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Notice

| | Comments (1)
July 17 6:00am: Trip to the Forbidden City

July 16 9:00am: Final Written Exam

               2:00pm: Special Lecture -- Research Areas in the Math Dept at PSU
                               By Chun Liu

               6:00pm: Group Meal (Yi Yuan Restaurant)

July 15 2:00pm: Final Project Report
Click on Comments to read comments and suggestions from students.

Experience in China

| | Comments (2)
Click on Comments to read more.

Schedule: Fourth Week

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July 14: Truncation error
        (10.3) By Prof. Zhiping Li

July 14 2:00pm Review Session
        By Chensong Zhang

July 15: Convergence analysis
        (10.3) By Prof. Zhiping Li

July 15 2:00pm -- 5:00pm Final Project Report

July 16 9:00am--11:00am: Final Exam
       
July 16 2:00pm: Special Lecture -- some research topics
        By Chun Liu


July 17: Culture activities: The Forbidden City


July 18: Students departure

Schedule: Third Week

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July 7:  Error estimate of the finite difference method
        (7.6) By Xiantao Li

July 8:  Finite difference method for parabolic equations
        (4.1) By Xiantao Li

July 9: Stability analysis of the finite difference methods
        (4.3, 4.4, 4.5) By Xiantao Li

July 10: Finite difference method for the wave equation
        (5.3) By Chensong Zhang

July 10 4:00pm--5:00pm: The Interplay Between Analysis and Algorithms
        By Prof. Ingrid Daubechies

July 10 6:00pm: PSU Students Dinner Party

July 11: Iterative solvers for linear systems
        By Chensong Zhang

July 11: Special Lecture -- some research topics 
        By Chensong Zhang

Schedule: Second Week

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June 30: Green's Function and Two-dimensional elliptic equation
        (7.1, 7.2.1) By Prof. Chun Liu

July 1: Wave Equation
        (5.1, 5.2) By Prof. Chun Liu

July 2: Introduction to finite difference methods
        (2.2, 4.1)  By Chensong Zhang

July 3: Maximum principle and convergence of the finite difference methods
        (2.3) By Xiantao Li

July 4: Finite difference method for two-dimensional elliptic equations
        (7.5) By Xiantao Li

Schedule: First Week

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June 24 (T): Student Arrival

June 25 (W): Activity cancelled due to flight cancelation. 

June 26 (Th): Morning 8:30am (Science I Room 1114) : Orientation 

        Two-point boundary value problem: General solutions and Green's functions 
        (2.1.1, 2.1.2) By Prof. Chun Liu. New Project

June 27 (F): Culture activity (7:55am): the Great Wall

June 28 (Sat): Smoothness and Maximum principle 
        (2.1.3, 6.1) By Prof. Chun Liu
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This special topics course is part of the international undergraduate program organized by Penn State and Peking University.

Summer Program Schedule:

Main topics for the summer program: (37 lectures)

Introduction  (1.1, 1.2, 1.3, 1.4)

Elliptic equations in 1D: Two point boundary value problems
General solutions and the Green's function (2.1.1, 2.1.2)
Smoothness and the maximum principle (2.1.3, 6.1)
A finite difference approximation (2.2.1, 2.2.2)
Gaussian elimination of a tridiagonal system (2.2.3)
The finite difference equation (2.3.1)
The maximum principle and convergence (2.3.4, 2.3.5)

Elliptic equations in 2D: Poisson's equation
General solutions in a rectangular domain (7.1)
General solutions in a disc (7.2.1)
Maximum principle for Harmonic functions (6.4.1)
A finite difference approximation (7.5)
An error estimate (7.6)
Finite element approximation*  (2 lectures)
Solution of the linear system* (2 lectures)

Parabolic equations in 1D: The heat equation
General solutions: separation of variables (3.2)
Fourier coefficients (3.3, 3.4)
Neumann problem (3.6)
Fundamental solutions and the heat kernel*
Energy estimate (3.7)
Maximum principle (6.2.1)
A finite difference scheme (4.1)
Von Neumann stability analysis (4.3.1) (2 lectures)
Numerical stability by energy method (4.5)
Implicit methods (4.4)   
Maximum principle for the difference equation (6.2.3, 6.2.4)
Truncation error (10.3)
Convergence analysis (10.3)

The heat equation in 2D
Finite difference approximation*
Stability analysis*
Finite element method*

Hyperbolic equations in 1D: the wave equation
General solutions: separation of variables (5.1)
Energy estimate (5.2)
Finite difference scheme (5.3)
Stability analysis (5.3.1)

September 2010

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