By Stephen A. Wirkus, Visit Amazon's Randall J. Swift Page, search results, Learn about Author Central, Randall J. Swift,
"Featuring real-world functions from engineering and technological know-how fields, A direction in traditional Differential Equations is the 1st ebook on usual differential equations (ODEs) to incorporate appropriate machine code and directions of MATLAB®, Mathematica®, and Maple. The ebook embeds the pc algebra code all through, featuring the syntax subsequent to the proper idea. It absolutely describes approximations used to obtain numerical options. The authors additionally current reasons on tips to use those courses to resolve ODEs and to qualitatively comprehend self sustaining ODEs. With a variety of appendices to complement studying, this publication is perfect for college students and pros in arithmetic, engineering, and the sciences"--Publisher description. �Read more...
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Additional info for A course in ordinary differential equations
5 m/sec and at the end of 4 sec was 1 m/sec, when will the speed decrease to 1 cm/sec? What total distance will the raft travel? The amount of light absorbed by a thin layer of water is proportional to the amount of incident light and to the thickness of the layer. If a layer of water 35 cm thick absorbs half the light incident on its surface, what proportion of the incident light will be absorbed by a layer of water 200 cm thick? A uniform extensible cord 1 m long is stretched k · f meters by a force of f kg.
Y + 2)dx = (2x + y − 4)dy y+2 2 50. 3 Some Physical Problems Arising as Separable Equations Now that we have studied separable equations in detail, we consider some applications. The wide variety of application problems that we will consider all lead to equations in which variables can be separated. 3. 1 29 Free Fall, Neglecting Air Resistance We will begin this application section with an easy problem from elementary physics. This application should be very familiar. If x(t) represents the position of a particle at time t, then the velocity of the particle is given by dx v(t) = .
Integrating gives −1 2 1 −1 + 2 = + 3 +C x x y y as the general solution. This is deﬁnitely a case where giving the solution in an implicit representation is acceptable! We also refer the reader to the end of this section for the computer code used to plot these types of solutions with one of the software packages. There is, however, a more important idea that is illustrated by this example. Note that when we divided by x3 y 4 , we implicitly assumed that x = 0 and y = 0. If we rewrite the original diﬀerential equation as (x − 4)y 4 dy = 3 2 , dx x (y − 3) then one can clearly see that y = 0 is a solution.
A course in ordinary differential equations by Stephen A. Wirkus, Visit Amazon's Randall J. Swift Page, search results, Learn about Author Central, Randall J. Swift,