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10602 自然科學
高等微積分二
高淑蓉
本課程以訓練嚴謹的邏輯推導、撰寫明確的證明、流利的口語表達為手段，追求如何思考、如何有效的學習為目標。
 
 
 
 
【課程簡述】
     Brief course description 
    本課程以訓練嚴謹的邏輯推導、撰寫明確的證明、流利的口語表達為手段，追求如何思考、如何有效的學習為目標。 
    This course is based on teaching you how to think logically, how to prove clearly and 
express yourself fluency.Also,how to think and how to learn effectively and the goals of this course.
  
 
 
【課程說明】
     Course Description 
    本課程以訓練嚴謹的邏輯推導、撰寫明確的證明、流利的口語表達為手段，追求如何思考、如何有效的學習為目標。本課程內容探討歐幾里德空間的多變數函數之解析理論。本學期將介紹以下題材： 
    This course is based on teaching you how to think logically, how to prove clearly and 
express yourself fluency.Also,how to think and how to learn effectively and the goals of this course.The content of this course includes  the analysis of the multivariable functions in Euclidean space. The following topics are introduced in this semester:
 
  
 1. Differentiable Mappings 
 2. The Inverse and Implicit Function Theorems and Related Topics 
 3. Integration 
 4. Fubini's Theorem and The Change of Variables Formula 
 5. Fourier Analysis 
 
 
 
【指定用書】
     Text Books  
＊
 
 
 
【參考書籍】
     References  
＊ D. Widder, Advanced Calculus. 
＊ T. Apostal, Advanced Calculus. 
 
 

【教學方式/教學進度】
     Teaching Method/Syllabus
    黑板授課/循序漸進   
     Teaching with Blackboard / Step by step

 

10602 自然科學
幾何二
宋瓊珠

This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem.


【課程簡述】
      Brief course description
This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem.
 
 

【課程說明】
     Course Description
This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second 
fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem. 
 
Prerequisites：
            Successful completion of Linear Algebra and Advanced Calculus
 
 
 
【指定用書】
     Text Books 
* Differential geometry of curves and surfaces, by Manfredo P. Do Carmo. Prentice Hall.
 
 

【參考書籍】
     References 
* Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010. 
* Elementary Differential Geometry, 2nd Edition, by Barrett O'Nell. 
 

【教學方式】
     Teaching Method
Lectures. 講授，演習，討論.  
www.math.nthu.edu.tw/~cjsung/course/ug2018s.html

 

10601 自然科學
普通物理
吳國安

人類對於周遭事物，如何隨時間與環境而變化，都充滿好奇心。我們要如何用物理學推敲出萬物的變化，或基於系統性的觀察而提出新的想法，這就是普通物理（一）的課程目標。那要如何養成研究問題的邏輯與方法呢?


【課程說明 / Description of the course】
       What is this course about  
    人類對於周遭事物，如何隨時間與環境而變化，都充滿好奇心。我們要如何用物理學推敲出萬物的變化，或基於系統性的觀察而提出新的想法，這就是普通物理(ㄧ)的課程目標。那要如何養成研究問題的邏輯與方法呢?本課程以牛頓提出的力學為例，除了學習力學定律之外，也鼓勵同學探討牛頓提出這些理論的原因，同時思考章節之間的關聯性，例如在牛頓的向量力學架構下，已經可以解釋物體的運動，為何還需學習新的能量概念等等。 
     課程內容涵蓋基礎牛頓力學、功與能量概念，在熟悉單粒子運動後，將建構簡單的多粒子系統（剛體）所遵守的物理規則（轉動運動），基於以上的物理知識，詳細探討日常生活中常見的物理現象，如重力、固體與流體、振盪、波動等。同時也將探討愛因斯坦為何會提出不同於牛頓力學的特殊相對論，以及在特殊相對論中架構下，為何在不同慣性座標系的觀察者們，對時間、空間的認知會有所不同。

