Lecture 1  Play Video |
Introduction, Linear Elliptic Partial Differential Equations (Part 1)
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Lecture 2  Play Video |
Introduction, Linear Elliptic Partial Differential Equations (Part 2)
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Lecture 3  Play Video |
Boundary Conditions
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Lecture 4  Play Video |
Constitutive relations
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Lecture 5  Play Video |
Strong Form of the Partial Differential Equation, Analytic Solution
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Lecture 6  Play Video |
Weak Form of the Partial Differential Equation (Part 1)
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Lecture 7  Play Video |
Weak Form of the Partial Differential Equation (Part 2)
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Lecture 8  Play Video |
Equivalence Between the Strong and Weak Forms (Part 1)
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Lecture 9  Play Video |
The Galerkin, or finite dimensional weak form
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Lecture 10  Play Video |
Response to a question
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Lecture 11  Play Video |
Basic Hilbert Spaces (Part 1)
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Lecture 12  Play Video |
Basic Hilbert Spaces (Part 2)
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Lecture 13  Play Video |
FEM for the One Dimensional, Linear Elliptic PDE
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Lecture 14  Play Video |
Response to a question
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Lecture 15  Play Video |
Basis Functions (Part 1)
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Lecture 16  Play Video |
Basis Functions (Part 2)
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Lecture 17  Play Video |
The Bi-Unit Domain (Part 1)
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Lecture 18  Play Video |
The Bi-Unit Domain (Part 2)
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Lecture 19  Play Video |
Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 1)
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Lecture 20  Play Video |
Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 2)
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Lecture 21  Play Video |
The Matrix-Vector Weak Form - I (Part 1)
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Lecture 22  Play Video |
The Matrix-Vector Weak Form - I (Part 2)
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Lecture 23  Play Video |
The Matrix-Vector Weak Form - II (Part 1)
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Lecture 24  Play Video |
The Matrix-Vector Weak Form - II (Part 2)
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Lecture 25  Play Video |
The Matrix-Vector Weak Form - III (Part 1)
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Lecture 26  Play Video |
The Matrix-Vector Weak Form - III (Part 2)
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Lecture 27  Play Video |
The Final Finite Element Equations in Matrix-Vector form (Part 1)
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Lecture 28  Play Video |
The Final Finite Element Equations in Matrix-Vector form (Part 2)
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Lecture 29  Play Video |
Response to a question
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Lecture 30  Play Video |
The Pure Dirichlet Problem (Part 1)
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Lecture 31  Play Video |
The Pure Dirichlet Problem (Part 2)
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Lecture 32  Play Video |
Correction to boardwork
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Lecture 33  Play Video |
Higher Polynomial Order Basis Functions - I
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Lecture 34  Play Video |
Correction to boardwork
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Lecture 35  Play Video |
Higher Polynomial Order Basis Functions - 1 (Part 2)
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Lecture 36  Play Video |
Higher Polynomial Order Basis Functions - II (Part 1)
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Lecture 37  Play Video |
Higher Polynomial Order Basis Functions - III
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Lecture 38  Play Video |
The Matrix Vector Equations for Quadratic Basis Functions - I (Part 1)
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Lecture 39  Play Video |
The Matrix Vector Equations for Quadratic Basis Functions - I (Part 2)
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Lecture 40  Play Video |
The Matrix Vector Equations for Quadratic Basis Functions - II (Part 1)
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Lecture 41  Play Video |
The Matrix Vector Equations for Quadratic Basis Functions - II (Part 2)
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Lecture 42  Play Video |
Numerical Integration -- Gaussian Quadrature
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Lecture 43  Play Video |
Norms (Part 1)
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Lecture 44  Play Video |
Correction to boardwork
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Lecture 45  Play Video |
Norms (Part 2)
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Lecture 46  Play Video |
Response to a question
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Lecture 47  Play Video |
Consistency of the Finite Element Method
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Lecture 48  Play Video |
