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Farhad Azadi Namin
  Courses 

 Differential Equations(SPRING_2018)

Aims:

This course provides an introduction to topics involving ordinary differential equations. Emphasis is placed on the development of abstract concepts and applications for first-order and linear higher-order differential equations, systems of differential equations, series solutions, eigenvalues and eigenvectors, and Laplace transforms. Upon completion, students will be able to demonstrate understanding of the theoretical concepts and select and use appropriate models and techniques for finding so

Syllabus:

  • Initial value problems, boundary value problems. Eigenvalues and eigenfunctions
  • First order linear differential equations
  • Homogeneous constant coefficient differential equations
  • Power series solution of linear differential equations
  • Legendre and Bessel differential equations
  • Laplace transform and its properties
  • Impulse function and convolution theorem
  • Introduction and Basic Definitions
  • Special Types of First Order Equations
  • Methods for reduction of order
  • Linear non-homogeneous differential equations
  • Cauchy-Euler differential equation
  • Differential and inverse differential operators
  • Systems of differential equations
  • Separable and homogeneous differential equations
  • Exact differential equations and integrating factors

Text Book:

  • Elementary Differential Equations and Boundary Value Problems


 Metamaterials(SPRING_2018)

Aims:

The aim of this course is to introduce and discuss the groundbreaking and recent developments in metamaterials-artificially structured materials with sub-wavelength inclusions and strikingly unconventional electromagnetic properties. The course starts with a brief review of Maxwell’s equations and interaction of light with matter. Next, we discuss the topic of plasmonics and optical properties of metal-dielectric composites. We start our discussion on metamaterials by covering wire media and spl

Syllabus:

  • Localized Surface Plasmons
  • Split Ring Resonator and Artificial Magnetism
  • Electromagnetic waves in layered media
  • Scattering of Waves by Spheres and Coated Spheres
  • Transformation Optics
  • Introduction to light interaction with matter
  • Blochs theorem and waves in periodic media
  • Surface plasmon polariton
  • Wire Media and Low Frequency Plasmons
  • Negative Index Metamaterials
  • Optical Metamaterials
  • Graphene
  • Drude model for dielectric function

Text Book:

  • Optical Metamaterials: Fundamentals and Applications,W. Cai and V. Shalaev,
  • Plasmonics: Fundamentals and Applications, S. Maier


 Probability & Statistics(SPRING_2018)

Aims:

The aim of this course is to introduce the basic concepts of probability theory to students and then move onto more advanced topics such as random variables, probability distributions, functions of random variables, expected value, and joint probability distributions.

Syllabus:

  • Set theory, Probability Space. Axioms of Probability
  • Joint, Conditional, and total probabilities
  • Bayes theorem, combinatorics, and Bernoulli trials
  • Random variable, cumulative distribution function, and probability density function
  • Continuous and discrete random variables
  • Some common continuous random variable: Gaussian, exponential , uniform, Rayleigh
  • Some common discrete random variables : Bernoulli, Binomial, Poisson, negative binomial
  • Functions of random variables
  • Joint probability distribution
  • Conditional probability distribution

Text Book:

  • Probability, Random Variables, and Stochastic Processes, fourth ed, by A. Papoulis and S. U.. Pillai
  • Engineering probability and statistics


 Engineering Mathematics(FALL_2017)

Aims:

This course is about the mathematics that is most widely used in the electrical engineering core subjects. In general, three topics are considered: An introduction to Fourier analysis, including Fourier series and Fourier transform. Partial differential equations, in particular heat equation, wave equation, and Laplace’s equation. Finally complex analysis.

Syllabus:

  • Laurent Series. Residue Theorem
  • Conformal Mapping
  • Fourier series
  • Orthogonal Series. Generalized Fourier Series
  • Two-Dimensional Wave Equation
  • Complex numbers. Polar form. Powers and roots
  • Cauchy’s Integral Theorem
  • Sturm–Liouville Problems. Orthogonal Functions
  • Fourier integral. Fourier transform
  • Solution by Separating Variables. Use of Fourier Series
  • Heat Equation: Solution by Fourier Series.
  • Derivative. Analytic Function
  • Cauchy–Riemann Equations. Harmonic functions.
  • Exponential function. Trigonometric and Hyperbolic Functions. Logarithm.
  • Line Integral in the Complex Plane
  • Derivatives of Analytic Functions
  • Basic Concepts of PDEs
  • Vibrating String, Wave Equation
  • Heat Equation: Modeling Very Long Bars.
  • Laplacian in Polar Coordinates
  • Laplace’s Equation in Cylindrical and Spherical Coordinates.

