Topic outline

  • General

    • 最新消息(Latest News)
      • 1/17: Scores of Final Exam and Common HW Part3 have been announced.
        You may go to 蔡老師助教(92933) for the inquiring about your Final Exam only from 10:00 - 12:00 January 18.
        If you have questions on Common HW Part 3. Go to 蔡老師助教 for Problems 1, 4, 7 from 1:00-12:00, 1/18, 李老師助教 for Problems 2, 5, 8 from 10:00-12:00 1/18, and 楊老師助教 for Problems 3, 6, 9 from 12:00-17:00 1/18.
      • 1/11 期未考(Final exam): 10:10 - 12:00, 於原上課教室考試(92383)。
      • 1/7: 電磁學Others10%已公佈，此項成績包含Weekly Report(6/10)、Roll Call(1.5/10)、Quiz(1/10)、Term Report(1.5/10)，但在全班平均6分的基凖下做調整，如對成績有疑問，最遲於1/10前向詢問老師。考試前如有問題，請先用email和我約線上webex討論時間，會在Moodle上公告確定時間。

      • 根據教育部及學校的最新規範，上課不用採梅花座，因此教室恢復可容納70人，因此本課程將於10/26日起，採實體上課，但也開放同步線上上課，另錄製同步教學內容，放置於「Synchronous Course Videos 」，提供多方面的學習管道。進入教室人員遵守防疫規定，全程佩戴口罩且落實手部消毒，禁止飲食， 且每節課固定座位。

    • 公佈欄 Forum
      • Schedule of examinations:
        • First mid-term: 10/23 (Sat.) 10:00 - 12:00
        • Second midterm: 12/4 (Sat.) 10:00 - 12:00
        • Final: 1/11 (Tue.) 10:00 - 12:00
      • 於上課時間進入Moodle，請先點名(Roll call)登錄「出席」或「線上」。
      • 本課程於上課時間均會同步進行線上教學與錄影，可於上課時間進入「Webex 線上同步上課(Synchronous online learning)」頁面，點選對應的連結。錄影檔於後製完成後，放置於「Synchronous Course Videos」。
      • 如有任何問題，請寄送e-mail 至 bjli@ncku.edu.tw。
      • 在課程資訊和課程進度中，如有[...]，括號內是日期，表示為翻轉課程單元，應在課程日期之前先自行學習。
      • TA's email: n26102173@gs.ncku.edu.tw You may send e-mails to TA for the following requests:
        • Correction of your solutions to suggested problems
        • Correction of your solutions to past examinations and common homeworks
        • Grades of your common homeworks and examinations
      • Most of the files of course materials are accessed only through a gs account.


    • Webex 線上同步上課(Synchronous online learning) External tool

      Connect through the link to the corresponding course date and time.

  • 共同作業與繳交日期 Part 3 (Common Homework and dates of submission)

    本階段之共同作業以紙本形式繳交( The acceptable homework must be written on paper.)

    * 共同作業寫在A4空白紙上，各題要寫在分張的紙張上，不可有二題寫在同一張的情況。注意每題都要註明姓名、學號。作業每題10分，換算為總成績的1.1分。
     * 除紙本外，另於Moodle上線上繳交一份電子檔，以便日後如對成績有疑慮時，可供查證。如因疫情無法到校，只需繳交電子檔。
     * 於指定日期繳交作業，除非有特殊原因，逾期一律不批閱。可於課堂上繳交，也可交至老師11樓的辦公室窗台上。
     * 共同作業不發還，建議繳交前自行掃描或照相存檔，或以Moodle上的電子檔為備份。
     * 作業應該各人各自完成，切勿有任何部份抄自他人、或直接參考書籍、講義、網路上的解答再做答。
    * 同學之間不要進行作業的研討
    * 如果作業有困難，仍應先寫下自己的作法，就困難點向老師或同學請教。
    * 如果有同學向你詢問作業，(1) 不要把你的作業遞給同學看，(2) 只根據 同學的困難點提供部份指引，不要詳述步驟。
    * 每學期都有同學抄襲被識出，抄襲和被抄襲者均會被扣10分。
    * 作業的目的是幫助建立正確的觀念、磨練計算的能力，普遍的狀況是只見計算，不見想法。各人可以在寫作業的時候，訓練自己將想法和計算的根據或理由也寫在作業中，這樣可以幫助大家思考，釐清問題，找出解決之道。

  • 第三階段課程進度和活動(Course progress: Part III)

    • 問巻填寫與學期報告( 12/20 24:00前完成) Assignment

      I. 請至下列兩個網址填寫問巻：

      2. IEET 問卷調查系統 (ncku.edu.tw) (只限電機系學生)

      II. 上傳或線上填寫學期報告，報告內容可如下：

      1. 是否已完成問巻1和2之填答?

