Course Modules

1 Classification of PDEs

1 Classification of PDEs
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1 Classification of PDEs 560138  
  • Context Module Sub Header
    Lecture 1: Classification of PDEs
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    Skeleton-Notes-Lecture1.pdf Skeleton-Notes-Lecture1.pdf
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    Notes-Lecture1.pdf Notes-Lecture1.pdf
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  • Attachment
    Mysterious PDE (video) Mysterious PDE (video)
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    HW 1 HW 1
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2 Second-Order Elliptic Equations

2 Second-Order Elliptic Equations
Module Completed Module In Progress Module Locked
2 Second-Order Elliptic Equations 560139  
  • Context Module Sub Header
    Lecture 2: Elliptic maximum principle
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  • Page
    Pre-class video by Timm: An elliptic maximum principle Pre-class video by Timm: An elliptic maximum principle
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  • Attachment
    Skeleton-Notes-Lecture2.pdf Skeleton-Notes-Lecture2.pdf
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    Notes-Lecture2.pdf Notes-Lecture2.pdf
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  • Context Module Sub Header
    Lecture 3: From strong solutions to weak solutions
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  • Page
    Pre-class video by Timm: Poisson's Equation in Strong and Weak Form Pre-class video by Timm: Poisson's Equation in Strong and Weak Form
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    Skeleton-Notes-Lecture3.pdf Skeleton-Notes-Lecture3.pdf
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    Notes-Lecture3.pdf Notes-Lecture3.pdf
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  • Context Module Sub Header
    Lecture 4: Well posedness of weak formulations
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  • Page
    Pre-class video by Timm: Poincare's inequality Pre-class video by Timm: Poincare's inequality
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    Skeleton-Notes-Lecture4.pdf Skeleton-Notes-Lecture4.pdf
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    Notes-Lecture4.pdf Notes-Lecture4.pdf
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    HW 2 HW 2
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  • Context Module Sub Header
    Lecture 5: Finite Differences for Poisson's equation
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  • Page
    Pre-class video by Timm: Finite Differences for Poisson's Equation in 1D Pre-class video by Timm: Finite Differences for Poisson's Equation in 1D
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    Skeleton-Notes-Lecture5.pdf Skeleton-Notes-Lecture5.pdf
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    Notes-Lecture5.pdf Notes-Lecture5.pdf
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    HW 3 HW 3
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  • Context Module Sub Header
    Lecture 6: Conditiong of linear systems from Finite-Difference methods
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    Pre-class video by Timm: Diagonal dominance Pre-class video by Timm: Diagonal dominance
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    Skeleton-Notes-Lecture6.pdf Skeleton-Notes-Lecture6.pdf
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    Notes-Lecture6.pdf Notes-Lecture6.pdf
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    HW 4 HW 4
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  • Context Module Sub Header
    Lecture 7: Finite Element for the Poisson's equation
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  • Page
    Pre-class video by Timm: Best approximatiom theorem Pre-class video by Timm: Best approximatiom theorem
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    Skeleton-Notes-Lecture7.pdf Skeleton-Notes-Lecture7.pdf
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    Notes-Lecture7.pdf Notes-Lecture7.pdf
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  • Context Module Sub Header
    Lecture 8: Linear Finite Element
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    Skeleton-Notes-Lecture8.pdf Skeleton-Notes-Lecture8.pdf
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    Notes-Lecture8.pdf Notes-Lecture8.pdf
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  • Context Module Sub Header
    Lecture 9: Quadrature formulas
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    Skeleton-Notes-Lecture9.pdf Skeleton-Notes-Lecture9.pdf
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  • Page
    Post-class video with Timm: Data Structure for Triangulated Domains Post-class video with Timm: Data Structure for Triangulated Domains
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    Post-class video by Timm: Unisolvence Post-class video by Timm: Unisolvence
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    Notes-Lecture9.pdf Notes-Lecture9.pdf
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    HW 5 HW 5
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  • Assignment
    HW 6 HW 6
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  • Context Module Sub Header
    Lecture 10: General A Priori Error Analysis of Galerkin Methods
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    Skeleton-Notes-Lecture10.pdf Skeleton-Notes-Lecture10.pdf
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    Notes-Lecture10.pdf Notes-Lecture10.pdf
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  • Context Module Sub Header
    Lecture 11: Interpolation with Finite Elements
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    Skeleton-Notes-Lecture11.pdf Skeleton-Notes-Lecture11.pdf
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    Notes-Lecture11.pdf Notes-Lecture11.pdf
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    HW 7 HW 7
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  • Context Module Sub Header
    Lecture 12: Error estimates: FE versus FD
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    Skeleton-Notes-Lecture12.pdf Skeleton-Notes-Lecture12.pdf
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    Notes-Lecture12.pdf Notes-Lecture12.pdf
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  • Context Module Sub Header
    Lecture 13: Boundary Approximations on Non-Polygonal Domains
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  • Page
    Pre-class video by Timm: Parametric and Isoparametric Elements Pre-class video by Timm: Parametric and Isoparametric Elements
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    Skeleton-Notes-Lecture13.pdf Skeleton-Notes-Lecture13.pdf
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    Notes-Lecture13.pdf Notes-Lecture13.pdf
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  • Context Module Sub Header
    Lecture 14: A Posteriori Error Analysis and Adaptive Finite Elements
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    Pre-class video by Timm: A Priori vs A Posteriori Error Estimates Pre-class video by Timm: A Priori vs A Posteriori Error Estimates
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    Skeleton-Notes-Lecture14.pdf Skeleton-Notes-Lecture14.pdf
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    Notes-Lecture14.pdf Notes-Lecture14.pdf
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    aPosteriori.py aPosteriori.py
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    adaptivePoisson.ipynb adaptivePoisson.ipynb
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    adaptivePoisson.py adaptivePoisson.py
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    aPosteriori.ipynb aPosteriori.ipynb
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  • Context Module Sub Header
    Lecture 15: The Method of Manufactured Solutions
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    Skeleton-Notes-Lecture15.pdf Skeleton-Notes-Lecture15.pdf
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    Notes-Lecture15.pdf Notes-Lecture15.pdf
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    transport.py transport.py
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    transport.ipynb transport.ipynb
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    convergence_tofill.xlsx convergence_tofill.xlsx
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    convergence.xlsx convergence.xlsx
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  • Assignment
    HW 8 HW 8
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3 Second-Order Parabolic Equations

