一、課程簡介:
1. First-order differential equation
Basic concept
Geometrical meaning of y’=f(x,y)
Separable of differential equation
Separable equation
Exact differential equation
Integrating factors
Bernoulli equation
Orthogonal trajectory of curves
Picard iteration

2. Linear differential equations of second and higher order
Homogeneous linear equations of second order
Second-order homogeneous equation with constant coefficients
Case of complex roots
Free oscillation
Wronskian
Nonhomogeneous equations
Solution by undetermined coefficients
Solution by variation of parameters
Forced oscillation
Modeling of electric circuits
Higher order linear differential equations
Higher order linear differential equations with constant
coefficients
Higher order nonhomogeneous equations

3. Systems of differential equations, phase plane, qualitative
methods
Introduction: vectors, matrices, eigenvalues
Homogeneous systems with constant coefficient
Phase plane, critical point
Criteria for critical point, Stability
Qualtative method for non-linear systems
Nonhomogeneous linear systems

4. Series solution of differential equations
Power series method
Theory of power series method
Legendre’s equation
Fribenius method
Bessel’s equation
Bessel’s function of second
Sturm-Liouville problem
Orthogonal function expansion

5. Laplace transforms
Laplace transform, Linearity, Shift
Transform of derivatives and integrals
Unit step function, Dirac’s delta function
Differential and integral of transform
Convolution
Partial Fractions
Systems of Differential equation


二、先修課程:微積分

三、參考書目:

E. Kreyszig, “ Advanced Engineering Mathematics”, John Wiley & Sons, INC.