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y(x) = ax + b (3.1)
In-Class Exercises
Pb. 3.1 Generate four function M-files for the following four functions:
yx() = 3 x 2; ()+ y x = 3 x 5; ()+ y x = − x + 3; yx() = − x + 4
1 2 3 4
3 3
Pb. 3.2 Sketch the functions of Pb. 3.1 on the interval –5 < x < 5. What can
you say about the angle between each of the two lines’ pairs. (Did you
remember to make your aspect ratio = 1?)
Pb. 3.3 Read off the graphs the coordinates of the points of intersection of
the lines in Pb. 3.1. (Become familiar with the use and syntax of the zoom and
ginput commands for a more accurate reading of the coordinates of a point.)
Pb. 3.4 Write a function M-file for the line passing through a given point and
intersecting another given line at a given angle.
tan( ) tan( )a + b
Hint: tan(ab+ ) =
1 − tan( )tan( )a b
Application to a Simple Circuit
The purpose of this application is to show that:
1. The solution to a simple circuit problem can be viewed as the
simultaneous solution of two affine equations, or, equivalently, as
the intersection of two straight lines.
2. The variations in the circuit performance can be studied through
a knowledge of the affine functions, relating the voltages and the
current.
Consider the simple circuit shown in Figure 3.1. In the terminology of the
circuit engineer, the voltage source V is called the input to the circuit, and the
S
current I and the voltage V are called the circuit outputs. Thus, this is an
example of a system with one input and two outputs. As you may have stud-
ied in high school physics courses, all of circuit analysis with resistors as ele-
ments can be accomplished using Kirchhoff’s current law, Kirchoff’s voltage
law, and Ohm’s law.
• Kirchoff’s voltage law: The sum of all voltage drops around a
closed loop is balanced by the sum of all voltage sources around
the same loop.
© 2001 by CRC Press LLC
