Scientific Computing I

Explore pre-class lectures and slides for Scientific Computing 1 (Physics 280) at the University of Indianapolis. Delve into topics such as the Euler Method, Heun Method, Taylor Series, Monte Carlo simulations, matrix methods in optics, power laws, numerical integration, root finding, coupled oscillators, and an introduction to supervised machine learning with the Perceptron. Learn to apply Python, Numpy, and Jupyter Notebooks to solve complex scientific computing problems. Gain hands-on experience with Fourier transforms, curve fitting, and eigenvector applications in stochastic matrices and coupled oscillators. Master essential tools and techniques for computational physics and scientific analysis over the course of 6 hours of comprehensive content.

Euler Method (with python notebooks).
PH 280/Project 1.
Heun Method (fixed audio).
TaylorSeries: Approximating the Morse Potential.
pylab sympy together.
RK4 and Symplectic Methods of Integration.
Monte Carlo: Demon Algorithm.
The Drunken Sailor Problem with Numpy/Jupyter Notebook. (fixed!).
matrix methods: Optics with matrices.
Power Laws and Fitting Data with Matrices.
Numerical Integration: Large Amplitude Pendulum.
Root Finding: Energy Eigenstates.
Coupled Oscillators.
Project 12, The Perceptron: Intro to Supervised Machine Learning.
FFT Fun: Complex Numbers, Discrete Fourier Transforms.
Taylor Series in Scientific Computing.
Geometrical Optics.
Fitting Pendulum data with curve_fit.
Stochastic matrix as an Eigenvector application.
Coupled Oscillators as an application of Eigenvectors.
Fourier Series with basis functions.
Google Colab Setup.