Text Book:

  • ADVANCED ENGINEERING MATHEMATICS,ERWIN KREYSZIG. 10th ed.


 Fields & Waves(FALL_2017)

Aims:

This is an introductory course on electromagnetics, emphasizing fundamental concepts and applications of Maxwell equations. Topics covered include: wave equation, plane wave propagation and polarization, reflection and transmission of electromagnetic waves and transmission line theory.

Syllabus:

  • Time-domain Maxwell’s equations
  • Differential and integral forms of Maxwells Equations
  • Electromagnetic Boundary Conditions
  • Maxwell’s equations in frequency domain and time-harmonic fields
  • Plane Waves
  • Polarization of Plane Waves
  • Wave Propagation on a transmission lines
  • Reflection and Transmission
  • Rectangular Waveguides
  • The Lumped-Element Circuit Model for transmission lines
  • The Telegrapher Equations
  • Source-free wave equation
  • The Smith Chart
  • Generator and Load Mismatches

Text Book:

  • Field and Wave Electromagnetics (2nd Edition): David Cheng


 Special Topics (Boundary Value Problems in Electromagnetics)(FALL_2017)

Aims:

The aim of this course is to introduce graduate students to some advanced analytical methods in electromagnetics. Some of the topics it covers includes Lommel expansion methods in EM, Mie scattering, discrete dipole approximation, transfer matrix methods, and Floquet’s theorem.

Syllabus:

  • Gamma functions and the role of fractional order calculus in electromagnetics.
  • Cylindrical and spherical Bessel functions.
  • Sturm-Liouville problems and generalized Fourier series expansions.
  • Lommel Expansions in Electromagnetics.
  • Vector Cylindrical Wave Functions and Scattering from Cylindrical Structures.
  • VSWFs and Mie theory
  • Resonances of spheres.
  • Quasi-static approximation
  • Electromagnetic Wave Propagation and Scattering in Periodic Media

Text Book:

  • Advanced Engineering Electromagnetics, 2nd ed., C. A. Balanis,
  • Electromagnetic Wave Propagation, Radiation, and Scattering, A. Ishimaru,
  • Absorption and scattering of light by small particles, Bohren, Craig F., and Donald R. Hufman,


 Advanced Electromagnetics(SPRING_2017)

Aims:

This is a graduate level advanced electromagnetics course. It starts with a review of Maxwell’s equations and boundary conditions for time-varying fields, and then introduces the frequency domain form of Maxwell’s equations for time-harmonic fields. The next topics include electrical properties of matter, wave equation and its solutions, plane wave propagation and polarization, reflection and transmission, vector potentials, electromagnetic theorems, and finally waveguides.

Syllabus:

  • Maxwell’s equations and boundary conditions for time-varying fields
  • the frequency domain form of Maxwell’s equations for time-harmonic fields
  • electrical properties of matter
  • wave equation and its solutions
  • plane wave propagation and polarization
  • reflection and transmission
  • vector potentials
  • electromagnetic theorems
  • waveguides

Text Book:

  • Advanced Engineering Electromagnetics, 2nd Edition, Constantine A. Balanis


 Differential Equations(SPRING_2017)

Aims:

This course provides an introduction to topics involving ordinary differential equations. Emphasis is placed on the development of abstract concepts and applications for first-order and linear higher-order differential equations, systems of differential equations, series solutions, eigenvalues and eigenvectors, and Laplace transforms. Upon completion, students will be able to demonstrate understanding of the theoretical concepts and select and use appropriate models and techniques for finding so

Syllabus:

  • Introduction and Basic Definitions
  • First order linear differential equations
  • Separable and homogeneous differential equations
  • Exact differential equations and integrating factors
  • Special Types of First Order Equations
  • Methods for reduction of order
  • Homogeneous constant coefficient differential equations
  • Linear non-homogeneous differential equations
  • Cauchy-Euler differential equation
  • Differential and inverse differential operators
  • Initial value problems, boundary value problems. Eigenvalues and eigenfunctions
  • Power series solution of linear differential equations
  • Legendre and Bessel differential equations
  • Laplace transform and its properties
  • Impulse function and convolution theorem
  • Systems of differential equations

Text Book:

  • Elementary Differential Equations and Boundary Value Problems


 Metamaterials(SPRING_2017)

Aims:

