Syllabus

  • Elementary calculus, exponential and logarithmic functions, Taylor series expansion
  • Approximation methods
  • Complex number theory, complex integration and differentiation, simple functions in the complex domain
  • Special functions: Rectangular and triangular functions, delta-function and its derivatives, sinc function, etc.
  • The convolution operation
  • Linear, shift-invariant systems
  • Fourier transform theory, theorems, useful Fourier transform pairs
  • The method of stationary phase
  • Applications of Fourier theory to optical diffraction
  • Linear algebra, operations with matrices, matrix inversion
  • Eigen-values and eigen-vectors, matrix diagonalization
  • Vector algebra, vector identities
  • Divergence, curl, gradient, and Laplacian operators
  • Ordinary differential equations; elementary methods of solution
  • Partial differential equations, method of separation of variables
  • The diffusion equation
  • Maxwell’s equations; the wave equation
  • Solutions of the wave equation in Cartesian, cylindrical, and spherical coordinate systems
  • Special functions: Bessel functions of the 1st, 2nd, and 3rd kind; modes of an optical fiber
  • Probability theory
  • Statistical properties of thermal noise, shot noise, and modal noise in fiber optics systems
  • Introduction to Information Theory and Coding
  • Communication via noisy channels; Shannon’s noisy channel capacity
  • Compression codes, error-correction codes, modulation coding