This course on Scientific Computing I aims to teach learners the fundamentals of numerical methods and their applications in physics. By the end of the course, students will be able to implement Euler, Heun, RK4, and Symplectic methods for integration, utilize matrix methods for optics and data fitting, apply Monte Carlo simulations, understand Fourier Transforms, and work with Eigenvectors in various applications. The course employs a combination of Python programming, Jupyter Notebooks, and Google Colab for practical implementation. This course is designed for students studying physics or related fields who are interested in computational methods for scientific research and analysis.
Overview
Syllabus
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.
Taught by
Steve Spicklemire
