Readings and topics
References
 The class textbook
 Numerical Methods by Anne Greenbaum and Tim Chartier
 A fun reference
 Insight through computing by Charles van Loan and K.Y. Daisy Fan
Lecture 40
Newton's method, the secant method, the fixed point form of
a nonlinear equation, and a review before the final midterm.
 Reading
 Chapter 4 Sections 4.3, 4.4.3, 4.5
 Handout
 Nonlinear equations (Pages 3, 4)
 Slides
 Lecture 40
 Julia
 Lecture 40 (html)
(ipynb)
 Notes
 Lecture 40
Lecture 39
Introduction to nonlinear equations
 Reading
 Chapter 4 Sections 4.1, 4.2
 Handout
 Nonlinear equations
 Slides
 Lecture 39
 Julia
 Lecture 39 (Bisection) (html)
(ipynb)
 Notes
 Lecture 39
Lecture 38
Stiff equations, Implicit methods, BVPs
 Reading
 Chapter 11 Sections 11.4
 Chapter 13 Sections 13.1
 Handout
 Intro to BVPs
 BVPs questions
 Julia
 Lecture 38 (Backwards Euler) (html)
(ipynb)
 Lecture 38 (BVPs) (html)
(ipynb)
 Slides
 Lecture 38
Lecture 37
Absolute stability, consistency, stability, convergence, local truncation error,
 Reading
 Chapter 11 Sections 11.4
 Handout
 Intro to ODEs (Pages 34)
 Slides
 Lecture 37
 Julia
 Lecture 37 (html)
(ipynb)
 Notes
 Lecture 37
Lecture 36
Solving ODEs on a computer.
 Reading
 Chapter 11 Sections 11.1, 11.2
 Slides
 Lecture 36
 Handout
 Intro to ODEs (Pages 12)
 Julia
 Lecture 36 (html)
(ipynb)
 Lecture 36 Example ODE (html)
(ipynb)
Lecture 35
We saw the error analysis of a Newton Cotes formula, and also looked
at the error analysis of the piecewise trapezoidal rule. I mentioned
Simpson's rule (or the three point Newton Cotes rule) see the book for
more information.
 Reading
 Chapter 10.1,10.3
 Slides
 Lecture 35
 Notes
 Lecture 35
Lecture 34
(QUIZ!) We continued talking about quadrature rules and looked at deriving
NewtonCotes formulas.
 Reading
 Chapter 10.1,10.3
 Notes
 Lecture 34
Lecture 33
An introduction to numerical integration, the method of undetermined
coefficients and quadrature.
 Reading
 Chapter 10.1,10.3
 Slides
 Lecture 33
 Notes
 Lecture 33
Lecture 32
On the illconditioning of numerical differentiation, high dimensional
polynomial interpolation, and how to analytically differentiate
expressions for polynomials
 Reading
 Chapter 9 Chapter 8, 9
 Slides
 Lecture 32
 Julia
 Lecture 32 (html)
(ipynb)
 Notes
 Lecture 32
Lecture 31
The TA went over the last exam and quiz.
Lecture 30
Error combos in numerical differentiation and Richardson extrapolation.
 Slides
 Lecture 30
 Reading
 Chapter 9 Section 9.1, 9.2
 Julia
 Lecture 30 (html)
(ipynb)
 Notes
 Lecture 30
Lecture 29
We saw truncation error for numerical differentiation and how to derive
an accuracy estimate using Taylor series.
 Reading
 Chapter 9 Section 9.1
 Slides
 Lecture 29
 Notes
 Lecture 29
Lecture 28
The quiz! Then we saw the Barycentric form of the
Lagrange interpolant, as well as some error analysis.
Finally, we briefly discussed piecewise polynomial interpolation.
 Reading
 Chapter 8 Section 8.5
 Slides
 Lecture 28
 Julia
 Lecture 28 (html)
(ipynb)
Lecture 27
Today, we saw Lagrange interpolation.
 Reading
 Chapter 8 Section 8.1, 8.2
 Handout
 Polynomial Forms
 Slides
 Lecture 27
 Notes
 Lecture 27
 Julia
 Lecture 27 (html)
(ipynb)
Lecture 26
Introduction to applied mathematics and polynomial interpolation and ApproxFun
 Reading
 Chapter 8 Section 8.1, 8.2
 Handout
 Polynomial Approximation Intro
 Slides
 Lecture 26
 Julia
 Lecture 26 (html)
(ipynb)
 Lecture 26 (ApproxFun) (html)
(ipynb)
 Software
 Chebfun and the Julia counterpart
 ApproxFun
Lecture 25
The midterm
Lecture 24
We saw the power method convergence rate, the block power method, and then
reviewed for the midterm.
 Slides
 Lecture 24
 Notes
 Lecture 24
Lecture 23
We started covering eigenvalues of matrices and saw the basis for
the power method..
 Reading
 Chapter 12 Section 12.1 (Eigenvalue methods)
 Handouts
 Eigenvalues (Pages 12)
 Julia
 Lecture 23 Eigenvectors of a string (html)
(ipynb)
 Slides
 Lecture 23
 Notes
 Lecture 23
Lecture 22
We finished our coverage of condition numbers for linear systems, saw
matrix norms, and got a another brief intro to iterative methods. See the
handout for much more detail.
 Reading
 Chapter 7 Section 7.4 (Conditioning)
 Chapter 12 Section 12.2 (Iterative methods)
 Julia
 Lecture 21 Conditioning and Stability (html)
(ipynb)
 Handouts
 Iterative methods
 Slides
 Lecture 22
 Notes
 Lecture 22
Lecture 21
We finished up with least squares using the QR decomposition of a matrix. (This
involved a quick study of orthogonal matrices and how they generalize the
notion of a rotation.) We had a quick aside about iterative methods for linear
systems that gets you to where you need to be for the homework, then we dove
into conditioning and stability.
 Reading
 Chapter 7 Section 7.6 (Least squares)
 GramSchmidt process
 Chapter 7 Section 7.4 (Conditioning of linear systems)
 Handouts
 Iterative Methods
 Conditioning and Stability
 Julia
 Lecture 21 Conditioning and Stability (html)
(ipynb)
 Slides
 Lecture 21
 Notes
 Lecture 21
Lecture 20
 Today we continued our coverage of least squares problems
 and the geometry of a simple example; and the QR factorization
 of a matrix and it's relationship to GramSchmidt

Chapter 7 Section 7.6 (Least squares)

GramSchmidt process
 Slides
 Lecture 20
 Handouts
 Intro to Least Squares
Lecture 19
Today we covered PageRank as a linear system and least squares problems
 Reading
 Chapter 7 Section 7.6
 Slides
 Lecture 19
 Julia
 Lecture 19 Galileo's problem (html)
(ipynb)
 Handouts
 PageRank as a linear system
 Intro to Least Squares
Lecture 18
We counted the number of operations in Gaussian Elimination
and saw the midterm and saw an important property of LU. See
the slides and the videos online.
 Reading
 Chapter 7 Section 7.3
 Slides
 Lecture 18
 Handouts
 Flops in LU
Lecture 17
We saw code for Gaussian Elimination with LU and Pivoting.
 Reading
 Chapter 7 Section 7.3
 Slides
 Lecture 17
 Julia
 Lecture 17 (html)
(ipynb)
 Notes
 Lecture 17
Lecture 16
We went over Linear Systems of equations, where they come from, and how
to use Gaussian Elimination and the LU factorization to solve them!
In class next time, we will see code to implement these operations in Julia
 Reading
 Chapter 7 Section 7.2
 Julia
 Lecture 16 (html)
(ipynb)
 Notes
 Lecture 16
Lecture 15
This was the memory hierarchy and highperformance matrix matrix multiplication.
 Reading
 HowToOptimizeGEMM
 Memory hierarchy
 Slides
 Lecture 15
 Notes
 Lecture 15
Lecture 14
Today, we saw an introduction to matrix methods, why they
are important, where they occur, and an brief introduction
to matrixmatrix multiplication
 Reading
 Chapter 7 Section 7.0, 7.1
 Chapter 2
 Chapter 1
 Slides
 Lecture 14
 Notes
 Lecture 14
Lecture 13
The first midterm!
Lecture 12
We reviewed the class so far! This included a briefly summary of topics,
a review of HWs 1 and 2, and a set of potential questions for the midterm.
