language

Maple

SIMULTANEOUS LINEAR EQUATIONS

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Major

Civil

BACKGROUND

Introduction to Matrix Algebra [Complete textbook]

Introduction [PDF] [DOC]

Vectors [PDF] [DOC]

Binary Matrix Operations [PDF] [DOC]

Unary Matrix Operations [PDF] [DOC]

System of Equations [PDF] [DOC]

Test your knowledge of background of simultaneous linear equations [HTML] [PDF] [DOC]

PHYSICAL PROBLEM

How much pressure can a compounded cylinder take? [PDF] [DOC]

NUMERICAL METHOD

GAUSSIAN ELIMINATION METHOD

How does Gaussian Elimination method work? [PDF] [DOC]

Naive Gaussian elimination: Theory: Part 1 of 2 [YOUTUBE 10:27]

Naive Gaussian elimination: Theory: Part 2 of 2 [YOUTUBE 2:22]

Naive Gauss Elimination Method: Example: Part 1 of 2 (Forward Elimination) [YOUTUBE 10:49]

Naive Gauss Elimination Method: Example: Part 2 of 2 (Back Substitution) [YOUTUBE 6:40]

Pitfalls of Naive Gauss Elimination Method: [YOUTUBE 7:20]

Naive Gauss Elimination: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 7:20]

Naive Gauss Elimination: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 7:40]

Naive Gauss Elimination: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 8:07]

Gaussian Elimination With Partial Pivoting: Theory [YOUTUBE 10:39]

Gaussian Elimination With Partial Pivoting: Example: Part 1 of 3 (Forward Elimination) [YOUTUBE 7:15]

Gaussian Elimination With Partial Pivoting: Example: Part 2 of 3 (Forward Elimination) [YOUTUBE 10:08]

Gaussian Elimination With Partial Pivoting: Example: Part 3 of 3 (Back Substitution) [YOUTUBE 6:18]

Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 8:58]

Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 8:17]

Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 5:48]

Determinant of a Matrix Using Forward Elimination Method: Background [YOUTUBE 5:17]

Determinant of a Matrix Using Forward Elimination Method: Example [YOUTUBE 10:07]

A Power point presentation on Gaussian Elimination [PDF] [PPT]

Worksheet of Gaussian Elimination [PDF] [MWS]

Test your knowledge of Gaussian Elimination [HTML] [PDF] [DOC]

LU DECOMPOSITION

How does LU Decomposition work? [PDF] [DOC]

LU Decomposition: Basis [YOUTUBE 9:02]

LU Decomposition Method: Example  [YOUTUBE 10:29]

Why LU Decomposition:  Part 1 [YOUTUBE 4:58] 

Why LU Decomposition:  Part 2 [YOUTUBE 8:05]

Decomposing a Square Matrix:  Part 1 of 2 [YOUTUBE 6:56]

Decomposing a Square Matrix:  Part 2 of 2 [YOUTUBE 4:37]

Finding Inverse of a Matrix Using LU Decomposition: Background [YOUTUBE 6:03] 

Finding Inverse of a Matrix Using LU Decomposition: Example [YOUTUBE 10:20]

A Power point presentation on LU Decomposition method [PDF] [PPT]

Worksheet of LU Decomposition method [PDF] [MWS]

Test your knowledge of LU Decomposition [HTML] [PDF] [DOC]

GAUSS SEIDEL METHOD

How does Gauss-Seidel method work? [PDF] [DOC]

A Power point presentation on Gauss-Seidel method [PDF] [PPT]

Worksheet of Gauss-Seidel method [PDF] [MWS]

Convergence worksheet of Gauss-Seidel method [PDF] [MWS]

Test your knowledge of Gauss-Seidel Method [HTML] [PDF] [DOC]

ANECDOTES

Effect of significant digits on solution of equations

     Textbook notes [PDF] [DOC] | worksheet [PDF] [MWS]

Saving of computational time for finding inverse of a matrix using LU decomposition

      Textbook notes [PDF] [DOC] | worksheet [PDF] [MWS] 

Adequacy of Solutions

      Textbook notes [PDF] [DOC] | worksheet [PDF] [MWS]

Eigenvalues and Eigenvectors [DOC] [PDF]

Gauss [HTML] [PDF] [DOC]

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