      2. 本學期的課程安排的適應和意見。

      3. 個人本學期的學習成就、檢討和未來改進。

      4. 其它。


    • 本階段課程講義(Files of handout)：

    • Magnetic forces, materials, and devices

      [12/7] Sections 8.1, 8.2, 8.3: Sec0801_02_03.pdf

        • Magnetic force and magnetic dipole moment:  mp4
          • [Optional] Example 8.1: Motion of a charged particle in an E field, EX0801.pdf
          • [Optional] Example 8.2: Motion of a charged particle in a B field, EX0802.pdf
          • Example 8.3: Determine B from Lorentz force, EX0803.pdf, mp4
          • Example 8.4: Magnetic force on a current loop, EX0804.pdf, mp4
          • Example 8.5: Find a magnetic moment, EX0805.pdf, mp4
          • Problem 8.20: Torque on a triangular current loop, P0820.pdf, mp4

      [12/9] Section 8.4: Magnetic dipoles and induced magnetic fields, Sec0804.pdf, mp4

        • Example 8.6: torque on a current loop due to another current loop, EX0806.pdf, mp4
        • Example 8.13: mutual inductance, EX0813.pdf, mp4

      [12/14] Section 8.5: Magnetic fields in materials, Sec0805, mp4

        • Example 8.7: EX0807.pdf, mp4
      [12/16] Section 8.6: Magnetization and Classification of Materials, Sec0806.pdf, mp4


      [12/16] Section 8.7:       Magnetic Boundary Conditions, Sec0807.pdf, mp4

        • Example 8.8: Applications of boundary conditions, EX0808.pdf, mp4
        • Example 8.9: Dealing with surface current density, EX0809.pdf, mp4

      [12/21] Sections 8.10, 8.11: Magnetic circuits and force, Sec0810_11.pdf, mp4

        • Example 8.14: magnetic circuit of a toroidal core, EX0814.pdf, mp4
        • Example 8.15: a magnetic circuit with an air gap, EX0815.pdf, mp4
        • Example 8.16: a U-shaped electromagnet, EX0816.pdf, mp4

    • Maxwell's Equations

      [12/21] Sections 9.1, 9.2, 9.3: Sec0901_03.pdf

        • Faraday's law: mp4
          • Problem 9.5: A stationary loop in a time-varying B field, P0905.pdf, mp4
          • Example 9.1: emf due to a sliding bar, EX0901, mp4
          • Problem 9.7: Sliding bar with non-uniform B field,  P0907.pdf, mp4
          • Example 9.2: Rotating loop with static B field, mp4
          • Example 9.3: A transformer, EX0903, mp4
        • Issues on the applications of Faraday's law: mp4
          • Rao's Problem 2.16: Rotating loop with time-varying B, P02_16.pdf, mp4
        • (Optional) Voltmeter and emf: mp4

      [12/28] Section 9.4: Displacement current, Sec0904.pdf, mp4

        • Example 9.4: Find a displacement current, EX0904.pdf, mp4
        • Practice Exercise 9.4: PE0904.pdf, mp4

      [12/28] Section 3.9: Sec0309.pdf, Classification of Vector Fields, mp4

        • Example 3.12: EX0312.pdf

      [12/30] Sections 9.5 - 9.7: Sec0905_07.pdf

        • Maxwell's equations in final forms: mp4
        • Time-Varying Potentials: mp4
        • Time-Harmonic Fields: mp4
        • Example 9.5: Exercise on complex algebra, EX0905.pdf, mp4
        • Example 9.6:  Exercise on phasors, EX0906.pdf, mp4
        • Problem 9.20: Maxwell's equations in phasor form
        • Example 9.7: Find beta from Maxwell's equations, EX0907.pdf, mp4
        • Example 9.8: Find H from a given E field, EX0908.pdf, mp4

      [1/4] Preview on EM Waves: EM_Wave_Preview.pdf

        • Electromagnetic waves in general: mp4
          • Problem 9.21: Primary curl equations in free space, P0921.pdf
          • Example 10.1: find omega and beta, EX1001.pdf, mp4
          • Problem 10.23: Find H of a uniform plane wave, P1023.pdf, mp4
        • Power flow and Poynting vectors: mp4
          • Example 10.8(b)(c): Finding the power of a uniform plane wave, EX1008.pdf, mp4

  • 課程資訊與資源 (Resource and information of the course)

  • Synchronous Course Videos

  • 第二階段課程進度和活動(Course progress: Part II)

    • Electric Fields in Material Space:
      Section 5.3: Sec0503.pdf

        • Current in conductors: mp4
        • Example 5.1: EX0501.pdf, mp4,

      Section 5.4: Sec0504.pdf

        • Conductors: mp4
          • Example 5.3: EX0503.pdf
          • Example 5.4: EX0504.pdf

      Section 5.８: Sec0508.pdf

        • Conductivity equation: mp4
        • Suggested Problems: P5.29, P5.31, P5.40
        • Common Homework: P. 5


    • Vector Calculus: Sections 3.8: Sec0308.pdf

      • Laplacian operator: mp4
        • Example 3.11: EX0311.pdf

    • Electrostatic Boundary-Value Problems

      Sections 6.1, 6.2, 6.3: Sec0601_03.pdf

        • Poisson's and Laplace's Equations: mp4
        • [11/2] Uniqueness Theorem: mp4

      Section 6.4: Sec0604.pdf, 1D Boundary-value Problems

        • [11/2] Solving Laplace's Eq or Poisson's Eq (Introduction): mp4
        • [11/2] A parallel-plate capacitor, 1D problem: ChengEx0401.pdf, mp4
        • Example 6.2: EX0602.pdf, mp4
        • Example 6.3: EX0603.pdf, mp4
        • Example 6.4: EX0604.pdf, mp4
        • Example 6.1: EX0601.pdf
        • Common Homework: P. 1, P. 3

      Section 6.4: 2D  boundary-value Problems in Cartesian Coordinates

        • [11/4] Example 6.5: EX0605.pdf, mp4
          • ref: Fourier expansions.pdf
        • Example 6.6: EX0606.pdf
        • Case of separation number = 0: Lmda0.pdf, mp4
        • [11/9] Trial Solutions of  2D Laplace's Equations in Cartesian Coordinate: Solve 2D Laplace Eq.pdf, mp4
        • Example of a boundary set at infinity: ChengEx0406.pdf
        • [Optional] Superposition of boundary conditions: PlonseyEx0402,pdf, mp4
        • Suggested Problems: P. 6.26

      Section 6.4: Solving 2D Poisson's Equations

        • Example: ChengEx0402.pdf, mp4
        • Techniques to Solve Poisson’s Equations: Poisson Eq.pdf, mp4
        • Suggested Problems: P6.8

      Section 6.4: Solving 3D Laplace's Equation

        • [11/11] In Cartesian Coordinates: Solve 3D Laplace Eq.pdf, mp4
          • [11/11] Example: PlonseyEx0401.pdf, mp4
        • [11/16] In Cylindrical Coordinates: Ex0607.pdf, mp4
          • [11/16] Infinitely long cylinder: LaplaceCyl_App1.pdf, mp4
          • A problem with finite axial length: LaplaceCyl_App2.pdf, mp4
          • Common Homework: P. 2
        • [Optional] In Spherical Coordinates: PRACTICE EXERCISE 6.7(PE0607.pdf), mp4 

      Sections 6.6: Method of Image, Sec0606.pdf

        • Part 1: Background and principle,  mp4
          • Example 6.14: Point charge between two semi-infinite conducting planes, EX0614.pdf
        • Part 2: A line charge above a grounded conducting plane, mp4
        • [11/23] Part 3: Involving a conducting spherical shell, mp4
        • Common Homework: P. 4

      Sections 6.5: Application of Electrostatic Boundary-Value Problems, Sec0605.pdf

        • [11/23] Part 1: General steps to find capacitance and resistance, mp4
          • Example 6.8: Resistance, EX0608.pdf, mp4
          • Example 6.9: Conductance, EX0609.pdf
        • Part 2: Fundamental examples, mp4
          • Example 6.10: Spherical capacitor, EX0610.pdf
          • Example 6.11: Find a capacitance by assuming V, EX0611.pdf
          • Example 6.12: Capacitors in series and in parallel, EX0612.pdf
          • Example 6.13: A cylindrical capacitor, EX0613.pdf
          • Common Homework: P. 6

      Advanced Topics:

        • [Optional] Electric Fields and Potential in Conductors: Conductor_Field_Potential.pdf


    • Magnetostatic Fields

      Sections 7.1 - 7.4: Sec0701_04.pdf

        • Biot-Savart Law: mp4
          • Example 7.1:  H due to linear segments of current, EX0701.pdf, mp4
          • Example 7.2:  H due to two current filaments, EX0702.pdf, mp4
          • Example 7.3:  H due to a circular current loop, EX0703.pdf, mp4
          • Example 7.4:  A solenoid, EX0704.pdf, mp4
        • [11/30] Section 3.7:  Sec0307.pdf
          • Curl of a vector field: mp4
            • Example 3.8: curl of some vector fields, EX0308.pdf
          • Stokes' theorem: mp4
            • Example 3.9: Confirmation of Stokes' theorem, EX0309.pdf
          • Important results:
            • Example 3.10: div curl (a vector field)= 0, EX0310.pdf
            • Practice Exercise 3.10: curl grad (a scalar field) = 0, PE0310.pdf
        • [11/30] Ampere's circuit law: mp4
          • Example 7.5: Parallel infinite current sheets, EX0705.pdf, mp4
          • Example 7.6: A toroid, EX0706.pdf, mp4

      Sections 7.5, 7.6: Sec0705_06.pdf, mp4

        • Magnetic Flux Density:
          • Problem 2.6 of Rao's: Magnetic field in the hollow region, R02_06.pdf, mp4
        • Maxwell’s Equations for Static Fields
        • Common Homework: P. 7

      Section 7.7: Sec0707.pdf, Vector Potential, mp4

        • Example 7.7: Magnetic flux, EX0707.pdf, mp4
        • Example 7.8: Surface current and vector potential, EX0708.pdf, mp4
        • Common Homework: P. 8
      [Optional]Section 7.8: Sec0708.pdf, Derivation of Biot-Savart’s Law and Ampere’s Law from the Vector Potential

    • Inductance

      Sections 8.8, 8.9: 

        • Magnetic flux linkage and inductance: Magnetic_flux_linkage.pdf, mp4
        • Inductors, inductance and magnetic energy: Sec0808_09.pdf,  mp4
        • Example 8.10: Self-inductance of a long solenoid, EX0810.pdf, mp4
        • Example 8.11: internal and external inductances of a coaxial cable, EX0811.pdf, mp4
        • Example 8.12: two-wire system, EX0812.pdf, mp4
        • [Optional] Example 8.13: mutual inductance, EX0813.pdf, mp4
        • Common Homework: P. 9

  • Quiz

    Open-book and discussion are permissible. However, no plagiarism.

  • 第一階段課程進度和活動(Course progress: Part I)

    • Introduction and Vector Algebra: Chap01.pdf

      • [Optional] Introduction of Electromagnetics.pdf
      • [9/23] Scalars, vectors and fields: mp4
      • [9/23] Unit vectors, vector components and laws of vector algebra: mp4
      • Examples: EX0101.pdf, EX0102.pdf, [optional]EX0103.pdf
      • [9/23] Vector multiplication: mp4
        • Arithmetic order of operation of scalar triple product: mp4
      • [9/23] Cyclic permutation and Triple products: mp4
      • Examples: EX0104.pdf, EX0105.pdf, [optional]EX0106.pdf, EX0107.pdf
      • Numerical Softwares and Resources
      • Suggested problems: P1.11, P1.20, P1.42 

    • Coordinate Systems and Transformation: Chap02.pdf

      • [9/28] Cartesian coordinates: mp4
      • [9/28] Cylindrical coordinates
        • coordinates, unit vectors and conversions: mp4
        • conversion of vectors: mp4
      • [9/28] Spherical coordinates:
        • coordinates and unit vectors: mp4
        • conversion of unit vectors: mp4
        • conversion of vectors: mp4
      • Distance of two points: mp4
      • Summary: Table 2.1, Table0201.pdf
      • [Optional] Nonorthgonal coordinates: mp4
      • Examples:
        • Example 2.1: EX0201.pdf, mp4
        • Example 2.2: EX0202.pdf, mp4
        • Example 2.3: EX0203.pdf, mp4
        • Example 2.4: EX0204.pdf, mp4
      • Suggested problems: P2.20, P2.21, P2.24, P2.32
      • Common Homework: P. 1

    • Vector Calculus: Sections 3.1, 3.2, 3.3: Sec0301_03.pdf

      • [10/5] Differential elements: mp4
        • Example 3.1: Ex0301.pdf, mp4
      • [10/5] Line, surface and volume integrals: mp4
        • Example 3.2: Ex0302.pdf, mp4
        • Example 5.1: Ex0501.pdf
        • Problem 3.9: P0309.pdf
      • Optional tutorial on Youtube: Line, Surface, and Volume Integrals

    • Electrostatic Fields, Potential and Flux Density: 

      Sections 4.1, 4.2, 4.3: sec0401_04.pdf

        • Coulomb's law and the principle of superposition: mp4
        • Electric fields due to charges or charge distributions
          • Electric field: mp4
            • Example 4.1: Ex0401.pdf, mp4
          • Continuous charge distribution: mp4
          • [10/7] E field due to a line charge: mp4
            • Example 4.4(a circular ring of charge): Ex0404.pdf, mp4
          • Common Homework: P. 2, due by 10/12
          • E field due to surface charge: mp4
            • Example 4.5: Ex0405.pdf
            • Example 4.6: Ex0406.pdf
          • E field due to volume charge: mp4

      Sections 4.7: Sec0407.pdf

        • [10/12] Line integral of E and Electric potential: mp4
        • [10/12] V due to a point charge: mp4
          • Example 4.10: EX0410.pdf
          • Example 4.11: EX0411.pdf
      Section 4.4: sec0401_04.pdf
        • [10/12] Surface integral of E and Electric flux density: mp4
          • Example 4.7: Ex0407.pdf
          • [Optional] Why D flux? WhyDFlux.pdf

    • Vector Calculus: Sections 3.6, 3.4: Sec0306_04.pdf

      • Divergence of a vector field: mp4
      • Divergence theorem: mp4
        • Example 3.6: EX0306.pdf
        • Example 3.7: EX0307.pdf

    • Electrostatic Fields and Gauss' Law: Sec0405_06.pdf

      Sections 4.5: Gauss' Law: mp4

      Sections 4.6: Applications of Gauss' law: mp4

          • Example 4.8: EX0408.pdf
          • Example 4.9: EX0409.pdf
          • Common Homework: P. 3

    • Vector Calculus: Sections 3.5: Sec0305.pdf

      • [10/14] Gradient of a scalar field: mp4
        • Examples: 3.3, 3.4, 3.5

    • Sections 4.10: Electric energy density: Sec0410.pdf, mp4

        • Example 4.14: EX0414.pdf,  mp4
        • Example 4.15: EX0415.pdf, mp4

      Sections 4.09: Dielectric dipoles: Sec0409.pdf, mp4

          • Example 4.13: EX0413.pdf

    • Electric Fields in Material Space: 
          Section 5.1, 5.2: Sec0501_02.pdf, Appendix.pdf
        • Classification of materials: Sec05_01_02.pdf, Appendix.pdf, mp4
               Sections 5.5, 5.6, 5.7: Sec0505_07.pdf, Capacitor.pdf, Cylindrical capacitor.pdf

        • Dielectric Polarization: mp4
        • Bound charge densities: mp4
          • Example 5.5: EX0505.pdf, mp4
        • Displacement field vector in a dielectric: mp4
          • Example 5.6: EX0506.pdf
          • Example 5.7: EX0507.pdf
        • [10/21]Capacitors and dielectric strength: Capacitors.pdf, mp4
          • Summary of a coaxial capacitor: Cylindrical capacitor.pdf
          • Common Homework: P. 6, P. 7
          • Common Homework: P. 5

      Section 5.9: Sec0509.pdf

        • Dielectric-dielectric boundary conditions: mp4
        • Conductor-dielectric boundary conditions: mp4
        • Example 5.9: EX0509.pdf, mp4
        • Example 5.10: EX0510.pdf
        • Common Homework: P. 9

  • 共同作業與繳交日期 Part 1 (Common Homework and dates of submission)

    * 共同作業寫在A4空白紙上，各題要寫在分張的紙張上，不可有二題寫在同一張的情況。注意每題都要註明姓名、學號。作業每題10分，換算為總成績的1.1分。

    * 除紙本外，另於Moodle上線上繳交一份電子檔，以便日後如對成績有疑慮時，可供查證。如因疫情無法到校，只需繳交電子檔。

    * 於指定日期繳交作業，除非有特殊原因，逾期一律不批閱。可於課堂上繳交，也可交至老師11樓的辦公室窗台上。

    * 共同作業不發還，建議繳交前自行掃描或照相存檔，或以Moodle上的電子檔為備份。

    * 作業應該各人各自完成，切勿有任何部份抄自他人、或直接參考書籍、講義、網路上的解答再做答。
    *     同學之間不要進行作業的研討
    *     如果作業有困難，仍應先寫下自己的作法，就困難點向老師或同學請教。
    *     如果有同學向你詢問作業，(1) 不要把你的作業遞給同學看，(2) 只根據    同學的困難點提供部份指引，不要詳述步驟。
    *     每學期都有同學抄襲被識出，抄襲和被抄襲者均會被扣10分。
    *     作業的目的是幫助建立正確的觀念、磨練計算的能力，普遍的狀況是只見計算，不見想法。各人可以在寫作業的時候，訓練自己將想法和計算的根據或理由也寫在作業中，這樣可以幫助大家思考，釐清問題，找出解決之道。


    • Common Homework Part 1 File

      防疫期間不到校，共同作業一律採線上繳交方式。

      作業可以打字或手寫，但均須轉製成一個pdf檔案，方能上傳。請確認檔案內容必須清𥇦可辨別文字，

      The common homework must be handed in online.

      You may type or write your homework and convert your homework as a single pdf file for uploading. 

      共同作業不提供答案，如有做題上的困難，可以問老師，或問負責批改的助教。本階段的批改助教如下：
      1、4、7題: 楊老師助教( Q36104381@gs.ncku.edu.tw)
      2、5、8題: 李老師助教 n26102173@gs.ncku.edu.tw
      3、6、9題：蔡老師助教( Q36104381@gs.ncku.edu.tw)

    • P1_1 Assignment

      Submission of Common HW P. 1: due by 10/5

    • P1_2 Assignment

      Submission of Common Homework Problem 2: due by 10/12

    • P1_3 Assignment

      due by 10/19

    • P1_4 Assignment

      due by 10/19

    • P1_5 Assignment

      due by 10/21

    • P1_6 Assignment

      due by 10/21

    • P1_7 Assignment

      due by 10/21

    • P1_8 Assignment

      due by 10/19

    • P1_9 Assignment

      due by 10/26

  • 共同作業與繳交日期 Part 2 (Common Homework and dates of submission)

    本階段之共同作業以紙本形式繳交( The acceptable homework must be written on paper.)

    * 共同作業寫在A4空白紙上，各題要寫在分張的紙張上，不可有二題寫在同一張的情況。注意每題都要註明姓名、學號。作業每題10分，換算為總成績的1.1分。
     * 除紙本外，另於Moodle上線上繳交一份電子檔，以便日後如對成績有疑慮時，可供查證。如因疫情無法到校，只需繳交電子檔。
     * 於指定日期繳交作業，除非有特殊原因，逾期一律不批閱。可於課堂上繳交，也可交至老師11樓的辦公室窗台上。
     * 共同作業不發還，建議繳交前自行掃描或照相存檔，或以Moodle上的電子檔為備份。
     * 作業應該各人各自完成，切勿有任何部份抄自他人、或直接參考書籍、講義、網路上的解答再做答。
    * 同學之間不要進行作業的研討
    * 如果作業有困難，仍應先寫下自己的作法，就困難點向老師或同學請教。
    * 如果有同學向你詢問作業，(1) 不要把你的作業遞給同學看，(2) 只根據 同學的困難點提供部份指引，不要詳述步驟。
    * 每學期都有同學抄襲被識出，抄襲和被抄襲者均會被扣10分。
    * 作業的目的是幫助建立正確的觀念、磨練計算的能力，普遍的狀況是只見計算，不見想法。各人可以在寫作業的時候，訓練自己將想法和計算的根據或理由也寫在作業中，這樣可以幫助大家思考，釐清問題，找出解決之道。