Lecture Notes
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Notes
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Video
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Notes from 1/11/22:
We discussed exact and approximate numbers and investigated binary approximations
to decimal numbers.
Go here to see sagemath code used in class today.
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Video from 1/11/22
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1/13/22:
We discussed binary number approximations to decimal numbers and explored some sagemath code
Go here to see sagemath code used in class today.
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Video from 1/13/22
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| Notes from 1/18/22:
We discussed binary operations, significant figures, and the 5 rounding methods. We also worked on the sagemath labs.
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Video from 1/18/22
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Notes from 1/20/22:
We discussed binary expansions for rational and irrational numbers, and sagemath, and python.
Python Console from 1/20/22
Python Script from 1/20/22
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Video from 1/20/22
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Corrected Notes from 1/25/22:
We discussed floating point representation in computers and coding in python.
Python Script from 1/25/22
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Video from 1/25/22
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| Corrected Notes from 1/27/22:
We discussed floating point approximations and propagation of error.
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Video from 1/27/22
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| Corrected Notes from 2/1/22:
We discussed propagation of error and Taylor polynomials.
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Video from 2/1/22
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| Homework questions from 2/3/22:
We discussed homework questions that will be due Feb 8.
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Video from Q&A 2/3/22
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| Notes from 2/8/22:
We discussed the Taylor-Lagrange remainder formula and used it to determine the general formula for
propagation of error.
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Video from 2/8/22
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| Notes from 2/10/22:
We discussed questions from homework, error propagation formulas, and
we began discussing interpolation.
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Video from 2/10/22
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| Notes from 2/17/22:
We discussed polynomial interpolation, using Lagrange's formula and using Newton's Finite Difference method.
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Video from 2/17/22
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Notes from 2/22/22:
We discussed polynomial interpolation using sagemath, and we learned how to find cubic splines.
Sagemath Script used for calculating the Lagrange interpolating polynomial
Sagemath Script used for calculating the Newton finite differences
Sagemath Script used for calculating cubic splines
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Video from 2/22/22
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| Notes from 3/1/22:
We discussed cubic splines and the followibng numerical integration techniques: Left and Right Riemann sums, midpoint rule, trapezoid rule. We
also review Newton's finite difference formula with remainder and the intermediate value theorem.
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Video from 3/1/22
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Notes from 3/3/22
Sagemath Script used for calculating the left and right Riemann sums and the Trapezoid Rule
We discussed using the Newton finite difference formula to derive numerical integration methods.
We also studied the error in numerical integration methods as a function of the number of subdivisions of the integration interval.
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Video from 3/3/22
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| Notes from 3/15/22
We derived the formula for the error in the trapezoid rule approxsimation to a definite integral and showed how to find the formula for Simpson's Rule.
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Video from 3/15/22
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3/17/22: We utilized python and R to compare different quadrature methods.
Python Script from 3/17/22
R Script from 3/17/22
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Video from 3/17/22
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Notes from 3/22/22
We utilized R to compare different quadrature methods, and we discussed adaptive quadrature.
R Script from 3/22/22
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Video from 3/22/22
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Notes from 3/24/22
We discussed adaptive quadrature and multidimensional integrals, including Monte Carlo integration.
Sagemath Script from 3/24/22
on adaptive quadrature
Sagemath Script from 3/24/22
on Monte Carlo integration
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Video from 3/24/22
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Notes from 3/29/22
We discussed another example of Monte Carlo integration and started talking about the method of bisection, which is
used in numerically solving equations.
Python Script from 3/29/22
on Monte Carlo integral example
R Script from 3/29/22
on Monte Carlo integral example
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Video from 3/29/22
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Corrected Notes from 4/5-7/22
We discussed numerical methods to solve equations, including the bisection method and Regula Falsi. We also discussed how to iteract with
spreadsheets and GUIs in both python and R
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Video from 4/5/22
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Notes from 4/5-7/22
We discussed numerical methods to solve equations, including bisection, regula falsi, secant method, Newton-Raphson.
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Video from 4/7/22
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Notes from 4/12/22
We discussed order of convergence.
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Video from 4/12/22
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| Notes from 4/14/22
We discussed so python tips and then worked on the projects.
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Video from 4/14/22
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Notes from 4/19/22
We discussed order of convergence of the Newton-Raphson method, modified Newton Raphson method, and the secant method.
Sagemath code for 4/19/22
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Video from 4/19/22
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