Course Outline
- Matrix Methods for Mechanical Systems
- A Uniaxial Truss
- A Small Planar Truss
- The General Planar Truss
- The Column and Null Spaces
- The Column Space
- The Null Space
- The Fundamental Theorem of Linear Algebra
- The Row Space
- The Left Null Space
- Least Squares
- The Normal Equations
- Applying Least Squares to the Biaxial Test Problem
- Projections
- Matrix Methods for Dynamical Systems
- Nerve Fibers and the Dynamical Strang Quartet
- The Laplace Transform
- The Inverse Laplace Transform
- The Backward Euler Method
- Complex Numbers and Functions
- Complex Numbers, Vectors, and Matrices
- Complex Functions
- Complex Differentiation
- Complex Integration
- Cauchy's Theorem
- The Residue Theorem
- The Inverse Laplace Transform
- The Eigenvalue Problem
- The Transfer Function
- Partial Fraction Expansion
- The Spectral Representation
- The Characteristic Polynomial
- The Spectral Representation of a Symmetrix Matrix
- The Spectral Representation
- Gram-Schmidt Orthogonalization
- The Diagonalization of a Symmetric Matrix