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 -----

Action Items: (12/25/19) Homework 8: 11.1, 11.2, 11.3, Due 12/31 (in mailbox of MD-1F-717) Final Exam on 1/8 --- 4.6, 4.7, 5.1, 7.1-7.6, 11.1-11.3, 12.1 (13 sections) Week 18: Exam on 1/8/20: 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 References (updated on 10/2/19) Books: - Differential Equations with Boundary-Value Problems - by Dennis G. Zill, (9th Ed., 2018, metric version) - 代理商： 高立圖書 - 舊版資料： PDF of 7th Edition （參考用，非本學期使用教科書之版本） Notes: - 三角函數 - Brief Table Of Integrals - Review Of Differentiation - DE Applications - DE Models: Malthusian, Logistic, Predator-Prey - Solution Curves of General 2nd-order DEs 微分方程課程網頁與助教資訊: (9/18/19) 微分方程四班共同課程網頁： - http://cc.ee.ntu.edu.tw/~tomme/DE/DE.html (電機系)微分方程讀書會網頁： - http://cc.ee.ntu.edu.tw/~tomme/DE/DEHelper.html (教學中心)微分方程諮詢課表： - 預約 ----- - 課表 助教資訊： - 姓名：張峻豪 - Email：r07921012@ntu.edu.tw - Office Hours: Thur. 14:00~15:00 (MD601) - PS: 若有需要盡量先用 email 預約。 OLD news are moved to the bottom of the webpage.

----- 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: Lecture Room: EE-MD205 Webpage: http://cc.ee.ntu.edu.tw/~fengli/Teaching/DifferentialEquations/ 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) Books: - Book 1 Websites: - Website 1 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: