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工程數學下

112-2 開課

  • 流水號

    28601

  • 課號

    ME2002

  • 課程識別碼

    502 20002

  • 班次 04
  • 3 學分

  • 必修

    機械工程學系

      必修

    • 機械工程學系

  • 林以凡
  • 上課時間和地點
    • 一 3, 4綜604
    • 三 2綜401

  • 2 類

  • 修課總人數 36 人

    本校 36 人

  • 無領域專長

  • 英文授課
  • NTU COOL
  • 核心能力與課程規劃關聯圖
  • 備註

    本課程以英語授課。

  • 本校選課狀況

    已選上
    0/36
    外系已選上
    0/0
    剩餘名額
    0
    已登記
    0
  • 課程概述
    In this course, we will review vector calculus and introduce the elementary theory of the functions of a complex variable covering operations with complex numbers, analytic functions, complex integration, Cauchy’s theorem and its applications, poles and residues, and power series. In the second half oh this semester, we will discuss Fourier series and Fourier transforms. Then we will study different types of partial differential equation problems.
  • 課程目標
    The objective of this course is that by the end of the semester, you will learn ‧ gradient, divergence and curl of a vector point function and related identities; ‧ evaluation of line, surface and volume integrals using Gauss, Stokes and Green’s theorems and their verification; ‧ analytic functions and complex integration; ‧ Fourier series, integral, and transform; ‧ PDE in heat, wave, and Laplace equations. You will also ‧ compute vector differential calculus (knowing the physical meaning of gradient, divergence, and curl operators); ‧ compute vector integral calculus (knowing divergence theorem and Stoke’s theorem); ‧ represent complex numbers algebraically and geometrically; ‧ apply the concept and consequences of analyticity and the Cauchy-Riemann equations and of results on harmonic and entire functions including the fundamental theorem of algebra; ‧ evaluate complex contour integrals directly and by the fundamental theorem, apply the Cauchy integral theorem in its various versions, and the Cauchy integral formula; ‧ represent functions as Taylor, power and Laurent series, classify singularities and poles, find residues and evaluate complex integrals using the residue theorem; ‧ understand how partial differential equations arise in the mathematical description of heat flow and vibration; ‧ demonstrate the ability to solve initial boundary value problems; ‧ express and explain the physical interpretations of common forms of PDEs; ‧ be acquainted with applications of partial differential equations in various disciplines of study.
  • 課程要求
  • 預期每週課前或/與課後學習時數
    3
  • Office Hour
  • 指定閱讀
    P. V. O’Neil, Advanced Engineering Mathematics, CENGAGE Learning, 8th Ed, 2018.
  • 參考書目
    Dennis G. Zill, Advanced Engineering Mathematics, Jones & Bartlett Learning, 7th Ed, 2017.
  • 評量方式
    20%

    Quiz

    There will be twenty-minute quiz from 9 am to 9:20 am on every Wednesday. On each quiz, you will solve one to two questions chosen from our exercises and sample problems in the textbook. Quizzes are closed-book, closed-note. No electronics, including calculators, cell phones, or smart watches are allowed. Some formulas and tables may be provided.

    45%

    Midterms

    (15% each). There are three mid-term exams in this course. The mid terms are scheduled on – Mid-term I: March 20 in class. – Mid-term II: April 24 in class. – Mid-term III: May 15 in class. Mid-terms are closed-book, closed-notes. No electronics, including calculators, cell phones, or smart watches are allowed. Mid-terms will be used to access demonstration of the learning objectives and may include the combinations of true & false and work-out problems. Some formulas and tables may be provided.

    15%

    Final

    The date of the final exam will be on June 03. The final is closed-book, closed-notes. No electronics, including calculators, cell phones, or smart watches are allowed. The final is cumulative and may include the combinations of true & false and work-out problems. Some formulas and tables may be provided.

    0%

    Class Attendance and Attentiveness

    (2%). The purpose of this additional 2% is to encourage you to attend every class that you can. You should also be attentive during the lecture; there are many ways to show you are engaged, one being to answer questions as they are asked.

    20%

    Team Collaboration & Homework

    Form a MIXED cultural team of at most 4 people. There must be at least one Taiwanese student in the group. On this “international team,” you need to work together in class to solve the drills and may have a chance to demonstrate your work to other teams in class. Your team may also turn in the “Drills” in class competition. In addition, there will be four team homework assignments in this course. Each team will submit 2-3 applications of what you have learned on each topic. Also, the purpose to have a team in the class is to help your team members each other. Through the discussion in and out of class, all of the members make progress. 5% will be peer evaluation.

    1. 本校尚無訂定 A+ 比例上限。
    2. 本校採用等第制評定成績，學生成績評量辦法中的百分制分數區間與單科成績對照表僅供參考，授課教師可依等第定義調整分數區間。詳見 學習評量專區。
  • 針對學生困難提供學生調整方式
  • 補課資訊
  • 課程進度
    2/19, 2/21第 1 週Vector Differential Calculus Vector Differential Calculus - Acceleration and Curvature
    2/26, 2/28第 2 週The Gradient Field, Divergence, and Curl
    3/04, 3/06第 3 週Vector Integral Calculus - Line Integral Vector Integral Calculus
    3/11, 3/13第 4 週Vector Integral Calculus - Green’s Theorem Divergence Theorem and Stokes’ Theorem
    3/18, 3/20第 5 週Functions of a Complex Variable
    3/25, 3/27第 6 週Midterm I Functions of a Complex Variable
    4/01, 4/03第 7 週Integration in the Complex Plane
    4/08, 4/10第 8 週Integration in the Complex Plane
    4/15, 4/17第 9 週Series and Residues
    4/22, 4/24第 10 週Midterm II Fourier Series
    4/29, 5/01第 11 週Fourier Series Fourier Integral
    5/06, 5/08第 12 週Fourier Transform
    5/13, 5/15第 13 週Midterm III Partial Differential Equation
    5/20, 5/22第 14 週PDE - Heat Equation PDE - Laplace Equations
    5/27, 5/29第 15 週PDE - Laplace and Wave Equations PDE - Wave Equations
    6/03, 6/07第 16 週Final Exam