Table of Contents

## PH 427 (Periodic Systems) Math Bits

[Overall note from Paul for next year: find new SWBQ and activities, especially for Fourier Transform content, there is too much lecture here.]

### Unit: More Complex Numbers/Theta and Delta Functions

#### Complex Numbers

- Reading/Lecture: Powers and Roots (Lecture: 25 min)

#### Theta and Delta Functions

- Reading/Lecture: Step Functions (Lecture: 10 min)
- Theta Functions (SWBQ: 10 min)
- Reading/Lecture: Delta Functions (Lecture: 10 min)
- Reading/Lecture: Plane Wave Normalization (Lecture: 10 min)

### Unit: More Fourier

#### Fourier Transforms

- Reading/Lecture: Fourier Transforms (Lecture: 10 min)
*Optional*Reading/Lecture: Delta Function Representations (Lecture: 20 min)- Reading/Lecture: - FT of Gaussian (Lecture: 20 min)

### Unit: More Linear Algebra

#### Hermitian Matrices

- Reading/Lecture: Hermitian Matrix Proofs (Lecture: 30 min)
- Projections Operators are Hermitian (SWBQ: 10 min)

#### Unitary Matrices

- Reading/Lecture: Unitary Matrices (Lecture: 5 min)

[Note from Paul: there was some more stuff in the binder but nothing more that we did in class.]

[Note from Paul: The binder and the videos don't seem to match much for what was done in week 3, so I'm leaving this for later.]

#### Diagonalization

- Reading/Lecture: - Coupled Oscillators (Lecture: 20 min)
- Coupled Spring Force (SWBQ: 5 min)