About this Course

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Intermediate Level
Approx. 61 hours to complete
English

Skills you will gain

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

Learner Career Outcomes

40%

started a new career after completing these courses

33%

got a tangible career benefit from this course
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Intermediate Level
Approx. 61 hours to complete
English

Offered by

Placeholder

University of Michigan

Syllabus - What you will learn from this course

Content RatingThumbs Up95%(3,492 ratings)Info
Week
1

Week 1

6 hours to complete

1

6 hours to complete
11 videos (Total 200 min), 2 readings, 1 quiz
11 videos
01.02. Introduction. Linear elliptic partial differential equations - II 13m
01.03. Boundary conditions 22m
01.04. Constitutive relations 20m
01.05. Strong form of the partial differential equation. Analytic solution 22m
01.06. Weak form of the partial differential equation - I 12m
01.07. Weak form of the partial differential equation - II 15m
01.08. Equivalence between the strong and weak forms 24m
01.08ct.1. Intro to C++ (running your code, basic structure, number types, vectors) 21m
01.08ct.2. Intro to C++ (conditional statements, “for” loops, scope) 19m
01.08ct.3. Intro to C++ (pointers, iterators) 14m
2 readings
Help us learn more about you!10m
"Paper and pencil" practice assignment on strong and weak forms2h
1 practice exercise
Unit 1 Quiz30m
Week
2

Week 2

4 hours to complete

2

4 hours to complete
14 videos (Total 202 min)
14 videos
02.01q. Response to a question 7m
02.02. Basic Hilbert spaces - I 15m
02.03. Basic Hilbert spaces - II 9m
02.04. The finite element method for the one-dimensional, linear, elliptic partial differential equation 22m
02.04q. Response to a question 6m
02.05. Basis functions - I 14m
02.06. Basis functions - II 14m
02.07. The bi-unit domain - I 11m
02.08. The bi-unit domain - II 16m
02.09. The finite dimensional weak form as a sum over element subdomains - I 16m
02.10. The finite dimensional weak form as a sum over element subdomains - II 12m
02.10ct.1. Intro to C++ (functions) 13m
02.10ct.2. Intro to C++ (C++ classes) 16m
1 practice exercise
Unit 2 Quiz30m
Week
3

Week 3

7 hours to complete

3

7 hours to complete
14 videos (Total 213 min)
14 videos
03.02. The matrix-vector weak form - I - II 17m
03.03. The matrix-vector weak form - II - I 15m
03.04. The matrix-vector weak form - II - II 13m
03.05. The matrix-vector weak form - III - I 22m
03.06. The matrix-vector weak form - III - II 13m
03.06ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox12m
03.06ct.2. Intro to AWS, using AWS on Windows24m
03.06ct.2c. In-Video Correction3m
03.06ct.3. Using AWS on Linux and Mac OS7m
03.07. The final finite element equations in matrix-vector form - I 22m
03.08. The final finite element equations in matrix-vector form - II 18m
03.08q. Response to a question 4m
03.08ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h) 19m
1 practice exercise
Unit 3 Quiz30m
Week
4

Week 4

5 hours to complete

4

5 hours to complete
17 videos (Total 262 min)
17 videos
04.02. The pure Dirichlet problem - II 17m
04.02c. In-Video Correction 1m
04.03. Higher polynomial order basis functions - I 23m
04.03c0. In-Video Correction 57s
04.03c1. In-Video Correction 34s
04.04. Higher polynomial order basis functions - I - II 16m
04.05. Higher polynomial order basis functions - II - I 13m
04.06. Higher polynomial order basis functions - III 23m
04.06ct. Coding assignment 1 (functions: class constructor to “basis_gradient”) 14m
04.07. The matrix-vector equations for quadratic basis functions - I - I 21m
04.08. The matrix-vector equations for quadratic basis functions - I - II 11m
04.09. The matrix-vector equations for quadratic basis functions - II - I 19m
04.10. The matrix-vector equations for quadratic basis functions - II - II 24m
04.11. Numerical integration -- Gaussian quadrature 13m
04.11ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”) 14m
04.11ct.2. Coding assignment 1 (functions: “assemble_system”) 26m
1 practice exercise
Unit 4 Quiz30m

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