Probability

EE 503

  • Countable and Uncountable Sets, Outcomes, Events, Probabilities
  • Conditional Probabilities, Independence
  • Counting, Playing Cards and Balls and Bins
  • Baye’s Rule, Random Variables, CDFs and PDFs
  • Functions of Random Variables, Expectations, Iterated Expectations
  • Law of Large Numbers
  • Central Limit Theorem and Gaussians
  • Hypothesis Testing, Minimum Mean Square Distortion
  • Discrete Time Markov Chains
  • Discrete Time Queues, Simulation
  • Continuous Time Chains
  • Poisson Processes, M/M/1, Renewal Theory

 

Random processes

EE 562

  • Definition of random processes: random variables, random vectors, random sequences, random waveforms, etc.
  • Second order statistics: Properties of correlation functions
  • Covariance matrix factorization, eigenvalues, eigenvectors, causal factoring and whitening concepts
  • Gaussian processes
  • Simple hypothesis tests
  • Linear minimum-mean-square-error estimation, orthogonality principle
  • Linear operations on random processes, convergence concepts: convolution, integration, differentiation
  • Frequency domain analysis: time invariant linear operations
  • Energy spectra, power spectra, white noise approximations
  • Linear transformations of wide-sense stationary random processes, spectral factorization, and applications
  • Poisson distributed events in time, Campbell’s theorem
  • Karhuenen-Loeve expansions on finite intervals
  • Narrowband process representations
  • Time averages, ergodicity

 

Linear algebra

EE 510

  • Systems of Linear Equations
  • Review of Elementary Linear Algebra, Algebraic Structures
  • Vector Spaces
  • Normed and Inner Product Spaces
  • Linear Transformations
  • Linear Transformations and Orthogonality
  • The Moore-Penrose Pseudo-Inverse, Linear Least Squares Problems
  • Eigenvalues and Eigenvectors
  • Singular Value Decomposition
  • Review of Multivariable Calculus, Bilinear and Quadratic Forms
  • Application: Optimization
  • Application: Analysis of Linear Dynamical Systems
  • Application: Stability Analysis of Dynamical Systems
  • Tensor Analysis

 

Signals, Systems, and Comms

EE 467

 

 

EE 301

  • Time-Domain Analysis of Continuous-Time Systems
  • Laplace Transform (Continuous Time)
  • Fourier Series and Fourier Transform (Continuous Time)
  • Time-Domain Analysis of Discrete-Time Systems
  • Discrete-Time Fourier Analysis
  • z-Transform (z-Transform)

 

Electricity and Magnetism

EE 370

  • Calculate voltages, currents, waves, and impedance in transmission lines
  • Time and phasors domain analysis
  • Maxwell's equations and calculations of the energy of electromagnetic fields
  • Electric and magnetic fields of plane waves
  • Dipole antennas and their characteristics
  • Wireless communication and understanding receive power
Published on October 22nd, 2024Last updated on October 22nd, 2024