●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......
內容簡介
本教材主要介紹非線性問題的一些基本數學分析方法和理論，具體包括四部分：
常微分方程定性理論（包括不動點理論、混沌的簡介）;反應擴散方程（包括攝動法簡介）;橢圓型方程;雙曲型守恆率;應用分析個例（包括孤立子、斑圖選擇簡介）。
適合高年級本科生以及研究生閱讀。
