yetianning / 2018september

An introduction to mathematical computing in Python

MATH 210 Introduction to Mathematical Computing

MATH 210 at the University of British Columbia is an introduction to mathematical computing with Python and Jupyter. We start with basic Python programming including datatypes, logic, loops and functions and then we explore scientific computing packages NumPy, SciPy and Matplotlib. We use these packages to solve problems in calculus, linear algebra, differential equations and data visualization.

Lecture Notes

Date	Notebook	Topics	Resources
September 5	notes-2018-09-05	Jupyter notebooks	Jupyter
September 7	notes-2018-09-07	Markdown and LaTeX	Markdown, LaTeX, math symbols and Detexify
September 10	notes-2018-09-10	Numbers, variables and sequences	Python tutorial
September 12	notes-2018-09-12	Sequences, list comprehensions and series	Sequences and series in Python, and list comprehensions
September 14	notes-2018-09-14	Series and functions	Taylor series and functions
September 17	notes-2018-09-17	Functions and logic	Functions and logic
September 19	notes-2018-09-19	Logic and loops	Logic and loops
September 21	notes-2018-09-21	For loops and while loops	Loops
September 24	notes-2018-09-24	Bisection method	Roots and optimization and bisection method
September 26	notes-2018-09-26	Secant method	Roots and optimization and secant method
September 28	notes-2018-09-28	Newton's method	Roots and optimization and Newton's method
October 1	notes-2018-10-01	Introduction to SciPy	SciPy, NumPy and Matplotlib
October 3	notes-2018-10-03	NumPy arrays	NumPy tutorial, Matplotlib and (more) NumPy
October 5	notes-2018-10-05	More NumPy arrays	NumPy arrays
October 10	notes-2018-10-10	Plotting with Matplotlib	Pyplot commands
October 12	notes-2018-10-12	Riemann Sums	Riemann sums
October 15	-	Riemann Sums: Error Formulas	Riemann sums
October 17	notes-2018-10-17	Trapezoid Rule	Trapezoid rule
October 19	notes-2018-10-19	Trapezoid Rule: Error Formulas	Trapezoid rule and nonelementary integrals
October 22	notes-2018-10-22	Example: Bessel Functions	Trapezoid rule and Bessel functions
October 24	notes-2018-10-24	Numerical Differentiation	Numerical differentiation and finite differences
October 26	notes-2018-10-26	Example: Arc length	Arc length
October 29	notes-2018-10-29	Linear algebra with SciPy	scipy.linalg documentation
November 2	notes-2018-11-02	Linear systems	scipy.linalg.solve
November 5	notes-2018-11-05	Gaussian elimination and interpolation	Interpolation
November 7	notes-2018-11-07	Interpolation and linear regression	Linear regression and Vandermonde matrix
November 9	notes-2018-11-09	Linear regression (continued)
November 14	notes-2018-11-14	Polynomial regression	Polynomial regression
November 16	notes-2018-11-16	Eigenvalues and eigenvectors	Eigenvalues/eigenvectors, simple graphs and the adjacency matrix
November 19	notes-2018-11-19	Applications: graphs, linear systems of ODEs	Adjacency matrix and linear systems of ODEs
November 21	notes-2018-11-21	Applications: linear system of ODEs	Linear systems of ODEs
November 23	notes-2018-11-23	Euler's method	Euler's method
November 26	notes-2018-11-26	Euler's method and scipy.integrate.odeint	scipy.integrate.odeint
November 28	notes-2018-11-28	Second order equations	Vibrations and Van der pol oscillator
November 30	notes-2018-11-30	Planetary orbits	Orbits and Euler's 3-body problem