Electromagnetic fields in the presence of inhomogeneous media; separation of variables; analyses of waveguide, cavity, radiation, and scattering problems; numerical methods.

The topics covered in this course are fundamental for graduate students in the area of electromagnetics. This course builds upon undergraduate electromagnetic courses and enables the students to gain an in-depth understanding of fundamental electromagnetic concepts, theorems, and analytical techniques. The course also provides an introduction of numerical techniques that are becoming increasingly important in solving electromagnetic wave problems in complex geometries. Many topics covered in this course are essential for graduate courses in areas such as radio frequency and microwave engineering, antennas, photonics, and space sciences.

- Describe the fundamental principles of electromagnetic wave propagation subject to boundary conditions
- Apply the method of separation of variables in rectangular, cylindrical, and spherical coordinates to solve electromagnetic problems in these geometries
- Determine basic properties of electromagnetic waves in waveguides
- Apply electromagnetic techniques to solve problems that involve open geometries such as radiation and scattering and closed geometries such as cavities.
- Apply analytical and numerical techniques to solve practical engineering problems.

## Topic |
## Percentage of Course |

1. General Principle: a) General principle for solving electromagnetic waves subject to boundary conditions; b) The general concept of the separation of variables approach | 10% |

2. Waveguides: a) Introduction to waveguide devices; b) Apply the separation of variable analyses to solve waveguide problems in rectangular and cylindrical coordinates | 20% |

3. Cavities: a) Introduction and examples of electromagnetic cavities; b) Eigenmodes in electromagnetic cavities; c) Applications | 20% |

4. Scattering and Radiation: a) Introduction of electromagnetic problems in open geometries; b) Separation of variable analyses in spherical coordinates; c) General principle for solving electromagnetic problems that involves scattering and radiation | 20% |

5. Introduction of numerical methods: a) Numerical techniques such as the finite-difference time-domain (FDTD) method; b) Examples and applications | 20% |

6. Applications: a) Apply electromagnetic techniques to solve advanced engineering problems | 10% |

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