By John L. Casti (Eds.)

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**Sample text**

7. 2707. 5. 5. 75001〉, and so on. Formulate a conjecture as to how the value of ÓÑÔ Ö ÓØ ´ ¼¸ ¼µ increases with the value of 1/|Y0 − Z0|. (c) Double precision numbers are represented with about 16 digits (51 bits) of precision. Suppose that you start with a value of y 0 in double precision and compute the series y 0 , y 1 , y 2 , . .. Given your conjecture in (b), how many terms of the series can you compute before the values become completely unrelated to the true value? This page intentionally left blank I Linear Algebra This page intentionally left blank Chapter 2 Vectors Linear algebra is the study of vectors, discussed in this chapter, and matrices, discussed in Chapter 3.

The limitation of this approach, as opposed to (1), is that you can end up understanding each of the steps but not the overall progress of the proof; you hear the notes but not the overall tune. In either (1) or (2), if the book provides a picture or example, then you should carefully look at it and make sure you understand the connection between the picture or example and the proof. If the book doesn’t provide one, then you should draw a picture if the proof is geometric, or you should work through some numeric examples if the proof is numeric.

If any of the control parameters is omitted, then a default value is used. The default color is blue, the default data point indicator is none, the default line type is no line if a data point indicator is included and a solid line if it is not. For example: ÔÐÓØ´Ü¸Ýµ ÔÐÓØ´Ü¸Ý¸³¶ ³µ ÔÐÓØ´Ü¸Ý¸³ ³µ ÔÐÓØ´Ü¸Ý¸³¹¹Ú³µ Points connected by blue line, no marker at points Points marked by green asterisk, no line Points connected by dotted black line, no marker at points Blue points marked by downward triangle connected by blue dashed line.