      We are all curious about how nature works. In order to better grasp the fundamental rules that govern our daily life experiences, this course – General Physics (I) – aims to develop students’ abilities in logical reasoning and scientific problem solving. How do we achieve that goal? For example, we will learn Newton’s laws of motion and gravity in this course. The physics of these laws are important, but how Newton and other scientists discovered (or what motivates them to discover) these laws are equally important as well. In addition, we will learn their logical reasoning processes and systematic approaches to tackle problems. Furthermore, it is crucial to make connections between physics topics and form your own understanding of each topics. For example, since Newton’s laws of motion are sufficient to solve mechanics problem, why do we need to introduce the concept of energy to solve the same mechanics problem. 
      This course will cover Newton's laws of motion and the concept of work & energy. After fully understand the motion of single particle, we then construct a simple many-particle system (Rigid Body), and explore the physical laws it follows (Rotational Motion). Based on the understanding of motion of single particle and many-particle systems, we will discuss the physical phenomena occurred in our daily life, such as gravity, solid & fluid, oscillations and waves. Moreover, we will talk about why Einstein proposed special relativity despite success of Newton’s laws of motion in classical mechanics. Within Einstein’s framework of special relativity, we will demonstrate why observers have different perspectives on time duration and spatial length in different inertial reference frames?
 

 

【課程教材 / Course Material】
       What are the teaching materials 
* 物理學系吳國安教授教學投影片
    Lecture notes (PPT) from Dr. Wu,Kuo-An (Dept. of Physics)

   
  

【參考資料 / references】
       References
1.
 The Feynman Lectures on Physics
2.

 "Physics", Volume1, by R.Resnick, D.Halliday,
  and K. S. Krane.
3.

 "University Physics", 2nd revised edition,
  by H. Benson.
 
 
【適用對象 / Suitable Users】
       Who is this course for
*

 對生活中的物理現象有好奇心者，敬邀您一同探索日常生活中物理的奧秘！
This course is for people who have curiosity for anything or everything! 
 
 
  
【教學方式 / Teaching Method】
      How does this course work
*

 課程共 13章節，每一章節包含數個單元。
This course consists of 13 chapters; each chapter includes several segments.
*


 每單元為10~15分鐘的教學影片，針對單一概念講解，透過例題熟悉單元重點。
Each segment contains a 10-to-15-minitue video and focuses on a specific physics topic.
*


 全程由授課教師精製之投影片，最佳化課程單元影片，提供融會貫通之學習效果。
This course offers PPTs that are available for downloading.
*



 著重物理定律背後的意義，及思索問題的邏輯性與一致性，在課堂外，希冀能思辨不同問題之間的共通性，舉一反三，解決問題。
This course emphasizes the reasoning of physical laws and nurturing the logical reasoning ability, so that students can apply this training to solve problems outside the classroom.




 【教學進度 / Schedule】
      What do you expect to learn in this course

1

 動態系統與向量力學
Dynamical Systems & Vector Mechanics 
  

 —從牛頓力學談起（向量力學）Starting from Newtonian Mechanics 
2  功與能Work & Energy
   — 純量的角度來思考牛頓定律
     Understanding Motion from the Scalar Perspective
3

 位能與力學能守恆
Potential Energy & Conservation of Mechanical Energy
   —純量力學好簡單 Nothing is Simpler Than Scalar Mechanics
4

線性動量Linear Momentum
  —守恆量與物理問題的簡化
    Conservation Laws and How do They Simplify Physical Problems
5  多粒子系統Many-particle System 
  —  邁向真實世界的第一步 The First Step Towards The Real World
6

剛體轉動Rigid-body Rotation
  — 如何設計容易轉動的輪子
     A possible new design for Wheels
7

角動量Angular Momentum
   — 如何設計容易轉動的輪子
      A Possible New Design for Wheels
8

重力與行星運動Gravity & Planetary Motion
  — 不會砸落在牛頓頭上的月球（但是蘋果會）
     The Moon Doesn*t Fall on Newton*s Head, but Apples Do.
9

固體與流體Solid and Fluid
   — 巨觀的物理世界 The Macro-scopic Physical Word
10

振盪Oscillation
  — 彈簧振盪＊單擺運動＊金融市場有關係嗎？
     Is There a Common Feature for Spring Oscillator,
     Pendulum and Financial Marker?
11 波動(力學波)
Waves (Mechanical Waves)
   —力學波的普世性 The Universality of Mechanical Waves.
12 聲波Sound Waves
  — Sound waves for dummies
13 特殊相對論Special Relativity
 

— 站在月台上的你似乎瘦了？！
     You look thin when standing on the platform?!


