Exploring calculus and differential equations with the TI-89 and TI-92 Plus by Schneider, Michael B, Schneider, Michael, Gilligan, Lawrence (2000) Taschenbuch - Softcover

Softcover

ISBN 10: 1888808055 ISBN 13: 9781888808056

Inhaltsangabe

This text comes with an included diskette of over 50 programs in the areas of Calculus and Differential Equations. A "MUST" for college math and engineering majors with a TI-89 or TI-92 Plus calculator. Part one of the book is an overview of the calculators' features in the context of the mathematics. Part two contains sixteen explorations in the calculus (calc I, II, and III) and differential equations curricula. The TI-Graph Link is necessary to download the programs from the diskette to the calculator. This book is written by educators (M. Schneider is a professor at Southwest Illinois College and L. Gilligan is a professor at the University of Cincinnati) not technocrats!!!

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Über die Autorin bzw. den Autor

Michael Schneider is a professor of mathematics at Soutwestern Illinois College (Belleville, IL). Lawrence Gilligan is professor of mathematics at the University of Cincinnati's College of Applied Science and has written over 25 math/technology texts.

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Graphing Sequences

By selecting "4:SEQUENCE" from the  screen, we can graph sequences and partial sums of sequences. In this mode, the Y= editor allows us to enter sequences (as u1, u2, etc.) and initial values of sequences (ui1, ui2, etc.). For a first example, we consider the sequence . We enter u1(n) as 1  and also enter "1" (although it is optional) for the initial value ui1. To also examine the sequence of partial sums of the u1(n) sequence, we enter for u2(n). See the screens below. We chose to graph u1(n) in "square" style and u2(n) in "thick" style. The horizontal axis is n and the vertical axis is u.

If we trace to the last value of n (nmax = 75) , we can see that . . It can be shown in calculus that the exact value of .

For a second example, we will examine a sequence function that is defined recursively. That is, a sequence defined in terms of itself. We entered the function and ui1 = 0. This sequence is: . The screens below show the setup to determine how compositions of the cosine function converge. Upper left: The function and its initial value are entered. Upper right: Choose "1:TIME" under the r Axes option. Lower left: Window values

Lower right: The first 30 entries of the sequence.

To approximate the value to which the terms seem to be converging, we use the n TRACE option. The figure below shows that value to be about 0.739085. After selecting TRACE, enter 100 and press e twice.

An interesting variation of sequence graphing is something called a WEB plot. A WEB plot graphs the sequence by using u1(n) for the vertical axis and u1(n-1) values for the horizontal axis. If a sequence converges to one specific value, as we have in our example, the WEB plot should converge to that point.

To enter a WEB plot, from the Y= editor, select r Axes. For "Axes:" choose WEB and for "Build Web:" select TRACE.

The web is constructed as you TRACE by repeated pressing the right cursor key. 3D Graphing

The 3D graphing mode is used for viewing the graph of a function of two independent variables, . As with the other graphing types, choose the 3D graph type from the  screen. The window parameters are more complicated for 3D graphing and we delineate them below: eye is the rotation angle of the eye from the x axis (if  is 0, the line of sight is on the xz plane) eye is the angle of tilt from the positive z axis (if  is 90o, the eye is on the xy plane) eye is the angle of counterclockwise rotation around the line of sight set by eye and eye xgrid is the number of coordinates evaluated between xmin and xmax ygrid is the number of coordinates evaluated between ymin and ymax ncontour is the number of contours that will be evenly distributed vertically xmin, xmax, ymin, ymax, zmin, zmax are self-explanatory Consider the function . We display the graph with two different formats, hidden surface and wire frame.

Details zur Ausgabe

• Erscheinungsdatum: 1709
• Sprache: Englisch
• ISBN 10: 1888808055
• ISBN 13: 9781888808056
• Einband: Taschenbuch
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar