教學目標、、授課方式、課程進度及綱要、參考書籍及評分方式等內容。

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教學目標:

使學生知悉數學分析的方法與理論及其應用至微分方程與數值分析技巧，發展系列工具，使學生能以漸進及級數方法來算近似值。

課程範圍:

基礎課程包含微積分、高等微積分、線性代數、多變數分析技巧、 metric space, inner product space, Hilbert space, Sobelov space, Lp space.

授課方式:

課堂講授與實習

課程進度及綱要:

1. Quadratic functions on finite-dimensional vector space 2. Variational formulation of boundary value problems 3. The Ritz-Galerkin method

4. The finite element method

5. Finite element method with trigonometric functions

6. The trigonometric functions and ordinary differential equations 7. The Fourier series expansions of differential equations

8. The Fourier integrals

9. Integral operator and its applications to partial differential equations 10. The singular integral operators

11. Finite element series

參考書籍:

Finite Element Solution of Boundary Value Problems By O. Axelsson and V. A. Barker

評分方式:

期中作業6 次，學期報告乙次，作業及報告評分平均分配學期分數。