Lecture Outlines (Mathematics of Systems Engineering)

Bahman Gharesifard
Winter 2014

Lectures:

  • Lecture 1: (Introduction to general theory of systems)
  • Lecture 2: (Input-output discrete-time/continuous-time/memoryless/invariant systems)
  • Lecture 3: (Systems as signals, introduction to filters)
  • Lecture 4: (Paul Dirac and Sergei Sobolev's improper/generalized functions)
  • Lecture 5: (Other motivations for distributions: Sergei Sobolev's and Laurent Schwartz's notion of weak solutions)
  • Lecture 6: (Schwartz's formal theory of distributions)
  • Lecture 7: (Properties and examples of distributions)
  • Lecture 8: (Regular and non-regular distributions)
  • Lecture 9: (Operations on distributions)
  • Lecture 10: (Derivative in the sense of distributions)
  • Lecture 11: (Convergence in the sense of distributions)
  • Lecture 12: (Fourier series of Dirac comb: sampling and approximating)
  • Lecture 13: (Schwarz space of functions)
  • Lecture 14: (Tempered distributions)
  • Lecture 15: (Examples and properties of tempered distributions)
  • Lecture 16: (Fourier transform of tempered distributions I)
  • Lecture 17: (Fourier transform of tempered distributions II)
  • Lecture 18: (Distributions with compact support)
  • Lecture 19: (Back to systems: convolution on the space of functions)
  • Lecture 20: (Convolutions and Fourier transforms)
  • Lecture 21: (Convolutions on the space of distributions I)
  • Lecture 22: (Review on distributions)
  • Lecture 23: (Convolutions on the space of distributions II)
  • Lecture 24: (Causal and acausal distributions)
  • Lecture 25: (Convolutions of distributions and Fourier transforms I)
  • Lecture 26: (Convolutions of distributions and Fourier transforms II)
  • Lecture 27: (Introduction to sampling theorem)
  • Lecture 28: (Poisson summation formula for compactly supported distributions)
  • Lecture 29: (Poisson summation formula and convergence in Schwartz space)
  • Lecture 30: (Applications: Nyquist sampling rate)
  • Lecture 31: (Applications: Shannon's reconstruction formula)
  • Lecture 32: (Applications to communications: Narrow-band signals)
  • Lecture 33: (Applications to communications: Amplitude Modulation (AM))
  • Lecture 34: (Applications to communications: Frequency Modulation (FM))
  • Lecture 35: (Review session)

For questions, contact me with bahman at mast.queensu.ca or with 613-533-2441 (I prefer emails)