臺大課程網
預選課表

工程數學一

112-1 開課
  • 備註
    英語授課
  • 修課限制

    • 限生農學院學生(含輔系、雙修生)

  • 本校選課狀況

    已選上
    0/57
    外系已選上
    0/0
    剩餘名額
    0
    已登記
    0
  • 課程概述
    This course is an introduction to the methods of mathematical physics used in the environmental and hydrologic sciences. It is presented in the context of basic mathematical methods and their application in the environmental and hydrologic contexts. The lecture introduces ordinary differential equations (ODEs) and vectors. Both analytical and numerical methods of solution of differential equations are introduced. Analytical solutions 1. First-order ODEs 2. Second-order Linear ODEs 3. Higher Order Linear ODEs 4. System of ODEs (Eigenvalue Problems for Systems of ODEs) Series Solutions 5. Series Solutions of ODEs (Special Functions) Transforms 6. Laplace Transforms Some of the contents in the below chapters are merged into chapters 1 to 6 Linear algebra 7. Matrices, Vectors, Determinants, Linear system 8. Eigenvalue and Eigenvectors 9. Vector differential and integral calculus (Optinal) Numerical methods 20. Numeric Linear Algebra (20.6 – 20.8) 21. Numerics for ODEs (21.1 – 21.3)
  • 課程目標
    Primarily introduces analytical methods for solving commonly used mathematical equations in the fields of physics and engineering. Cultivates students' abilities to interpret and handle mathematical equations in their professional fields.
  • 課程要求
    Calculus
  • 預期每週課前或/與課後學習時數
  • Office Hour
  • 指定閱讀
    Erwin Kreyszig, Advanced Engineering Mathematics, Tenth Edition, Wiley
  • 參考書目
    Erwin Kreyszig, Advanced Engineering Mathematics, Tenth Edition, Wiley
  • 評量方式
    55%

    Midterm

    20%

    Homework

    25%

    Final

  • 針對學生困難提供學生調整方式
    調整方式說明
    A2

    以錄影輔助

    Assisted by video

    B1

    延長作業繳交期限

    Extension of the deadline for submitting assignments

    D1

    由師生雙方議定

    Negotiated by both teachers and students

  • 補課資訊
  • 課程進度
    9/6第 1 週Introduction
    9/13第 2 週Linear 1st order ODEs (modeling, separation variables, Euler’s method)
    9/20第 3 週Linear 1st order ODEs (Linear Equ., Exact Equ., Bernoulli Equ.)
    9/27第 4 週Linear 2nd ODEs with constant coefficients (homogeneous ODE, non-homogeneous ODE, Mass-Spring System)
    10/4第 5 週Linear 2nd ODEs with constant coefficients (non-homogeneous ODE, Resonance)
    10/11第 6 週Midterm
    10/18第 7 週System of Linear ODEs （Eigenvalue, Eigenvector, system ODEs with constant coefficients）
    10/25第 8 週System of Linear ODEs (homogeneous and nonlinear)
    11/1第 9 週Linear 2nd ODEs with variable coefficients and serious solutions (special functions) I
    11/8第 10 週Linear 2nd ODEs with variable coefficients and serious solutions (special functions) II
    11/15第 11 週No class 校慶停課
    11/22第 12 週Midterm
    11/29第 13 週Laplace transform （Linearity, first shifting theory, derivatives and integrals)
    12/6第 14 週Laplace transform (Unit step function, Heaviside function, second shifting theory)
    12/13第 15 週Laplace transform (convolution, solve ODEs)
    12/20第 16 週Final