**Finite Difference Method (FDM) I** |

Lecture 01 - Motivation and Background |

Lecture 02 - Finite Differencing |

Lecture 03 - Finite Differencing (cont.) |

Lecture 04 - Exercise 1: Laplace Equation |

Lecture 05 - Exercise 2: Poisson Equation |

Lecture 06 - Exercise 3: Heat Diffusion Equation |

Lecture 07 - Lab Tour 1 |

Lecture 08 - Summary: Finite Difference Method (FDM) I |

**Finite Difference Method (FDM) II** |

Lecture 09 - Accuracy, Dispersion |

Lecture 10 - Stability, Example |

Lecture 11 - Exercise 4: Helmholtz Equation |

Lecture 12 - Exercise 5: Capacitance Problem |

Lecture 13 - Exercise 6: Dealing with Instability Issues |

Lecture 14 - Summary: Finite Difference Method (FDM) II |

**Finite Difference Method (FDM) III** |

Lecture 15 - Maxwell PDE System |

Lecture 16 - Maxwell FDTD System |

Lecture 17 - Maxwell FDFD System |

Lecture 18 - Exercise 7: Maxwell Equations |

Lecture 19 - Exercise 8: Modeling Examples for Maxwell Equations |

Lecture 20 - Summary: Finite Difference Method (FDM) III |

**Boundary Conditions** |

Lecture 21 - Introduction to Boundary Conditions |

Lecture 22 - Absorbing Boundary Conditions (ABCs) |

Lecture 23 - Berenger's Perfectly Matched Layer |

Lecture 24 - Modeling Practical Electromagnetic Problems using ABCs |

Lecture 25 - Domain Truncation Techniques |

Lecture 26 - Solving Maxwell Equations |

Lecture 27 - Exercise 9: MATLAB Model |

Lecture 28 - Lab Tour 2 |

Lecture 29 - Summary: Boundary Conditions |

**Variational Methods** |

Lecture 30 - Background, Calculus of Variations |

Lecture 31 - Calculus of Variations |

Lecture 32 - Rayleigh-Ritz Method |

Lecture 33 - Method of Weighted Residuals |

Lecture 34 - Exercise 10: Rayleigh-Ritz Method |

Lecture 35 - Summary: Variational Methods |

**Finite Element Method (FEM) I** |

Lecture 36 - Background, FEM from Weighted Residuals |

Lecture 37 - Formulation (Basis Function, Mapping) |

Lecture 38 - Poisson Equation |

Lecture 39 - Time Domain FEM (FETD) |

Lecture 40 - Exercise 11: Capacitor Problem |

Lecture 41 - Summary: Finite Element Method (FEM) I |

**Finite Element Method (FEM) II** |

Lecture 42 - Exercise 12: Coaxial Cable Problem |

Lecture 43 - Exercise 13: Simple Coaxial Capacitor |

Lecture 44 - Exercise 14: Coaxial Capacitor - High Order Approach |

Lecture 45 - Exercise 15: PDE Tool |

Lecture 46 - Exercise 16: PDE Tool (cont.) |

Lecture 47 - Exercise 17: Dealing with Unstructured Grid - Triangular Domain |

Lecture 48 - Summary: Finite Element Method (FEM) II |

**Method of Moment (MoM)** |

Lecture 49 - Background, Theoretical Aspects of Method of Moments |

Lecture 50 - Green's Function, Incident and Radiated Field, Pocklington Integral Equation |

Lecture 51 - Galerkin Method, Integral Equation to Matrix Form |

Lecture 52 - Exercise 18: Capacitance Problem |

Lecture 53 - Exercise 19: Problem of Characteristic Impedance of a Transmission Line |

Lecture 54 - Lab Tour 3 |

Lecture 55 - Summary: Method of Moment (MoM) |

**Finite Volume Time Domain (FVTD) Method I and II** |

Lecture 56 - Motivation and Background |

Lecture 57 - Background Derivation of Eigenvalue Equation |

Lecture 58 - Discretization, Maxwell Equation |

Lecture 59 - Flux Calculation |

Lecture 60 - Flux Calculation (cont.) |

Lecture 61 - Domain Truncation |

Lecture 62 - Lab Tour 4 |

Lecture 63 - Summary: Finite Volume Time Domain Method (FVTD) I |

**Finite Volume Time Domain (FVTD) Method III** |

Lecture 64 - Domain Truncation Techniques |

Lecture 65 - Applications of Domain Truncation Techniques |

Lecture 66 - Domain Truncation Techniques: Applications to Antennas |

Lecture 67 - Fundamental Limitations of FVTD Method |

Lecture 68 - Exercise 20: Finite Volume Time Domain (FVTD) Method |

Lecture 69 - Lab Tour 5 |

Lecture 70 - Summary: Finite Volume Time Domain (FVTD) Method II |

**Algebraic Topological Method (ATM) I** |

Lecture 71 - Introduction and Motivation |

Lecture 72 - Theoretical Background |

Lecture 73 - Some of Topological Aspects |

Lecture 74 - Cochains |

Lecture 75 - Boundary Operator |

Lecture 76 - Summary: Algebraic Topological Method (ATM) I |

**Algebraic Topological Method (ATM) II, Mimetic Method** |

Lecture 77 - Space Orientations |

Lecture 78 - Time Orientation |

Lecture 79 - Mimetic (Finite Difference) Method |

Lecture 80 - Exercise 21: Algebraic Topological Method |

Lecture 81 - Exercise 22: Conical Capacitor Problem using ATM |

Lecture 82 - Summary: Algebraic Topological Method |