The aim of this course is to introduce and discuss the groundbreaking and recent developments in metamaterials-artificially structured materials with sub-wavelength inclusions and strikingly unconventional electromagnetic properties. The course starts with a brief review of Maxwell’s equations and interaction of light with matter. Next, we discuss the topic of plasmonics and optical properties of metal-dielectric composites. We start our discussion on metamaterials by covering wire media and spl

Syllabus:

  • Introduction to light interaction with matter
  • Electromagnetic waves in layered media
  • Blochs theorem and waves in periodic media
  • Scattering of Waves by Spheres and Coated Spheres
  • Drude model for dielectric function
  • Transformation Optics
  • Surface plasmon polariton
  • Localized Surface Plasmons
  • Wire Media and Low Frequency Plasmons
  • Split Ring Resonator and Artificial Magnetism
  • Negative Index Metamaterials
  • Optical Metamaterials
  • Graphene

Text Book:

  • Plasmonics: Fundamentals and Applications, S. Maier
  • Optical Metamaterials: Fundamentals and Applications,W. Cai and V. Shalaev,


 Engineering Mathematics(FALL_2016)

Aims:

This course is about the mathematics that is most widely used in the electrical engineering core subjects. In general, three topics are considered: An introduction to Fourier analysis, including Fourier series and Fourier transform. Partial differential equations, in particular heat equation, wave equation, and Laplace’s equation. Finally complex analysis.

Syllabus:

  • Fourier series
  • Sturm–Liouville Problems. Orthogonal Functions
  • Orthogonal Series. Generalized Fourier Series
  • Fourier integral. Fourier transform
  • Basic Concepts of PDEs
  • Vibrating String, Wave Equation
  • Solution by Separating Variables. Use of Fourier Series
  • Heat Equation: Solution by Fourier Series.
  • Heat Equation: Modeling Very Long Bars.
  • Two-Dimensional Wave Equation
  • Laplacian in Polar Coordinates
  • Laplace’s Equation in Cylindrical and Spherical Coordinates.
  • Complex numbers. Polar form. Powers and roots
  • Derivative. Analytic Function
  • Cauchy–Riemann Equations. Harmonic functions.
  • Exponential function. Trigonometric and Hyperbolic Functions. Logarithm.
  • Line Integral in the Complex Plane
  • Cauchy’s Integral Theorem
  • Derivatives of Analytic Functions
  • Laurent Series. Residue Theorem
  • Conformal Mapping

Text Book:

  • ADVANCED ENGINEERING MATHEMATICS,ERWIN KREYSZIG. 10th ed.


 Fields & Waves(FALL_2016)

Aims:

This is an introductory course on electromagnetics, emphasizing fundamental concepts and applications of Maxwell equations. Topics covered include: wave equation, plane wave propagation and polarization, reflection and transmission of electromagnetic waves and transmission line theory.

Syllabus:

  • Time-domain Maxwell’s equations
  • Differential and integral forms of Maxwells Equations
  • Electromagnetic Boundary Conditions
  • Maxwell’s equations in frequency domain and time-harmonic fields
  • Source-free wave equation
  • Plane Waves
  • Polarization of Plane Waves
  • Reflection and Transmission
  • Rectangular Waveguides
  • The Lumped-Element Circuit Model for transmission lines
  • Wave Propagation on a transmission lines
  • The Telegrapher Equations
  • The Smith Chart
  • Generator and Load Mismatches

Text Book:

  • Field and Wave Electromagnetics (2nd Edition): David Cheng


 Special Topics (Boundary Value Problems in Electromagnetics)(FALL_2016)

Aims:

The aim of this course is to introduce graduate students to some advanced analytical methods in electromagnetics. Some of the topics it covers includes Lommel expansion methods in EM, Mie scattering, discrete dipole approximation, transfer matrix methods, and Floquet’s theorem.

Syllabus:

  • Gamma functions and the role of fractional order calculus in electromagnetics.
  • Cylindrical and spherical Bessel functions.
  • Sturm-Liouville problems and generalized Fourier series expansions.
  • Lommel Expansions in Electromagnetics.
  • Vector Cylindrical Wave Functions and Scattering from Cylindrical Structures.
  • VSWFs and Mie theory
  • Resonances of spheres.
  • Quasi-static approximation
  • Electromagnetic Wave Propagation and Scattering in Periodic Media

Text Book:

  • Advanced Engineering Electromagnetics, 2nd ed., C. A. Balanis,
  • Electromagnetic Wave Propagation, Radiation, and Scattering, A. Ishimaru,
  • Absorption and scattering of light by small particles, Bohren, Craig F., and Donald R. Hufman,


 
 
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