 

 

10601 自然科學
高等微積分（一）
高淑蓉

本課程著重訓練思考邏輯及解決問題的思維方式；培養聽說讀寫的能力，以奠定自學的能力。

 
 
【課程大綱】
    著重訓練思考邏輯及解決問題的思維方式；培養聽說讀寫的能力，以奠定自學的能力。
 
 
  
【課程說明】
The Topology of Euclidean Space, Compact And Connected Sets, Contiinuous Mappings, Uniformly Convergence.
 
 
【指定用書】
Elementary Classical Analysis, 2nd Edition, by Jerrold E. Marsden, Michael J. Hoffman.*採購書籍可參閱此*
 
 
 
【教學進度與成績考核】
1. 循序漸進

2.

 
演習課小考30% 
二次期中考各30%、30%
期末考30%

 

 

10601 自然科學
幾何一
宋瓊珠
This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem. 
 
  

【課程說明】
     Course Description
This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem. 
 
Prerequisites：
            Successful completion of Linear Algebra and Advanced Calculus
 
 
【指定用書】
     Text Books
* 

 Differential geometry of curves and surfaces, by Manfredo P. Do Carmo.Prentice Hall,  
* 
Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010. 
 
 
 
【參考書籍】
     References 
*   Elementary Differential Geometry, 2nd Edition, by   Barrett O'Nell. 
  
 
【教學方式】
     Teaching Method 
*  Lectures、講授、演習、討論

 

10502 自然科學
統計學
鄭少為
NTHU Open Courses Ware has planted a learning-material forest, now it’s waiting for you to explore! Now, go into the OCW forest, and taste the sweetest knowledge fruits.


Course outline
    The course will be given on the basis of 3 hours a week (Tuesday, 10~12 AM and Thursday, 11~12 AM) in 綜合三館 room 203.  The materials for teaching will be regularly posted on the course website (http://www.stat.nthu.edu.tw/~swcheng/Teaching/math2820/).
       This course is an introduction to the theory and application of statistical methods. We will particularly focus on probability models and modern statistical concepts, and methods developed in a mathematical framework. Topics to be covered include random variables and their various properties,statistical inference (point and interval estimation, hypothesis testing), statistical modeling for experimental and observational data, survey sampling, some aspects of experimental design, Bayesian analysis, decision theory, and a variety of real applications such as two-sample comparison and analysis of variance.


Textbook
    Rice, John A. (2007), Mathematical Statistics and Data Analysis, 3rd Edition. Duxbury Press.


References
1. Rice, John A. (1995), Mathematical Statistics and Data Analysis, 2nd Edition. Duxbury Press.
2. Roussas, G.. G. (1997), A Course in Mathematical Statistics, 2nd Edition. Academic Press.
3. Hogg, R. V., McKean, J. W., and Craig, A. T. (2005), Introduction to Mathematical Statistics, 6th Edition. Pearson Prentice Hall.
4. Wackerly, D.D., Mendenhall, W., and Scheaffer, R.L. (2007), Mathematical Statistics with Applications, 7th Edition. Duxbury Press.


Grading
    Your grade will be determined by  homework (30 %), a midterm (30 %), and a final exam (40 %).


Prerequisites
Knowledge of Calculus and Probability.

10502 自然科學
分數教學
林碧珍

尋找興趣，提早準備，贏在起跑點！！想追求更多課本以外的專業知識嗎？ 清華大學開放式課程為你種植了一座學習資源森林，等你來探索！現在就走進開放式課程的森林，品嚐最甜美的知識果實！

 

教學進度Syllabus

講 次
【     教         學         進          度        】
第1講  ◆分數在不同階段之教材發展與各種意義
第2講  ◆學生學習分數的困難與迷思概念
第3講  ◆分數的不同意義
第4講  ◆九年一貫分數的能力指標
第5講  ◆分數的乘法教材、分數意義的歸納
第6講  ◆為什麼在第三階段要引入分數為兩數相除的結果

 

