工程科学中的应用分析
Douban
Applied Analysis for Engineering Sciences
唐少强
résumé
教材主要介绍非线性问题的一些基本数学分析方法和理论，具体包括四部分：<br><br>常微分方程定性理论（包括不动点理论、混沌的简介）;反应扩散方程（包括摄动法简介）;椭圆型方程;双曲型守恒率;应用分析个例（包括孤立子、斑图选择简介）。适合高年级本科生以及研究生阅读。
contenus
1 ODE 10
1.1 Basic notions
1.2 Local existence
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
3.1 Sobolev spaces
3.2 Variational Formulation
3.3 Neumann boundary value problem
4 Hyperbolic Equations 93
4.1 Linear advection equation, characteristics method
4.2 Nonlinear hyperbolic equations
4.3 Discontinuities in inviscid Burgers' equation
4.4 Elementary waves in inviscid Burgers' equation
4.5 Wave interactions in inviscid Burgers' equation
4.6 Elementary waves in a polytropic gas
4.7 Riemann problem in a polytropic gas
4.8 Elementary waves in a polytropic ideal gas
4.9 Soliton and inverse scattering transform