## Mathematics 210 - Spring 2003

• 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.

• 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 ]
• Linear
• Cubic
• 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 ex
• Harmonic series and cousins
• Solving differential equations
• Numerical-valued 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 two-hour reserve in the Mathematics Library.
• J. B. Rosser & Carl de Boor, Pocket calculator supplement for calculus, Addison-Wesley. 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.