The Best Approximation Property
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Lecture 49  Play Video |
The "Pythagorean Theorem"
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Lecture 50  Play Video |
Response to a question
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Lecture 51  Play Video |
Sobolev Estimates and Convergence of the Finite Element Method
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Lecture 52  Play Video |
Finite Element Error Estimates
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Lecture 53  Play Video |
Functionals, Free Energy (Part 1)
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Lecture 54  Play Video |
Functionals, Free Energy (Part 2)
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Lecture 55  Play Video |
Extremization of Functionals
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Lecture 56  Play Video |
Derivation of the Weak Form Using a Variational Principle
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Lecture 57  Play Video |
The Strong Form of Steady State Heat Conduction and Mass Diffusion (Part 1)
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Lecture 58  Play Video |
The Strong Form of Steady State Heat Conduction and Mass Diffusion (Part 2)
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Lecture 59  Play Video |
Response to a question
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Lecture 60  Play Video |
The Strong Form, continued
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Lecture 61  Play Video |
Correction to boardwork
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Lecture 62  Play Video |
The Weak Form
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Lecture 63  Play Video |
The Finite Dimensional Weak Form (Part 1)
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Lecture 64  Play Video |
The Finite Dimensional Weak Form (Part 2)
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Lecture 65  Play Video |
Three-Dimensional Hexahedral Finite Elements
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Lecture 66  Play Video |
Aside: Insight to the Basis Functions by Considering the Two-Dimensional Case
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Lecture 67  Play Video |
Field Derivatives: The Jacobian (Part 1)
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Lecture 68  Play Video |
Field Derivatives: The Jacobian (Part 2)
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Lecture 69  Play Video |
The Integrals in Terms of Degrees of Freedom
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Lecture 70  Play Video |
The Integrals in Terms of Degrees of Freedom - Continued
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Lecture 71  Play Video |
The Matrix-Vector Weak Form (Part 1)
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Lecture 72  Play Video |
The Matrix-Vector Weak Form (Part 2)
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Lecture 73  Play Video |
The Matrix-Vector Weak Form, continued (Part 1)
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Lecture 74  Play Video |
Correction to boardwork
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Lecture 75  Play Video |
The Matrix Vector Weak Form, continued (Part 2)
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Lecture 76  Play Video |
The Matrix-Vector Weak Form, continued further (Part 1)
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Lecture 77  Play Video |
Correction to boardwork
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Lecture 78  Play Video |
The Matrix-Vector Weak Form, continued further (Part 2)
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Lecture 79  Play Video |
Correction to boardwork
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Lecture 80  Play Video |
Lagrange Basis Functions in 1 Through 3 Dimensions (Part 1)
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Lecture 81  Play Video |
Lagrange Basis Functions in 1 through 3 dimensions (Part 2)
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Lecture 82  Play Video |
Quadrature Rules in 1 Through 3 Dimensions
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Lecture 83  Play Video |
Triangular and Tetrahedral Elements-Linears (Part 1)
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Lecture 84  Play Video |
Triangular and Tetrahedral Elements Linears (Part 2)
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Lecture 85  Play Video |
The Finite Dimensional Weak Form and Basis Functions (Part 1)
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Lecture 86  Play Video |
The Finite Dimensional Weak Form and Basis Functions (Part 2)
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Lecture 87  Play Video |
The Matrix Vector Weak Form
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Lecture 88  Play Video |
The Matrix Vector Weak Form (Part 2)
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Lecture 89  Play Video |
Correction to boardwork
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Lecture 90  Play Video |
The Strong Form of Linearized Elasticity in Three Dimensions (Part 1)
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Lecture 91  Play Video |
The Strong Form of Linearized Elasticity in Three Dimensions (Part 2)
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Lecture 92  Play Video |
The Strong Form, continued
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Lecture 93  Play Video |
The Constitutive Relations of Linearized Elasticity
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Lecture 94  Play Video |
The Weak Form (Part 1)
