Modeling

Ordinary differential equations and dynamical systems

ODE and dynamical systems, critical points, phase space & stability analysis; Hamiltonian dynamical systems; ODE system with gradient structure, conservative ODE’s. 

Partial differential equations and applications

Basic theory for elliptic, parabolic, and hyperbolic PDEs; calculus of variations: Euler-Lagrange equations; shock waves and rarefaction waves in scale conservation laws; method of characterization, weak formulation, energy estimates, maximum principle; Hamilton-Jacobi equations, Lax-Milgram, Fredholm operator.

Mathematical modeling, simulation, and applied analysis

Scaling behavior and asymptotics analysis, stationary phase analysis, boundary layer analysis,

qualitative and quantitative analysis of mathematical models,  Monte-Carlo method.

Linear and nonlinear programming

Simplex method, interior method, penalty method, Newton’s method, homotopy method and fixed point method, dynamic programming.

References:

1. W. D. Boyce and R. C. DiPrima, Elementary Differential Equations, Wiley, 2009.
2. V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer.
3. F.Y.M. Wan, Introduction to Calculus of Variations and Its Applications, Chapman & Hall, 1995
4. J. Keener, “Principles of Applied Mathematics”, Addison-Wesley, 1988.
5. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, 1999.
6. A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, 2000.

《数学建模》Frank R.Giordano，Willam P.Fox，Steven B.Horton，叶其孝等译

原名《A First Course in Mathematical Modeling》，是很好的书。

230《数学建模与数学实验.第3版》赵静, 但琦主编

231《数学建模及其基础知识详解》王文波编著

232《数学建模方法及其应用》韩中庚编著

233《数学建模》Maurice D. Weir, (美) William P. Fox著

Modeling

Ordinary differential equations and dynamical systems

ODE and dynamical systems, critical points, phase space & stability analysis; Hamiltonian dynamical systems; ODE system with gradient structure, conservative ODE’s.

Partial differential equations and applications

Basic theory for elliptic, parabolic, and hyperbolic PDEs; calculus of variations: Euler-Lagrange equations; shock waves and rarefaction waves in scale conservation laws; method of characterization, weak formulation, energy estimates, maximum principle; Hamilton-Jacobi equations, Lax-Milgram, Fredholm operator.

Mathematical modeling, simulation, and applied analysis

Scaling behavior and asymptotics analysis, stationary phase analysis, boundary layer analysis,

qualitative and quantitative analysis of mathematical models, Monte-Carlo method.

Linear and nonlinear programming

Simplex method, interior method, penalty method, Newton’s method, homotopy method and fixed point method, dynamic programming.

References:

1. W. D. Boyce and R. C. DiPrima, Elementary Differential Equations, Wiley, 2009.

2. V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer.

3. F.Y.M. Wan, Introduction to Calculus of Variations and Its Applications , Chapman & Hall, 1995

4. J. Keener, “Principles of Applied Mathematics“, Addison-Wesley, 1988.

5. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, 1999.

6. A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, 2000.

Of the mathematical modeling Frank R.Giordano , Willam P.Fox , Steven B.Horton And ye qixiao, translated

Formerly known as the A First Course in Mathematical Modeling , Is a very good book.

230 The mathematical modeling and experiment . 3 Zhao Jing , But Chi editor

231 The mathematical modeling and detailed explanation of the basics of written by Wang wenbo

232 The mathematical modeling method and its application in Korean g-authoring

233 Of the mathematical modeling Maurice d. Weir, ( United States ) William p. Fox The