| 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 |
| ＊ | |
| second edition. |
| ＊ | D. Widder, Advanced Calculus. |
| ＊ | T. Apostal, Advanced Calculus. |
【教學方式/教學進度】
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.
| * | Differential geometry of curves and surfaces, by Manfredo P. Do |
| Carmo. Prentice Hall. |
| * | Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010. |
| * | Elementary Differential Geometry, 2nd Edition, by Barrett O'Nell. |
www.math.nthu.edu.tw/~cjsung/course/ug2018s.html
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....
【課程說明 / Description of the course】
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。
【課程教材 / Course Material】
| * | 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) |
| 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. |
| * | 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! |
| * | 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
| |
| 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？！
|
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。
| * | Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010. |
| * | Differential geometry of curves and surfaces, by Manfredo P. Do Carmo.Prentice Hall, 1976. |
| * | Elementary Differential Geometry, 2nd Edition, by Barrett O'Nell. |
| * | Lectures、講授、演習、討論 |
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！
| ♠ | Campbell Biology (10th Edition), Jane B. Reece , Lisa A. Urry, Michael L. Cain, Steven A. Wasserman , Peter V. |
| ♠ | Minorsky, Robert B. Jackson (2013) |
| 【Week 1】 | Life on Earth I - Ch01: Biology and Its Themes Life on Earth II - Ch25: Macroevolution ♠Instructor: Li |
| 【Week 2】 | Life on Earth I - Ch01: Biology and Its Themes Life on Earth II - Ch25: Macroevolution ♠Instructor: Li |
| 【Week 3】 | Ch03: The Chemistry of Water ♠Instructor: Chiao |
| 【Week 4】 | Ch04: Carbon: The Basis of Molecular Diversity Ch05: Biological Macromolecules and Lipids ♠Instructor: Chiao |
| 【Week 5】 | Ch06: Energy and Life Ch07: Cell Structure and Function ♠Instructor: Chiao |
| 【Week 6】 | Week 6 2014 / 10 / 23 : Ch09: Cellular Signaling ♠Instructor: Chiao |
| 【Week 7】 | Ch10: Cell Respiration Ch11: Photosynthetic Processes ♠Instructor: Chiao |
| 【Week 8】
| Ch12: Mitosis Ch13: Sexual Life Cycles and Meiosis ♠Instructor: Chiao |
| 【Week 9】 | Midterm Examination ( Ch01-13 & Ch25) |
| 【Week 10】 | Ch14: Mendelian Genetics Ch15: Linkage and Chromosomes ♠Instructor: Chuang |
| 【Week 11】 | Ch16: Nucleic Acids and Inheritance Ch17: Expression of Genes ♠Instructor: Chuang |
| 【Week 12】 | Ch18: Control of Gene Expression Ch26: Introduction to Viruses ♠Instructor: Chuang |
| 【Week 13】 | Ch19: DNA Technology ♠Instructor: Chuang |
| 【Week 14】 | Ch20: The Evolution of Genomes ♠Instructor: Chuang |
| 【Week 15】 | Ch21: How Evolution Works Ch22: Phylogenetic Reconstruction ♠Instructor: Li |
| 【Week 16】 | No class |
| 【Week 17】 | Ch23: Microevolution Ch24: Species and Speciation ♠Instructor: Li |
| 【Week 18】 | Final Examination ( Ch14-24 & Ch26) |
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)
【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
【指定用書】
Textbooks
References
【教學方式】
Teaching Method
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. |
【指定用書】
Textbooks
References
【教學方式】
Teaching Method
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. |