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Lecture 95  Play Video |
Response to a Question
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Lecture 96  Play Video |
The Weak Form (Part 2)
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Lecture 97  Play Video |
The Finite-Dimensional Weak Form-Basis Functions (Part 1)
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Lecture 98  Play Video |
The Finite-Dimensional Weak Form-- Basis functions (Part 2)
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Lecture 99  Play Video |
Element Integrals (Part 1)
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Lecture 100  Play Video |
Correction to boardwork
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Lecture 101  Play Video |
Element Integrals (Part 2)
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Lecture 102  Play Video |
The Matrix-Vector Weak Form (Part 1)
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Lecture 103  Play Video |
The Matrix Vector-Weak Form (Part 2)
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Lecture 104  Play Video |
Assembly of the Global Matrix-Vector Equations (Part 1)
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Lecture 105  Play Video |
Assembly of the Global Matrix-Vector Equations II
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Lecture 106  Play Video |
Correction to boardwork
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Lecture 107  Play Video |
Dirichlet Boundary Conditions (Part 1)
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Lecture 108  Play Video |
Dirichlet Boundary Conditions (Part 2)
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Lecture 109  Play Video |
The Strong Form
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Lecture 110  Play Video |
Correction to boardwork
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Lecture 111  Play Video |
The Weak Form, and Finite Dimensional Weak Form (Part 1)
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Lecture 112  Play Video |
The Weak Form, and Finite Dimensional Weak Form (Part 2)
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Lecture 113  Play Video |
Basis Functions, and the Matrix-Vector Weak Form (Part 1)
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Lecture 114  Play Video |
Correction to Boardwork
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Lecture 115  Play Video |
Basis Functions, and the Matrix-Vector Weak Form (Part 2)
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Lecture 116  Play Video |
Response to a question
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Lecture 117  Play Video |
Dirichlet Boundary Conditions; The Final Matrix Vector Equations
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Lecture 118  Play Video |
Time Discretization; The Euler Family (Part 1)
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Lecture 119  Play Video |
Time Discretization; The Euler Family (Part 2)
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Lecture 120  Play Video |
The V-Form and D-Form
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Lecture 121  Play Video |
Integration Algorithms for First-Order, Parabolic, Equations-Modal Decomposition (Part 1)
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Lecture 122  Play Video |
Integration Algorithms for First-Order, Parabolic, Equations-Modal Decomposition (Part 2)
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Lecture 123  Play Video |
Modal Decomposition and Modal Equations (Part 1)
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Lecture 124  Play Video |
Modal Decomposition and Modal Equations (Part 2)
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Lecture 125  Play Video |
Modal Equations and Stability of the Time Exact Single Degree of Freedom Systems (Part 1)
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Lecture 126  Play Video |
Modal Equations and Stability of the Time-Exact Single Degree of Freedom Systems (Part 2)
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Lecture 127  Play Video |
Stability of the Time-Discrete Single Degree of Freedom Systems
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Lecture 128  Play Video |
Behavior of Higher-Order Modes; Consistency (Part 1)
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Lecture 129  Play Video |
Behavior of Higher-Order Modes; consistency (Part 2)
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Lecture 130  Play Video |
Convergence (Part 1)
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Lecture 131  Play Video |
Convergence (Part 2)
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Lecture 132  Play Video |
The Strong and Weak Forms
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Lecture 133  Play Video |
The Finite-Dimensional and Matrix-Vector Weak Forms (Part 1)
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Lecture 134  Play Video |
The Finite-Dimensional and Matri-Vector Weak Forms (Part 2)
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Lecture 135  Play Video |
The Time-Discretized Equations
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Lecture 136  Play Video |
Stability (Part 1)
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Lecture 137  Play Video |
Stability (Part 2)
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Lecture 138  Play Video |
Behavior of High-Order Modes
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Lecture 139  Play Video |
Convergence
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Lecture 140  Play Video |
Correction to boardwork
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