Table of Contents
Unit: Matrices and Vectors
Matrix Manipulations (45 minutes)
- Review of matrix manipulations (Lecture, 45 minutes)
Introduction to Bra-ket notation (15 minutes)
- Introduction to bra-ket notation (Lecture, ?? minutes) -
Emphasize normalization and finding components. Add a good SWBQ or small group activity.
Unit: Operators and Transformations in Linear Systems
Linear Transformations (1 1/2 hr)
- Linear Transformations Activity (Small Group Activity)
Tangible Metaphor for Complex Vectors (10 minutes)
- Visualizing Complex Two Component Vectors (Kinesthetic Activity)
Properties of Linear Vector Spaces (30 min)
- Properties of linear vector spaces (Optional Lecture, ?? minutes)
Inner Products and Norms
- Calculating Inner Products and Normalization of Vectors (Lecture, ?? minutes)
Write these lecture notes. Emphasize complex vectors.
Matrix Components (40 min)
- Finding Matrix Elements (Small Group Activity) Work in comments about Fourier series into wrap-up.
Rotation Matrices in 2 and 3 Dimensions (10 min)
- Rotation Matrices in 2 and 3 Dimensions (Lecture, ?? minutes).
Unit: Eigenvalues and Eigenvectors
Eigenvalues & Eigenvectors (2 hr)
- Eigenvectors and Eigenvalues Activity (Small Group Activity)
Special Properties of Hermitian Matrices (40 min)
- Properties of Hermitian matrices (Lecture, ?? minutes)
- Diagonalization of matrices (Lecture, ?? minutes)
- Diagonalizing Matrices (Small Group Activity).
Commuting Matrices (10 min)
- Properties of commuting matrices (Lecture, ?? minutes)