10301 自然科學
生命科學一
李家維 / 莊永仁 / 焦傳金

尋找興趣，提早準備，贏在起跑點！！想追求更多課本以外的專業知識嗎？ 清華大學開放式課程為你種植了一座學習資源森林，等你來探索！現在就走進開放式課程的森林，品嚐最甜美的知識果實！

 

 

Text Book :
Campbell Biology (10th Edition), Jane B. Reece , Lisa A. Urry, Michael L. Cain, Steven A. Wasserman , Peter V.
Minorsky, Robert B. Jackson (2013)
 
Course Schedule :
Week 1  2014 / 09 / 18 :
Life on Earth I - Ch01: Biology and Its Themes
Life on Earth II - Ch25: Macroevolution
Instructor: Li

Week 2  2014 / 09 / 25 :
Life on Earth I - Ch01: Biology and Its Themes
Life on Earth II - Ch25: Macroevolution
Instructor: Li

Week 3  2014 / 10 / 02 :
Ch03: The Chemistry of Water
Instructor: Chiao

Week 4  2014 / 10 / 09 :
Ch04: Carbon: The Basis of Molecular Diversity
Ch05: Biological Macromolecules and Lipids
Instructor: Chiao

Week 5  2014 / 10 / 16 :
Ch06: Energy and Life
Ch07: Cell Structure and Function
Instructor: Chiao

Week 6  2014 / 10 / 23 :
Ch09: Cellular Signaling
Instructor: Chiao

Week 7  2014 / 10 / 30 :
Ch10: Cell Respiration
Ch11: Photosynthetic Processes
Instructor: Chiao

Week 8  2014 / 11 / 06 :
Ch12: Mitosis
Ch13: Sexual Life Cycles and Meiosis
Instructor: Chiao

Week 9  2014 / 11 / 13 :
Midterm Examination ( Ch01-13 & Ch25)

Week 10  2014 / 11 / 20 :
Ch14: Mendelian Genetics
Ch15: Linkage and Chromosomes
Instructor: Chuang

Week 11  2014 / 11 / 27 :
Ch16: Nucleic Acids and Inheritance
Ch17: Expression of Genes
Instructor: Chuang

Week 12  2014 / 12 / 04 :
Ch18: Control of Gene Expression
Ch26: Introduction to Viruses
Instructor: Chuang

Week 13  2014 / 12 / 11 :
Ch19: DNA Technology
Instructor: Chuang

Week 14  2014 / 12 / 18 :
Ch20: The Evolution of Genomes
Instructor: Chuang

Week 15  2014 / 12 / 25 :
Ch21: How Evolution Works
Ch22: Phylogenetic Reconstruction
Instructor: Li

Week 16  2015 / 01 / 01 :
No class

Week 17  2015 / 01 / 08 :
Ch23: Microevolution
Ch24: Species and Speciation
Instructor: Li

Week 18  2015 / 01 / 15 :
Final Examination ( Ch14-24 & Ch26)

10202 自然科學
普通物理二
林秀豪

近年來，普通物理的課本越長越厚。老師怎麼教？學生如何讀？物理系專業的課程，教科書也沒長到這般怪獸的厚度，這真的是最有效率的學習方法嗎？我不以為然。在99學年，我決意進行一項普物教學的改革：每個學期我只教十個問題...

Ten Questions we will discuss this semester
Q1: Why are most materials charge neutral?
Chapter 21 – Electric Charge and Electric Field
Chapter 22 – Gauss’s Law

Q2: What causes lightning?
Chapter 22 – Electric Potential Chapter 24– Capacitance, Dielectrics, Electric Energy Storage

Q3: Can magnetic forces do work?
Chapter 27 – Magnetism

Q4: How does the geomagnetic field arise?
 Chapter 28 – Sources of Magnetic Field

Q5: Why can light propagate in vacuum?
Chapter 29 – Electromagnetic Induction and Faraday’s Law
Chapter 30 – Inductance, Electromagnetic Oscillations and AC Circuits
Chapter 31 – Maxwell equations and Electromagnetic Waves

Q6: What is the nature of light?
Chapter 34 – The Wave Nature of Light; Interference
Chapter 37 – Early Quantum Theory and Models of the Atom

Q7: Why are atoms stable?
 Chapter 38 – Quantum Mechanics
Chapter 39 – Quantum Mechanics of Atoms

Q8: How is the secret of life encoded?
Chapter 40 – Molecules and Solids

Q9: How can we date fossils?
Chapter 42 – Nuclear Physics and Radioactivity

Q10: What are the building blocks of our universe?
Chapter 43 – Elementary Particles Chapter 44 – Astrophysics and Cosmology


Lectures (Spring, 2014) 下列為暫定課程時間，學期間的更新與變動請見：http://hsiuhau.wikispaces.com/Physics＋II 

【Week 1】
 Feb 18 (Tue) Course introduction Feb 20 (Thu) Why are most materials charge neutral?


