Pre-Engineering 220 Introduction to MatLab ® & Scientific Programming j kiefer
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We used the (ln) button on our pocket calculator, followed by the (ex) button. In earlier times, we’d have used log tables. But, whence cometh those tables and how does the calculator evaluate ln 467 or e2.0488? 3. Series
The infinite series are exact. However, in practice we always keep a finite number of terms. In principle, we can achieve arbitrary precision, if we have the necessary patience. Pocket calculators and computer programs add up enough terms in a series to achieve a specified precision, say 8 or 16 significant digits. 4. ErrorIn this context, the term error does not refer to a mistake. Rather, it refers to the ideas of deviation or of uncertainty. Every measured value is uncertain, according to the precision of the measuring instrument. Every computed value is uncertain, according to the number of significant digits carried along or according to the number of terms retained in the summation of a series. Consequently, all numerical solutions are approximate. Oftentimes, in discussing an example problem, the correct exact solution is known, so it is possible to determine how an approximate numerical solution deviates from that exact solution. Indeed, algorithms are often tested by applying them to problems having known exact solutions. However, in real life, we don’t know the correct exact solution. We can’t know how far our approximate solutions deviate from the correct, exact, but unknown solution. In other words, we have to approximate the solution to a problem, but also we can only estimate the error. Fortunately, we have means of estimating error. A goodly portion of the discussion in a Numerical Methods textbook is devoted to rigorous estimation of error. In this course, we won’t concern ourselves with a detailed discussion of error analysis. Nonetheless, we want to be always aware of the error issue, keeping in mind at least qualitatively the limitations of a numerical solution. From time to time in the paragraphs that follow some aspects of the error involved with a particular algorithm will be briefly discussed. Directory: physics physics -> Photometer and Optical Link Sensitivity issues, needs editing 1/2010 Purpose physics -> Photometer and Optical Link Purpose physics -> - physics -> Teacher Notes – Activity 14: Momentum in Collisions physics -> Teacher Notes – Activity 15: Impulse and Change in Momentum physics -> Linear Momentum Definition Download 8.69 Mb. Share with your friends:
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