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Lecture
Fourier transforms: Light-matter interaction
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Properties of Fourier and inverse Fourier transforms
Explores the properties of Fourier and inverse Fourier transforms, analyzing finite wave trains, Gaussian functions, and 3D space transformations.
Crystallography: Describing Periodic Structures
Covers crystallography, lattice structures, vectors, and diffraction patterns.
Reciprocal lattice: Shape effects
Explains how sample geometry affects the size and shape of reciprocal lattice nodes in multiple beam scattering.
Complex Integration: Fourier Transform Techniques
Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.
Wave Propagation: General Solutions
Explores the general solutions for wave propagation and Fourier transforms in periodic functions.
Numerical Methods: Boundary Value Problems
Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.
Frequency Response of LTI Systems
Explores LTI systems, impulse response, convolution, system properties, and frequency response, including low-pass and band-pass filters.
Electron Diffraction: Basics & Applications
Explores electron diffraction basics, including Bragg's law, reciprocal lattice, and applications like crystal phase discrimination.
Fourier Transform: Derivatives and Formulas
Explores Fourier transform properties with derivatives, crucial for solving equations, and introduces the Laplace transform for signal transformation.
Fourier Transform: Diffusion Equation
Explores the derivation of the diffusion equation using Fourier transforms and discusses the significance of Dirac delta functions in mathematical analysis.
