Next:
Contents
Contents
IKC-MH.55
Scientific Computing with Python
Lecture Notes
Cem Özdoğan
Date:
9 January 2024
Contents
List of Tables
List of Figures
Preliminaries
First Meeting
Lecture Information
Course Overview
Text Book
Online Resources
Grading Criteria
Policies
Installation of Required Tools/Programs
Linux System
Windows System
Others
Introduction
Introduction to Python
Python Libraries for Data Science
NumPy
SciPy
Matplotlib
Programming Examples in Python
Numerical Fundamentals
Analysis vs Numerical Analysis
Some disasters attributable to bad numerical computing
Floating-Point Arithmetic
Computer Number Representation
Kinds of Errors in Numerical Procedures
Absolute vs Relative Error, Convergence
Root Searching
Solving Nonlinear Equations
Blackbody Radiation
Interval Halving (Bisection)
Linear Interpolation Methods-The Secant Method
Newton's Method
Differentiation and Integration
Numerical Differentiation and Integration with a Computer
Variable force in one dimension
Differentiation with a Computer
Simple Pendulum
Numerical Integration - The Trapezoidal Rule
The Composite Trapezoidal Rule
Differential Equations
Initial Value Problems
Projectile Motion with Air Resistance
Planetary Motion
Euler Method
Runge-Kutta Method
Second Degree Equations
Boundary Value Problems
Trial-and-Error (Linear Shooting) Method
Laplace Equation in Electrostatics
Eigenvalue Problems
Standing Waves on a String
Numerical Solutions of Schrödinger Equation
Hydrogen Atom
Special Functions
Legendre Polynomials
Hermite Polynomials
Quantum Harmonic Oscillator
Linear Algebra and Matrix Computing
Solving Sets of Equations
Matrices and Vectors
Some Special Matrices and Their Properties
Elimination Methods
Gaussian Elimination
Kirchhoff's Rules
Using the LU Matrix for Multiple Right-Hand Sides
The Inverse of a Matrix
Eigenvalues and Eigenvectors of a Matrix
Normal Modes of Coupled Oscillation
Iterative Methods
Jacobi Method
Interpolation and Curve Fitting
Interpolation and Curve Fitting
Interpolating Polynomials
Interpolation versus Curve Fitting
Fitting a Polynomial to Data
Lagrangian Polynomials
Neville's Method
Divided Differences
Spline Curves
The Equation for a Cubic Spline
Least-Squares Approximations
Nonlinear Data (Curve Fitting)
Least-Squares Polynomials
Millikan oil-drop experiment
References:
About this document ...
