Physics

Topics include Fourier analysis: Fourier series, Fourier transform, Dirac delta function, sifting property, Fourier representation, convolution, correlations, Parseval's theorem power spectrum, sampling; Nyquist theorem, data compression, solving ordinary differential equations with Fourier methods, driven damped oscillators, Green's functions for 2nd order ODEs, partial differential equations, PDEs and curvilinear coordinates, Bessel functions, and Sturm-Liouville theory. Topics for probability and statistics include concept and origin of randomness, randomness as frequency and as degree of belief, discrete and continuous probabilities, combining probabilities, Bayes theorem, probability distributions and how they are characterized, moments and expectations, error analysis, permutations, combinations, and partitions, Binomial distribution, Poisson distribution, the Normal or Gaussian distribution, shot noise and waiting time distributions, resonance and the Lorentzian, growth and competition and power-law distributions, hypothesis testing, parameter estimation, Bayesian inference, correlation and covariance, and model fitting.

This course provides an introduction to the concepts, formalism, and applications of quantum mechanics in different disciplinary fields of science and technology: mathematics, computer science and information technology, basic physics, and physico-chemistry. It includes instruction from specialists within these disciplines in connection with current research issues. 

This course offers an introduction to equilibrium thermodynamics. The course covers the First and Second Laws of thermodynamics, along with the concepts of temperature, internal energy, heat, entropy, and the thermodynamic potentials. The course also considers the applications of thermodynamic concepts to topics such as heat engines, the expansion of gases, and changes of phase. The Third Law, and associated properties of entropy, completes the course.