Course description 7

24. Western Economics

Short description of macro and mecro economics.

25. Finite Element Method

Short description, small deformation non-linear solid mechanics problems, non-linear quasi-harmonic field problems. Iterative techniques, Ritz-Galerkin approximation, error estimates, piecewise polynomial apaces - the Finite Element Method.

26. Computer Application Technology VB

Short description , basis concepts , overview of computers and programming , algorithm, data type, expression type, parameter passing among functions, local and global variables and the recursive programming . Design Using VB, variables and basic types, arrays and pointers, functions, algorithms, tools for large programs, specialized tools and techniques.

27. Elementary Number Theory

Short description, Integral the most basic property. Sums of higher powers and fermat’s last theorem. Divisibility and the greatest common divisor, linear equations, factorization and the fundamental theorem of arithmetic, congruences， powers， and Fermat’s little theorem, computing kth roots, Roots.

28. Computer Graphics

Short description, overview of graphics systems, geometric transformations. Two-dimensional viewing, three-dimensional viewing, three-dimensional object representations, visible-surface detection nethods, color models and color applications, computer animation, etc..

29. Spectral Method Numerical Analysis

Short description ,Chebyshev difierentiation matrices, Chebyshev difrentiation by FFT, Clenshaw curtis quadrature, complex arithmetic, eigenvalue problems, finite difference methods. GauSS quadrature, Laplace and Poisson problems, nonlinear problems, spectral accuraecy.

30.The website design

Short description and introduce various website design software. For example, Dreamweaver, ASP, JSP, FrontPage, HTML, JavaScript, VBScript.

Course description 6

19. Matrix Theory

Matrix analysis, general linear systems, special linear systems, linear space and linear transformation, orthogonalization and least squares. The unsymmetric eigenvalue problem, the symmetric eigenvalue problem. Iterative methods for linear systems, reductions and transformations. Methods for the dominant eigenvalue. Methods for the subdominant eigenvalue. Inverse iteration. Jacobi's methods, Givens and Householder's methods. Eigensystem of a symmetric tridiagonal matrix. The LR and QR algorithms. Extensions of Jacobi's method, extension of Givens' and Householder's methods. QR Algorithm for Hessenberg matrices. SOR method and related methods.

20. Visual C++

Short description ,basic facilities. Design using C++, variables and basic types, library types, arrays and pointers, functions, algorithms, tools for large programs, specialized tools and techniques.

21. Partial Differential Equations

Short description, basics of functional analysis. Lax-Milgram lemma, Sobolev spaces, Galerkin methods, the finite element method, basic features, convergence analysis for 1D problems. Error control, a-priori and a-posteriori analysis. Advection-diffusion problems. Stabilization techniques, Galerkin Generalized schemes for boundary layer problems. Parabolic problems. Space-time approximations with finite elements and finite differences. Hyperbolic (convection) problems. conservative finite difference schemes for scalar problems. Continuous and discontinuous finite elements.

22. MATLAB 2

Short description , mainstream areas of image processing. intensity transformations, linear and nonlinear spatial filtering, filtering in the frequency domain, image restoration and registration, color image processing, image data compression, morphological image processing, image segmentation, region and boundary representation and description, and object recognition. Solve image processing problems using MATLAB and IPT functions. New function was written and documented , implement new image processing software solutions.

23.The information science and foundation

Short description, entropy，relative entropy and mutual information, entropy rates of stochastic process, channel capacity, differential entropy, the Gaussian channel, information theory, coding, channel coding theorem.

Course description 5

15. Methods of Optimizations

General outline ,basic definitions, linear programming, maximize and minimize problems. Decision making under uncertainty and decision making with multiple objectives. Linear programming and related topics, the simplex algorithm. One-variable case, descent methods, analysis of quadratic objective functions, quadratic-fitting algorithms, nelder-meade algorithm and simulated annealing, constrained minimization.

16. Discrete Mathematics ,

Short description. Digital logic, set theory, proposition logic, conditional statements , valid andinvalid arguments ,graphics, predicate logic, the logic of quantified statements, two classical theorems, algorithms, sequences, mathematical induction, sets, set theory and axion system. Relation function, chain and ring, tree, binomial theorem, Euler graph and Homulton graph.

17. Numerical Analysis

Short . description ,mathematical preliminaries, Taylor’s Theorm, orders of convergence ,computer arithmetic, floating-point numbers and errors, stable and unstable computations conditioning. Solution of nonlinear equations, bisection (Interval Halving Method, Newton’s Method, Secant Method), fixed points. and functional iteration,computing roots of polynomials. Homotopy and continuation methods. Solving systems of linear equations, matrix algebra, LU and Cholesky factorizations, pivoting and constructing an algorithm,norms and the analysis of errors, neumann Series and iterative refinement,analysis of roundoff error in the Gaussian algorithm. Selected topics in numerical linear algebra, QR-algorithm of francis for the eigenvalue problem,approximating functions, Hermite interpolation, spline interpolation,Taylor series,interpolatlon in higher dimensions,continued fractions, adaptive approximation, Gaussian quadrature, Romberg integration,Bernoulli polynomials and the Euler-Maclaurin formula,numeriral solution ot ordinary differential equations. Runge-Kutta methods, multistep methods,boundary-value problems,linear differential equations.

18.Data structure

Short description, programming languages, object oriented programming, basic concepts and experiences. Advanced concepts and techniques, multi-threaded programming, basic mathematical techniques, recurrence equations, algorithm analysis. Fundamental algorithms and data structures, lists, queues, stacks, search and sorting, binary trees. Advanced algorithms and data structures, specialized tree data structures, tree search, graphs, search, order.

