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## 50%

### 您将获得的技能

Finite DifferencesC++C Sharp (C#) (Programming Language)Matrices

1

## 1

11 个视频 （总计 200 分钟）, 2 个阅读材料, 1 个测验
11 个视频
01.02. Introduction. Linear elliptic partial differential equations - II 13分钟
01.03. Boundary conditions 22分钟
01.04. Constitutive relations 20分钟
01.05. Strong form of the partial differential equation. Analytic solution 22分钟
01.06. Weak form of the partial differential equation - I 12分钟
01.07. Weak form of the partial differential equation - II 15分钟
01.08. Equivalence between the strong and weak forms 24分钟
01.08ct.1. Intro to C++ (running your code, basic structure, number types, vectors) 21分钟
01.08ct.2. Intro to C++ (conditional statements, “for” loops, scope) 19分钟
01.08ct.3. Intro to C++ (pointers, iterators) 14分钟
2 个阅读材料
"Paper and pencil" practice assignment on strong and weak forms2小时
1 个练习
Unit 1 Quiz8分钟
2

## 2

14 个视频 （总计 202 分钟）
14 个视频
02.01q. Response to a question 7分钟
02.02. Basic Hilbert spaces - I 15分钟
02.03. Basic Hilbert spaces - II 9分钟
02.04. The finite element method for the one-dimensional, linear, elliptic partial differential equation 22分钟
02.04q. Response to a question 6分钟
02.05. Basis functions - I 14分钟
02.06. Basis functions - II 14分钟
02.07. The bi-unit domain - I 11分钟
02.08. The bi-unit domain - II 16分钟
02.09. The finite dimensional weak form as a sum over element subdomains - I 16分钟
02.10. The finite dimensional weak form as a sum over element subdomains - II 12分钟
02.10ct.1. Intro to C++ (functions) 13分钟
02.10ct.2. Intro to C++ (C++ classes) 16分钟
1 个练习
Unit 2 Quiz6分钟
3

## 3

14 个视频 （总计 213 分钟）
14 个视频
03.02. The matrix-vector weak form - I - II 17分钟
03.03. The matrix-vector weak form - II - I 15分钟
03.04. The matrix-vector weak form - II - II 13分钟
03.05. The matrix-vector weak form - III - I 22分钟
03.06. The matrix-vector weak form - III - II 13分钟
03.06ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox12分钟
03.06ct.2. Intro to AWS, using AWS on Windows24分钟
03.06ct.2c. In-Video Correction3分钟
03.06ct.3. Using AWS on Linux and Mac OS7分钟
03.07. The final finite element equations in matrix-vector form - I 22分钟
03.08. The final finite element equations in matrix-vector form - II 18分钟
03.08q. Response to a question 4分钟
03.08ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h) 19分钟
1 个练习
Unit 3 Quiz6分钟
4

## 4

17 个视频 （总计 262 分钟）
17 个视频
04.02. The pure Dirichlet problem - II 17分钟
04.02c. In-Video Correction 1分钟
04.03. Higher polynomial order basis functions - I 23分钟
04.03c0. In-Video Correction 57
04.03c1. In-Video Correction 34
04.04. Higher polynomial order basis functions - I - II 16分钟
04.05. Higher polynomial order basis functions - II - I 13分钟
04.06. Higher polynomial order basis functions - III 23分钟
04.06ct. Coding assignment 1 (functions: class constructor to “basis_gradient”) 14分钟
04.07. The matrix-vector equations for quadratic basis functions - I - I 21分钟
04.08. The matrix-vector equations for quadratic basis functions - I - II 11分钟
04.09. The matrix-vector equations for quadratic basis functions - II - I 19分钟
04.10. The matrix-vector equations for quadratic basis functions - II - II 24分钟
04.11. Numerical integration -- Gaussian quadrature 13分钟
04.11ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”) 14分钟
04.11ct.2. Coding assignment 1 (functions: “assemble_system”) 26分钟
1 个练习
Unit 4 Quiz8分钟

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• You will need computing resources sufficient to install the code and run it. Depending on the type of installation this could be between a 13MB download of a tarred and gzipped file, to 45MB for a serial MacOSX binary and 192MB for a parallel MacOSX binary. Additionally, you will need a specific visualization program that we recommend. Altogether, if you have 1GB you should be fine. Alternately, you could download a Virtual Machine Interface.

• You will be able to write code that simulates some of the most beautiful problems in physics, and visualize that physics.

• You will need to know about matrices and vectors. Having seen partial differential equations will be very helpful. The code is in C++, but you don't need to know C++ at the outset. We will point you to resources that will teach you enough C++ for this class. However, you will need to have done some programming (Matlab, Fortran, C, Python, C++ should all do).

• Apart from the lectures, expect to put in between 5 and 10 hours a week.