Teaching
I have a license to teach mathematics at the secondary level in the state of Minnesota.
As an instructor for Linear Algebra and Differential Equations, I prepared these PDFs as a review of the sections in Edward and Penney's "Differential Equations and Linear Algebra." It includes example problems which have been worked out in some detail. I hope you find these useful.
1.1 Differential Equations and Mathematical Models1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations
1.5 Linear First-Order Equations
2.1 Mathematical Models and Numerical Methods
2.2 Equilibrium Solutions and Stability
2.3 Acceleration Velocity Models
2.4 Euler Method
2.5 Advanced Euler Method
3.1 & 3.2 Linear Systems
3.3 Reduced Echelon Matrices
3.4 Matrix Operations
3.5 Inverses of Matrices
3.6 Linear Equations and Curve Fitting
3.6 Determinants
4.1 Vector Space
4.2 Subspaces
4.3 Linear Combinations and Independence of Vectors
4.4 Bases and Dimension for Vector Spaces
4.5 Row and Column Spaces
4.5 General Vector Spaces
5.1 Second-Order Linear Equations
5.2 General Solutions of Linear Equations
5.3 Homogeneous Equations with Constant Coefficients
5.4 Mechanical Vibrations
5.5 NonHomogeneous Equations Undetermined Coefficients
5.6 Forced Oscillations and Resonance
6.1 Eigenvalues
6.2 Diagonals of Matrices
6 3 Powers of Matrices
7.1 First-Order Systems
7.2 Matrices and Linear Systems
7.3 Eigenvalue Method for Linear Systems
7.4 Solution Curves Linear Systems
7.5 Second Order Systems and Mechanical Applications
7.6 Multiple Eigenvalue
9.1 Stability Phase Plane
9.2 Linear Systems
9.3 Ecological Models
10.1 Laplace Transform
10.2 Laplace Transformation of Initial Value Problems
10.3 Translation and Partial Fractions