應用泛涵分析二   (88年度 下學期)

             N=新數館   Ns=新數館討論室   O=舊數館

應用泛涵分析（一） Chapter 1. Sources of Functional Analysis and Preliminaries 1. Iteration method for Cauchy problem of ODE. Metric space. Banach contraction principle 2. Separation of variables. Fourier series. Spaces l2 and L2 3. Sturm-Liouville problem and integral equations. 4. Calculus of variations. Euler-Lagrange equation. Convexity. 5. Approximation methods. 6. Elementary distribution theory and Green's functions. 7. Compact sets in metric space. Chapter 2. Hilbert Spaces 1. Orthogonal projections. Orthonormal basis. Bessel inequality. Fourier expansion. Sequential weak compactness. 2. Riesz representation theorem. Energy space of positive definite quadratic functionals. Sobolev spaces. 3. Minimization of positive definite quadratic functionals. Dirichlet priuciple. 4. Spectral theory for positive operators and Sturm-Liouville problem. 5. Spectral theory for completely continuous operators and integral equations of Fredholm type. Chapter 3. Banach spaces 1. Normed vector spaces. Hahn-Banach theorem. Separation theorems. 2. Uniform boundedness principle. Open mapping principle. Closed graph theorem. Closed operators. Differential operators. 3. Completely continuous operators. Fredholm alternative theorem. 4. Operators of potential type. Applications. 5. Spectral theorem for bounded linear operators. 6. Compact maps. Schauder principle. 應用泛涵分析（二） Chapter 4. Topics on spectral theory for differential operators. Chapter 5. Topics on Sobolev spaces and finite elements method for elliptic boundary value problem. Chapter 6. Topics on convex analysis and applications.

參考書籍 1. R.Courant & D. Hilbert, Methods of Mathematical Physics, Vol. I. 2. D. H. Griffel, Applied Functional Analysis. 3. A. Wouk, A Course of Applied Fucntional Analysis.