


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 firstorder and linear higherorder 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 nonhomogeneous differential equations
 CauchyEuler 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 metamaterialsartificially structured materials with subwavelength 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 metaldielectric 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
 TwoDimensional 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:
 Timedomain Maxwell’s equations
 Differential and integral forms of Maxwells Equations
 Electromagnetic Boundary Conditions
 Maxwell’s equations in frequency domain and timeharmonic fields
 Plane Waves
 Polarization of Plane Waves
 Wave Propagation on a transmission lines
 Reflection and Transmission
 Rectangular Waveguides
 The LumpedElement Circuit Model for transmission lines
 The Telegrapher Equations
 Sourcefree 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.
 SturmLiouville 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.
 Quasistatic 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 timevarying fields, and then introduces the frequency domain form of Maxwell’s equations for timeharmonic 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 timevarying fields
 the frequency domain form of Maxwell’s equations for timeharmonic 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 firstorder and linear higherorder 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 nonhomogeneous differential equations
 CauchyEuler 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 metamaterialsartificially structured materials with subwavelength 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 metaldielectric 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.
 TwoDimensional 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:
 Timedomain Maxwell’s equations
 Differential and integral forms of Maxwells Equations
 Electromagnetic Boundary Conditions
 Maxwell’s equations in frequency domain and timeharmonic fields
 Sourcefree wave equation
 Plane Waves
 Polarization of Plane Waves
 Reflection and Transmission
 Rectangular Waveguides
 The LumpedElement 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.
 SturmLiouville 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.
 Quasistatic 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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