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
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