### Class Supplements and Research Notes

The following documents are all PDF files. They were written for class use or research projects.

There is no warranty against mistakes in these documents! Use them at your own risk.

There is no specific copyright information in the individual files, but they may all be considered to be licensed as follows:

Class supplements by Kenneth H. Carpenter are licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.

Permissions beyond the scope of this license may be available. Send requests to khc at ksu.edu.

#### Mathematics -

- A Short Introduction to Matrices and Vectors
- Supplemental Notes on Basic Matrices and Determinants
- Solving equations - Gaussian elimination example
- Lagrange Multipliers for Quadratic Forms With Linear Constraints
- Tensor Analysis

#### Circuits -

- Matrix fundamentals for circuit analysis (1974)
- Using Implicit Differentiation for Sensitivity Analysis of Electric Circuits
- 3-phase relationships
- Example of phasor diagram
- Proof of Norton's Theorem
- Example of using SPICE for transmission line with pulse input
- Transmission lines as two-port networks
- Transmission line equations in phasor form
- Standing wave ratio nomograph for square law detectors

#### Electronics -

- Notes On Semiconductor Physics for Electron Devices
- A Short SPICE Tutorial for Students of Electronics

#### Electromagnetic theory -

- The equations of wave motion
- Plane waves in arbitrary directions
- Derivation of vector identities using Cartesian tensors
- On the derivation of curl formulas
- Motion of charges with relativistic energies
- Torque on a current loop
- Line integrals
- Field of a Finite Line Charge
- Symmetry definitions and supplemental problems on symmetry and Gauss's law
- Finding fields by solving Laplace's equation
- Dipoles and Dielectrics
- Magnetic Dipoles and Magnetic Materials
- Continuity of fields across material boundarys
- Electromagnetic potentials for time varying fields
- emf of a spinning loop in a magnetic field
- The Poynting vector
- The Distortionless Transmission Line in the Time Domain

#### Computer graphics -

- Computer Graphics Hardware
- Partial Derivatives for Computer Graphics
- The Affine Group of Transformations
- Rotation Matrices Made Easy
- A General Rotation Matrix
- A simple derivation of Bresenham's algorithm
- The Midpoint Ellipse Algorithm
- An introduction to interpolation and splines
- B-Splines
- Stereoscopic viewing and hardware