●1 ODE 10
●1.1 Basic notions
●1.2 Local existence
●1.2.1 Normed spaces and fixed point theorem
●1.2.2 Applications to ODE system and linear algebraic system
●1.3 Critical point
●1.4 Plane analysis for the Duffing equation
●1.5 Homoclinic orbit and limit cycle
●1.6 Stability and Lyapunov function
●1.7 Bifurcation
●1.8 Chaos: Lorenz equations and logistic map
●2 Parabolic Equations 53
●2.1 Introduction: BVP and IBVP, equilibrium
●2.2 Dispersion relation, linear and nonlinear stability
●2.3 Invariant domain
●2.4 Perturbation method
●2.5 Traveling waves
●2.6 Burgers' equation and Cole-Hopf transform
●2.7 Evolutionary Duffing equation
●3 Elliptic Equations 85
●部分目錄