【Week 2】
 Feb 25 (Tue) Coulomb’s law and electric field Feb 27 (Thu) Gauss’s law

【Week3】
 Mar 4 (Tue) What causes lightning? Mar 6 (Thu) electrostatic potential energy

【Week4】
 Mar 11 (Tue) Can magnetic forces do work? Mar 13 (Thu) Hall effect

【Week5】
 Mar 18 (Tue) Magnetic materials Mar 20 (Thu) How does the geomagnetic field arise?

【Week6】
 Mar 25 (Tue) Biot-Savart law Mar 27 (Thu) Ampere’s law

【Week7】
 Apr 1 (Tue) Why can light propagate in vacuum? Apr 3 (Thu) 校際活動週(停課) Week 8 


【Week8】
 Apr 8 (Tue) dynamics of electric and magnetic fields Apr 10 (Thu) Maxwell equations

【Week9】
 Apr 15 (Tue) Maxwell equation 2 Apr 17 (Thu) energy and momentum in EM waves

【Week 10】
 Apr 20 (Sun) 期中考 Apr 22 (Tue) 期中考講解 Apr 24 (Thu) What is the nature of light?

【Week 11】
 Apr 29 (Tue) resolution limit May 1 (Thu) blackbody radiation 

【Week 12】
 May 6 (Tue) Why are atoms stable? May 8 (Thu) de Broglie wave 

【Week 13 】
 May 13 (Tue) Schrodinger equation May 15 (Thu) Schrodinger equation 2

【Week 14 】
 May 20 (Tue) angular momentum and spin May 22 (Thu) Pauli exclusion principle

【Week 15】
 May 27 (Tue) How is the secret of life encoded? May 29 (Thu) band theory of solids

【Week 16】
 Jun 3 (Tue) How can we date fossils? Jun 5 (Thu) magnetic resonance imaging

【Week 17】
 Jun10 (Tue) What are the building blocks of our universe? Jun 12 (Thu) after the big bang 

【Week 18】
 (Final Week) Jun15 (Sun) 期末考 Jun 19 (Thu) 期末考講解

10202 自然科學
常微分方程二
許世壁
清大數學系重量級教授退休前的最後一堂課，讓許世璧教授以嚴謹仔細的教學，讓你從源頭開始輕鬆理解ODE！沒上過許世璧教授的課，別說你懂常微分方程！體驗經典，就是現在！

 
一、課程說明(Course Description)  
      本課程著重於常微分方程之定性理論,預備知識需高等微積分及線性代數. 
      本課程提供三學分的常微分方程基本理論，為研究生之標準課程。 
 
二、指定用書(Text Books)  
      Sze-Bi Hsu: Ordinary Differential Equations with Applications. World Scientific, 2013, 2nd edition 
 
 
三、參考書籍(References)  
      Jack Hale: Ordinary Equations 
      Jack Hale and Kocak: Dynamics and bifurcations 
 
四、教學方式(Teaching Method)  
      演講及計算. 
 
 
五、教學進度(Syllabus) 
1.   Fundamental Theory of ODE: Existence: Uniqueness of System of ODE, Continuously dependence on parameter and initial conditions, Differential Inequality.
2 Linear system : Linear systems with constant coefficients and Periodic Linear Systems, Louiville Formula, Two-Dimensional Phase plane analysis, 
 
3 Stability of Nonlinear Systems: Linearization, Variation of Constant Formula,. Stable and unstable manifolds, Orbital stability. 
 
六、成績考核(Evaluation) 
     Homework: 30% 
     Mid term :30% 
     Final Exam.: 40% 
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