Course description 4

11. Probability & Statistics
Short description, sample space and axiomatic definition of a probability measure. Probabilistic models of the real line. Conditional probability and independence. Random variables and probability distributions. Main discrete and continuous random variables. Expectation, moments and characteristic functions. Independence of random variables. Multidimensional gaussian laws. Different kinds of convergence of sequences of random variables. Law of Large Numbers and Central Limit Theorem.
12. Mathematical Modeling
Short description, Modeling process , Modeling Change , the elementary grade model, stability model. simulation modeling, discrete probabilistic modeling, graphs of functions as modeling and examples.

13. Matlab 1
Short description, introduction to the fundamentals of MATLAB functions and programming, the class proceeds to address the mainstream areas of image processing. Compiler, a new function was written and documented, M-files, code optimization. Cell arrays and structure, visualizing data and function, notebook, M-functions, generating and plotting image histograms etc..
14. Database Management System
Short description, brief introduction to data models and formal languages for databases , how to develop server-side and client-side database applications and analyze business intelligence data. All of the brand-new features, Reporting Services, Integration Services, Notification Services, and Service Broker, create custom management scripts with SQLCMD, and improve performance with SQL Profiler, relation data theories, database design. Using SQL both as a query and data manipulation language, designing and querying databases, Entity-Relationship.

Course description 3

8. Analytical Mathematics (Calculus)
Short description, basics of logic and set theory. Real numbers numerical sequences and series,cartesian coordinates. Differential and integral calculus for real functions of several variables, limits, continuity, partial derivatives, gradient, differential, implicit functions and Parametric curves, curvilinear integrals of scalar fields. Multiple integrals, parametric surfaces and surface integrals, differential forms and conservative fields. Gauss, Green, and Stokes theorems. Sequences and series of functions, pointwise and uniform convergences. Fourier series of periodic functions. Euler formula. Real functions, derivatives and differentiation rules, properties of differentiable functions on intervals, searching maxima and minima, differential. Taylor polynomial and Taylor formula. Convex functions, qualitative study of the graph of a function. Riemann proper integral. Fundamental Theorem of Calculus. Integration methods. Cauchy problem, existence and uniqueness, continuous dependence on data, regularity and extension of the solution. Qualitative study of solutions to first order differential equations. phase space, stability analysis in the linear case and in the nonlinear case, Discrete dynamical systems, graphical and qualitative analysis, equilibria and periodic orbits, stability criteria, bifurcation, logistic growth, chaotic phenomena. Analytic functions. Functional analysis. Distributions. Fourier transform, Laplace transform and Z transform.
9. C-Programming Language
Short description , basis concepts , overview of computers and programming , algorithm, data type, expression type, parameter passing among functions, local and global variables and the recursive programming.
10. Ordinary Differential Equations
First order equations, explicit first order equations. The linear differential equation. Implicit first order differential equations, complex differential equations, the higher differential equation power series expansions, upper and lower solutions. Maximal and minimal integrals.

Course description 2

5. Linear Algebra
Polynomial, matrices , binomial ,linear spaces, linear transformations, λ-matrix. Euclid space . Determinant of a square matrix and its properties. Rank of a matrix, inverse matrix, linear systems of equations. Eigenvalues and eigenvectors of a matrix, matrix similitude and diagonal form of a real symmetric matrix. Orthogonal matrix and their basic properties, vector spaces linear dependence and linear independence. Bases and dimension. Linear maps . Matrices related to a linear map, rank and nullity theorem, analytic geometry. Geometric vectors and their algebra. Chauchy-Schwartz Theorem. Straight lines and planes in the space. Parallelism and orthogonality properties. Matrices and determinants. Methods for solving linear systems. Eigenvalues and eigenvectors. Matrix diagonalization. canonical forms.
6.Analytic geometry
Basis concepts of vector and coordinate, locus and equation, plane and space, space line, cylindercal surface, conical surface, revolve surface and quadratic surface. Planar and spatial vectors. Vector space and scalar product. Straight lines and planes. Parallelism and orthogonality. Linear applications. Changes of planar and spatial coordinates. Polar coordinates. Conic sections and quadric surfaces, qualitative study of the graph of a function.
7. General Physics
Short description ,the electric field and magnetic field, electromagnetics, vibrate and undulate, quantum physics.

Course description 1

1.Fundamental Mathematics & Geometry
Basis concepts，equation and systems of equations, function, complex number, inequation, ordered series of numbers, permutation, combination and binomial formula, analytic functions. Functional analysis, vector, space, camber.
2.Fundamental Chemistry
Basis concepts, elements and compounds, chemical formula, mole, simple reactions, stoichiometry. Atomic structure, nucleus, molecules and electrons. The electronic structure of atoms and the periodic system. The chemical bond, ionic bonding, crystal structure and properties of ionic compounds, description of the gaseous state by the ideal-gas equation of state and of solids and liquids by phase diagrams. Chemical thermodynamics, first and second principles of thermodynamics. Application to the calculation of the heat, spontaneity and equilibrium conditions of chemical reactions. The molecular collision model of chemical reactions. Parameters affecting reaction rates. Catalysts, reactions and equilibria in aqueous solutions. Acids, bases and acid-base equilibria . Autoprotolysis of water and the pH. Red-ox reactions. Electrochemical cells, electromotive force, electrolysis.
3. Fundamental Physics
Short description , basis concepts of mechanical vibration and the mechanical wave, thermodynamics, electromagnetics, optics etc..
4. Computer Science
Short description, Introduction to the structure of operating systems with reference to Windows 98, processes description and Microsoft office .Introductory concepts of TCP/IP, Internet. multi-media technique and MPC ,HTML , memory management and virtual memory ,memory and I/O devices interfacing, etc..