - 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 4.1, 4.2, 4.3, 4.4, 4.5
      - 120 mins, about 15 questions/sub-questions
  • Exam on 11/6 & Quiz on 10/30: (10/16/19)
    • 1st Quiz on 10/30
      - 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 4.1, 4.2, 4.3
      - 30 mins, 3 questions
    • Midterm Exam on 11/6
      - 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 4.1, 4.2, 4.3, 4.4, 4.5
      - 120 mins, about 15 questions/sub-questions
  • Week 08: (10/30/19)
    • Chapter 4: Higher-Order DE
      - (4.4) Undetermined Coefficients – Superposition
      ............ 求解:particular solution
      ............ 假設:某些特定的函數類型
      ............ 結果:只要決定該函數前面的係數!
      ............ 哪些類型不適用!
      ............ 出現意外狀況!
      - (4.5) Undetermined Coefficients – Annihilator
      ............ 求解:particular solution
      ............ 想辦法,把右邊的函數消滅掉
      ............ 變成單純的 Homogeneous Differential Equation!
      ............ 就可以用 4.3 的方法求解!
    • Homework 4.4, 4.5, (不用交)
  • Week 07: (10/23/19)
    • Chapter 4: Higher-Order DE
      - (4.2) Reduction of Order
      - (4.3) Homogeneous Linear Equations with Constant Coefficients
      ............ Auxiliary Equation
      ............ Three Cases
      ............ Two Special Equations
      ............ Higher-Order Equations
    • Homework 3: 4.1, 4.2, 4.3, Due 10/30 (in class)
  • Week 06: (10/16/19)
    • Chapter 4: Higher-Order DE
      - (4.0) Models of EE/ME Examples
      - (4.1) PreliminaryTheory
      ............ IVP & BVP
      ............ Homogeneous Equations
      ............ Nonhomogeneous Equations
      ............ Differential Operator / Polynomial Operator
      ............ Linear Dependence / Independence
      ............ Wronskian
    • Homework 3: 4.1, 4.2, 4.3, Due 10/30 (in class)
  • Week 05: (10/9/19)
    • Chapter 3: Modeling 1st-Order DE
      - (3.2) NonlinearModels
      ............ Population Dynamics
      ............ Logistic Equation: Growth, Harvest, Restock
      ............ Chemical Reactions
      - (3.3) SystemsDEsModels
      ............ Radioactive Series: Decay
      ............ Mixtures of multiple tanks
      ............ Lotka-Volterra Predator-Prey Model, Competition Model
      ............ Networks and Circuits
    • Chapter 4: Higher-Order DE
      - (4.1) PreliminaryTheory
    • Homework 2: 2.5, 3.1, 3.2, Due 10/16 (in class)
  • Week 04: (10/2/19)
    • Chapter 2: 1st-Order DE
      - (2.5) Substitution
    • Chapter 3: Modeling 1st-Order DE
      - (3.1) LinearModels
      -------- Growth and Decay: Bacterial Growth, Half-Life of Plutonium
      -------- Carbon Dating: C-14, Age of a Fossil
      -------- Newton’s Law of Cooling/Warming, Cooling of a Cake
      -------- Mixtures of Two Salt Solutions
      -------- Series Circuits
    • Homework 2: 2.5, 3.1, 3.2, Due 10/16 (in class)
      - (2.5) 5, 14, 17, 25
      - (3.1) 5, 10, 11, 32
      - (3.2) 2, 9, 15
  • Week 03: (9/25/19)
    • Chapter 2: 1st-Order DE
      - (2.3) LinearDE
      - (2.4) ExactDE
      - (2.5) Substitution
    • Homework 1: Chapter 2, Due 10/2 (in class)
      - (2.2) 7, 25, 32, 38
      - (2.3) 9, 22, 27, 37
      - (2.4) 3, 17, 25, 29
  • Week 02: (9/18/19)
    • Chapter 2: 1st-Order DE
      - (2.1) SolutionCurve
      - (2.6) Numerical
      - (2.2) SeparableDE
      - (2.3) LinearDE
    • Homework 1: Chapter 2, Due 10/2 (in class)
      - (2.2) 7, 25, 32, 38
      - (2.3) 9, 22, 27, 37
      - (2.4) 3, 17, 25, 29
      - (2.5) 5, 14, 17, 25
  • Week 01: (9/11/19)
    • Introduction
    • 簡介課程範圍:
    • 課程時間表:
    • 評分項目: