Applied Analysis for Engineering Sciences

工程科学中的应用分析(英文版)

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Author: Tang Shaoqiang
Language: English
ISBN/ISSN: 9787301267615
2016-03;  Soft Cover

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
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



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
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



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