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Equations of Lines
In this part we need to take a view at the equation of a line in R3. As we saw in the earlier section the equation y = mx+b does not explain a line in R3, in place of it describes a plane. Though, this doesn't mean that we can't write down an equation for a line in 3-D space. We're just going to require a new way of writing down the equation of a curve.
Thus, before we get into the equations of lines we first require to briefly looking at vector functions. We are going to take a much more in depth look at vector functions later. At the moment all that we need to worry about is notational issues and how they can be employed to give the equation of a curve.
Find out the general formula for the tangent vector and unit tangent vector to the curve specified by r → (t) = t 2 i → + 2 sin t j → + 2 cos t k → . Solution First,
DISTINCT EIGENVALUES -SYSTEM SOLVING : E xample Solve the following IVP. Solution : Therefore, the first thing that we must to do that is, get the eigenvalues
The Mean Value Theorem : In this section we will discuss the Mean Value Theorem. Before we going through the Mean Value Theorem we have to cover the following theorem. Ro
Calculate the area of CIRCLE ? A circle is a set of all points that are at a given distance from a center point. The diameter (d) of a circle is the length of a line that goes
1. Discuss lyapunov function theory and how it can be used to prove global assmptotic stability of solutions.(Give an example form natural and engineering sciences.) --- Draw le
HOW TO ADD MIXED FRACTION
Evaluate following limits. Solution In this part what we have to note (using Fact 2 above) is that in the limit the exponent of the exponential does this, Henc
Velocity and Acceleration - Three Dimensional Space In this part we need to take a look at the velocity and acceleration of a moving object. From Calculus I we are famili
Bill traveled 117 miles in 2.25 hours. What was his average speed? Use the formula d = rt (distance = rate × time). Substitute 117 miles for d. Substitute 2.25 hours for t and
Without solving, find out the Wronskian of two solutions to the subsequent differential equation. t 4 y'' - 2t 3 y' - t 8 y = 0 Solution : First thing that we want to d
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