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¤@¯ë¦ÛµM¬Éªº²{¶H¡A§Ú­Ì±`¥Î·L¤À¤èµ{ªº«¬¦¡¨Ó¼Ò«¬¤Æ¡A¨Ò¦p¦bª«²z¬É¡A±q¤û¹yªº²Ä¤G©w«ß¨ìªñ¥NªºMaxwell ¤èµ{¡B Einstein ªº¼s¸q¬Û¹ï½×¤¤ªº­«¤O³õ¤èµ{©M Yang-Mills ³õ¤èµ{¡AÁÙ¦³ª«²z¶q (½è¶q¡B°Ê¶q¡B¯à¶q) ªº¦uùÚ©w«ß³£¥i¥H¥Î³æ¤@©Î¤@²Õ¤èµ{¦¡¨Óªí¥Ü¡F¦b¥Íª«¬É«h¦³Lotka-Volterra ¼Ò«¬ (±`·L¤À¤èµ{²Õ) ¨Óªí¥Ü prey ©M predator ¼Æ¶q¤§¶¡ªºÃö«Y¡C

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  1. Intriduction: Some Basic Mathematical Models, Direction Fields; Solutions of Some Differential Equations; Classification of Differential Equations
  2. First Order Differential Equations: Linear Equations;Separable Equations; Modeling with First Order Equations; Differences Between Linear and Nonlinear Equations; Autonomous Equations and Population Dynamics; Exact Equations and Integrating Factors; Numerical Approximations, Euler Methods; The Existence and Uniqueness Theorem; First Order Difference Equations

  3. Second Order Linear Equations: Homogeneous Equations with Constant Coefficients; Fundamental Solution of Linear Homogeneous Equations; Linear Independence and the Wronskian; Nonhomogeneous Equations; Mechanical and Electrical Vibrations; Forced Vibrations
  4. Higher Order Linear Equations: General Theory of nth Order Linear Equations; The Methods of Undetermined Coefficients and Variation of Parameters
  5. Series Solutions of Second Order Linear Equations: Series Solutions of Euler Equations, Legendre Equation, , Chebyshev Equation and Bessel's Equations
  6. The Laplace Transform: Solution of Initial Value Problems; Differential Equations with Discontinuous
  7. System of First Order Linear Equations
  8. Boundary Value Problems

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  1. Nonlinear Differential Equations and Stability
  2. Partial Differential Equations and Fourier Series
  3. Numerical Methods

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  1. W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems
  2. F. John, Partial Differential Equations


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