 Slides
 Lecture 12
Lecture 11
We reviewed the problems on the Quiz. Then we went back into Monte Carlo
methods and gave a visual explanation for how Monte Carlo integration works.
This then led to a discussion of how to compute the variance properly
 Reading
 Chapter 3
 Slides
 Lecture 11
 Julia
 Lecture 11 (Monte Carlo) (html)
(ipynb)
 Lecture 11 (Variance) (html)
(ipynb)
Lecture 10
We reviewed some of the basics of probability, random variables, and expectations.
We saw how to compute Pi via a Monte Carlo method, and saw how to turn an
integral into an expectation so we can use Monte Carlo. Then we saw the CLT.
 Reading
 Chapter 3
 Slides
 Lecture 10
 Notes
 Lecture 10
Lecture 9
Introduction to Monte Carlo methods via three examples: the Monty Hall problem,
a popquiz on a property of the unit circle, and Google's PageRank problem.
 Reading
 Chapter 3
 Slides
 Lecture 9
 Julia
 Lecture 9 (Monty Hall) (html)
(ipynb)
 Lecture 9 (Circle points) (html)
(ipynb)
 Lecture 9 (PageRank random surfer) (html)
(ipynb)
Lecture 8
Today we had a quiz on floating point arithmetic and then we
saw a few guidelines on how to ensure good floating point computations;
and why you must always be careful!
 Reading
 Chapter 5
 Once dead by Richard Phillips (See intro to Chapter 55, page 208)
 Julia
 Lecture 8 (Accurate norms) (html)
(ipynb)
 Slides
 Lecture 8
Lecture 7
Today we covered how computers do floating point arithmetic, IEEE rounding
modes, and the guarantees of IEEE floating point arithmetic.
 Reading
 Chapter 5  Section 5.5 and 5.6
 Further reading
 The mathematics of the Intel Floating Point Bug
 Numerical Computing with IEEE Floating Point Arithmetic by Michael Overton
 Julia
 Lecture 6 (Floating point numbers) (html)
(ipynb)
(Holdover from last time!)
 Slides
 Lecture 7
 Notes
 Lecture 7
Lecture 6
Today, we saw an intro to floating point arithmetic.
 Slides
 Lecture 6
 Notes
 Lecture 6
 Reading
 Chapter 5
Lecture 5
We did a quick intro to Latex, and more Julia including control flow,
function, and plotting. Then we did a review of the Quiz.
 Slides
 Lecture 5
 Julia
 Lecture 4 (control flow examples) (html)
(ipynb)
 Lecture 5 (plotting) (html)
(ipynb)
 Lecture 5 (functions) (html)
(ipynb)
 Lecture 5 (functions, filledin) (html)
(ipynb)
 Lecture 4 (script) (html)
(ipynb)
 Latex
 Simple Latex Document
 Simple Latex Document Compiled
 Edited Homework 1
 Edited Homework 1 Compiled
 Edited Homework 1 Extra Files
Lecture 4
In this lecture, we did a long intro the to the julia language.
 Slides
 Lecture 4
 Reading
 Chapter 2 (but using our Julia conversion below)
 Chapter 2 converted: Using Julia (html)
(ipynb)
 Chapter 2 converted: Plotting in Julia (html)
(ipynb)
 Julia
 Lecture 4 (control flow examples) (html)
(ipynb)
Lecture 3
We had a quiz and saw how to use the Julia language.
 Slides
 Lecture 3
 Reading
 Chapter 2
 Julia
 Chapter 2 converted: Using Julia (html)
(ipynb)
 Chapter 2 converted: Plotting in Julia (html)
(ipynb)
 Lecture 3 in class commands (html)
(ipynb)
Lecture 2
We reviewed what happens in mathematical modeling and how we take a problem
from an initial statement into a compute model. We saw two examples: the
XKCD Raptor Problem as well as Google's PageRank problem.
 Slides
 Lecture 2
 Notes
 Lecture 2
 Reading
 Chapter 1
 Julia
 Lecture 2: The XKCD Raptor Problem (html)
(ipynb)
Lecture 1
We reviewed the syllabus, and saw the importance of computing.
 Slides
 Lecture 1
 Reading
 Syllabus
 Chapter 1
 Julia
 Lecture 1: Polygon Midpoints (html)
(ipynb)