Homogeneous Linear Systems
1 hr 53 min 10 Examples
- Overview of Linear Systems, Matrices, and Writing Systems in Matrix Form (Examples #1-2)
- Verifying Vector Solutions (Example #3)
- Overview of Solving Linear Systems using Eigenvectors
- Distinct, Real Eigenvalues (Examples #4-6)
- Complex Eigenvalues (Examples #7-8)
- Repeated Eigenvalues (Examples #9-10)
Phase Plane Portraits
30 min 7 Examples
- Overview of Phase Plane Portraits for Linear DE Systems
- Distinct Real Eigenvalues: Saddle, Nodal Source, and Nodal Sink
- Complex Eigenvalues: Center, Spiral Source, and Spiral Sink
- Repeated Roots: Degenerate or Improper Nodes, and Unstable Nodes
- Sketching Phase Plane Trajectories (Examples #1-7)
Chapter Test
54 min 6 Practice Problems
- Writing Linear Systems in Matrix Form (Problems #1a-b)
- Verifying Vector Solutions (Problem #2)
- Finding General Solutions with Repeated Roots (Problem #3)
- Solving IVPs with Distinct Real Roots (Problem #4)
- Finding General Solutions with Complex Roots (Problem #5)
- Sketching Phase Plane Portraits at X(0) (Problems #6a-c)