Review: Systems of Equations - The traditional initial point for a linear algebra class. We will utilize linear algebra techniques to solve a system of equations.
Review: Matrices and Vectors - A brief introduction to vectors and matrices. We will see arithmetic including matrices and vectors, determinant of a matrix and inverse of a matrix and linearly independent vectors and systems of equations revisited.
Review: Eigenvalues and Eigenvectors- Determining the eigen values and eigen-vectors of a matrix. This matter will be important to solving systems of differential equations.
Systems of Differential Equations - Now we will look at several of the basics of systems of differential equations.
Solutions to Systems - We will see what is included in solving a system of differential equations.
Phase Plane - A brief introduction to the phase portraits and plane.
Real Eigenvalues - Solving systems of differential equations along with real eigen-values.
Complex Eigenvalues - Solving systems of differential equations along with complex eigen-values.
Repeated Eigenvalues- Solving systems of differential equations along with repeated eigen-values
Nonhomogeneous Systems- Solving non-homogeneous systems of differential equations by using undetermined coefficients and variation of parameters
Laplace Transforms - An extremely brief look at how Laplace transforms can be utilized to solve a system of differential equations.
Modeling - Under this section we'll take a rapid look at some extensions of several of the modeling we did in previous section that lead to systems of equations.