### Videos of Lectures

##### Here are some of the videos of the lectures of fall 2009
• Lecture 1: linear algebra up to linear independence.
• Lecture 2: dimension of a vector space, inner and outer products, and Dirac notation.
• Lecture 3: laser demo on polarization vectors, identity operators, vectors and their components, linear operators and their matrix elements, determinants.
• Lecture 4: determinants, systems of linear equations, eigenvectors and eigenvalues, the adjoint of a linear operator, hermitian operators, unitary operators, anti-unitary and anti-linear operators, Wigner's theorem on symmetry in quantum mechanics, eigenvalues of a square matrix.
• Lecture 5: eigenvalues of a square matrix, functions of matrices, hermitian matrices.
• Lecture 6: hermitian matrices, normal matrices, determinant of a normal matrix, tricks with Dirac notation, compatible normal matrices.
• Lecture 7: compatible normal matrices, a matrix satisfies its characteristic equation, the singular-value decomposition.
• Lecture 8: Part 1 Part 2: applications of the singular-value decomposition, LAPACK, the rank of a matrix, the tensor or direct product, density operators.
• Lecture 9: on tensor products, density operators, correlation functions, groups, and complex Fourier series.
• Lecture 10: on the Fourier series for $\exp(-m |x|)$, real Fourier series, the Fourier series for x, complex and real Fourier series for an interval of length L.
• Lecture 11: on Fourier series in several variables, the convergence of Fourier series, and quantum-mechanical examples.
• Lecture 12: on quantum-mechanical examples, the harmonic oscillator, non-relativistic strings, periodic boundary conditions, and the transition to the Fourier transform.
• Lecture 13: on the transition to the Fourier transform, the Fourier transform of a gaussian and of a real function, a representation of the delta-function, Parseval's identity, derivatives of a Fourier transform, and momentum and momentum space.
• Lecture 14: on the uncertainty principle, Fourier transforms in several variables, application to differential equations, Fick's law, and diffusion.
• Lecture 15: on the wave equation, diffusion, convolutions, Gauss's law, and the magnetic vector potential.
• Lecture 16: on the Fourier transform of a convolution, finding Green's functions, Laplace transforms, examples of Laplace transforms, how to measure the lifetime of a fluorophore, differentiation and integration of Laplace transforms, inverting Laplace transforms, convergence of infinite series, tests of convergence, series of functions, uniform convergence, the Riemann zeta function, and power series.
• Lecture 17: on power series, the geometric series, the exponential series, factorials and the Gamma function, Taylor series, Fourier series, the binomial theorem, the binomial coefficient, double factorials, the logarithmic series, Bernoulli numbers and polynomials, the Lerch transcendent, asymptotic series, and the exponential integrals.
• Lecture 18: on dielectrics, analytic functions, Cauchy's integral theorem, Cauchy's integral formula, the Cauchy-Riemann conditions, and harmonic functions.
• Lecture 19: on the Cauchy-Riemann conditions and the contour integral of a general function, harmonics functions, applications to two-dimensional electrostatics, Earnshaw's theorem, Taylor series, and Cauchy's inequality.
• Lecture 20: on Cauchy's inequality, Liouville's theorem, the fundamental theorem of algebra, Laurent series, poles, essential singularities, and the calculus of residues.
• Lecture 21 Part 1  Part 2: on the calculus of residues, ghost contours, third-harmonic microscopy, and several examples of the use of ghost contours.
• Lecture 22: on logarithms, cuts, roots, contour integrals around cuts, Cauchy's principal value, i-epsilon rules, and application to Feynman's propagator.