Linear Algebra for Civil Engineering MATH 4422

Upon successful completion of this course, the student will be able to:

• Demonstrate working familiarity with the basics of matrix algebra:
• Addition and scalar multiplication.
• Matrix multiplication.
• Identity, transpose, adjoint, triangular and row echelon matrices.
• Elementary row operations.
• Similar matrices.
• Solve independent and determinate systems of linear equations using:
• Gauss-Jordan Elimination.
• Inverse matrix techniques.
• Use vector products.
• Apply matrix algebra to investigate truss stability.
• Apply matrix algebra to analyze simple loaded trusses.
• Apply matrix transformations
• Use the Stiffness Matrix method to analyse a loaded planar truss and determine the displacement of the joints under load and all internal axial forces.
• Rotate vectors and matrices and apply this to i) rotating a stress matrix and ii) to transforming between a member local rotated coordinate system to a global coordinate system.
• Calculate the direction of principle stress or a vibrational frequency using eigenvalues and eigenvectors.
• Diagonalize a matrix/system of equations using a similarity transformation.
• Use spreadsheet and other software to numerically analyze linear algebra problems.

Effective as of Winter 2008