 Section 201
 Mathematics 203
 MWF 11:00 plus a laboratory hour Mondays 12:00
Outline.
This term will begin with work on the spread
sheet used in Mathematics 102/103. You can access it at the
MathSheet home page.
One principal goal is to
understand the mathematics of limits and calculus
by exploring examples. Another is to
learn the limitations of computers
as well as their potential.
 Introduction to the spreadsheet
 Numerical calculation of integrals

Not all integrals have formulas, for
example e^{x2}

Rectangle rule

Error analysis of the rectangle rule leads to the trapezoid rule

Taylor's series

Error analysis of the trapezoid rule (by applying
Archimedes' method) leads to Simpson's rule

How to use error estimates [ Notes in .pdf form ]
 Interpolation of tables [ Notes in .pdf form ]
 Asymptotic formulas [ Notes in .pdf form ]
 Archimedes' calculation of
 Richardson's extrapolation technique
 Real numbers in machines
 Numbers and approximations to them
 Cancellation and stable formulas
 Rounding errors
 Discrete probability distributions
 Sums of independent events & convolution
 Continuous probability distributions
 Mean, variance, standard deviation
 Approximation by normal distributions
 Series [ Notes in .pdf form ]
 Geometric series
 Series for e^{x}
 Harmonic series and cousins
 Solving differential equations

Numericalvalued functions [ Notes in .pdf form ]

Systems of functions and higher order equations [ Notes in .pdf form ]
 Matrix operations [ Notes in .pdf form ]
 Eigenvectors, eigenvalues
 Matrix exponentials
Later in the term,
we are likely to move to Maple programming
in order to get access to calculations with
arbitrarily high precision.
Source material.
There will be no required text, but as the term progresses
class notes will appear here.
A few references are listed here; they are out of print.
 Peter Henrici, Essentials of numerical analysis,
John Wiley. This is my own principal source.
There is a copy on twohour
reserve in the Mathematics Library.
 J. B. Rosser & Carl de Boor,
Pocket calculator supplement for calculus,
AddisonWesley. Not very dense in good
ideas, but occasionally useful.
 On line material about Maple programming
The midterm examination
The midterm examination will be closed book  no notes, just calculator and pen.
Show up in Mathematics 201/202 as early as possible.
Some will be told to go the MSRC building.
In order to avoid problems caused by crashes, freezes, etc.,
open two copies of Netscape running simultaneously. One for reading these
pages, and one for running the spreadsheet.

To run the spreadsheet,
go to the MathSheet home page
and then to the applet page. Open a running
copy of the spreadsheet.

Log in immediately: File/Log in. Use m210
as your group. Remember to save your work frequently.

The exam itself
The assignments
My sample spreadsheets for these assignments will appear among
the files you have access to if you enter
"m210" as your group when you log in.