3 Second-Order Parabolic Equations
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  • Context Module Sub Header
    Lecture 16: Characteristic features
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    Skeleton-Notes-Lecture16.pdf Skeleton-Notes-Lecture16.pdf
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    Notes-Lecture16.pdf Notes-Lecture16.pdf
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  • Context Module Sub Header
    Lecture 17: Finite Element for the heat equation - Time-stepping methods Part I
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    Skeleton-Notes-Lecture17.pdf Skeleton-Notes-Lecture17.pdf
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    Notes-Lecture17.pdf Notes-Lecture17.pdf
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  • Assignment
    HW 9 HW 9
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  • Context Module Sub Header
    Lecture 18: Finite Element for the heat equation - Time-stepping methods Part II
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    Skeleton-Notes-Lecture18.pdf Skeleton-Notes-Lecture18.pdf
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    Notes-Lecture18.pdf Notes-Lecture18.pdf
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  • Context Module Sub Header
    Lecture 19: Space-time discretization - additional comments
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    Skeleton-Notes-Lecture19.pdf Skeleton-Notes-Lecture19.pdf
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    Notes-Lecture19.pdf Notes-Lecture19.pdf
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4 Second-Order Hyperbolic Equations

4 Second-Order Hyperbolic Equations
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  • Context Module Sub Header
    Lecture 20: The wave equation
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  • Page
    Pre-class video by Timm: Solving Hamiltonian Systems with Symplectic Runge-Kutta Methods Pre-class video by Timm: Solving Hamiltonian Systems with Symplectic Runge-Kutta Methods
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    Skeleton-Notes-Lecture20.pdf Skeleton-Notes-Lecture20.pdf
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    Notes-Lecture20.pdf Notes-Lecture20.pdf
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  • Attachment
    4.2.1 standingWave.mp4 4.2.1 standingWave.mp4
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    4.2.1 travellingWave.mp4 4.2.1 travellingWave.mp4
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    4.2.1 travellingWave2.mp4 4.2.1 travellingWave2.mp4
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  • Assignment
    HW 10 HW 10
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5 Conservation equations

5 Conservation equations
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5 Conservation equations 560142  
  • Context Module Sub Header
    Lecture 21: The transport term
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    Skeleton-Notes-Lecture21.pdf Skeleton-Notes-Lecture21.pdf
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    Notes-Lecture21.pdf Notes-Lecture21.pdf
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  • Context Module Sub Header
    Lecture 22: DG for the diffusion term and operator-splitting methods
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    Skeleton-Notes-Lecture22.pdf Skeleton-Notes-Lecture22.pdf
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    Notes-Lecture22.pdf Notes-Lecture22.pdf
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  • Attachment
    OnOperatorSplittingMethods.pdf OnOperatorSplittingMethods.pdf
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minimum score must view must submit must contribute