微分方程 Differential Equations

• 大學部一年級必修課程。
• 近五年開課情形：1102、1112、1122。
• 112學年度第二學期課程大綱。
• Textbook
  • “Differential Equations with Boundary-Value Problems”, Dennis G. Zill, Cengage Learning, 2018 (9th Edition).
• Topics include
  • Introduction to differential equations
    • Definitions and Terminology
    • Initial-Value Problems
    • DEs as Mathematical Models
  • First-order differential equations
    • Solution Curves Without a Solution
    • Separable Equations
    • Linear Equations
    • Exact Equations
    • Solutions by Substitutions
    • Numerical Method
  • Higher-order differential equations
    • Preliminary Theory
    • Reduction of Order
    • Homogeneous Linear Equations with Constant Coefficients
    • Undetermined Coefficients
    • Variation of Parameters
    • Cauchy-Euler Equations
    • Nonlinear Differential Equations
  • Series solutions of linear equations
    • Power Series
    • Solution about Ordinary Points
    • Solution about Singular Points
  • Systems of linear first-order differential equations
    • Linears Systems
    • Homogeneous Linear Systems
    • Nonhomogeneous Linear Systems
  • Fourier Series
    • Orthogonal Functions
    • Fourier Series
    • Fourier Cosine and Sine Series
  • Partial differential equations
    • Separable Partial Differential Equations
    • Heat Equation
    • Wave Equation
    • Laplace's Equation
• Grading
  • Four exams (25% for each exam)
• Released News
  • 本課程將採用Google Classroom作為課程進度或考試公告的主要平台，請選課同學務必加入。