Polynomial Approximations 
Sunday, February 7, 2010, 11:10 AM - Calculus
Posted by Administrator
Last time, we went into the Taylor and Macluarin Series.  This time we are going to go into the background of series and sequences in calculus and work our way up to Taylor Series.  This is the concept of Polynomial Approximations...

add comment ( 3 views )   |  permalink   |   ( 3 / 5 )

Taylor And Maclaurin Series 
Saturday, February 6, 2010, 07:11 PM - Calculus
Posted by Administrator
In mathematics, the Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. It is named after the English mathematician Brook Taylor. If the series is centered at zero, the series is also called a Maclaurin series, named after the Scottish mathematician Colin Maclaurin. It is common practice to use a finite number of terms of the series to approximate a function. The Taylor series may be regarded as the limit of the Taylor polynomials.

add comment ( 2 views )   |  permalink   |   ( 3 / 5 )

Displacement, Speed, Velocity And Acceleration 
Wednesday, February 3, 2010, 07:28 PM - Calculus
Posted by Administrator
Displacement (vector), in Newtonian mechanics, specifies the change in position of a point in reference to a previous position. In simple terms, it's the difference between the initial position and the final position of an object
The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.
This article is about velocity in physics. In physics, velocity is the rate of change of position. It is a vector physical quantity; both speed and direction are required to define it. In the SI (metric) system, it is measured in meters per second: (m/s) or ms−1.
In physics, and more specifically kinematics, acceleration is the change in velocity over time. Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows down. However, as a vector quantity, acceleration is also the rate at which direction changes. Acceleration has the dimensions L T−2. In SI units, acceleration is measured in metres per second squared (m/s2).

add comment ( 2 views )   |  permalink   |   ( 3 / 5 )

Linear Approximations 
Tuesday, February 2, 2010, 02:39 AM - Calculus
Posted by Administrator
In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.

add comment ( 2 views )   |  permalink   |   ( 3 / 5 )

Related Rates 
Saturday, January 30, 2010, 06:29 PM - Calculus
Posted by Administrator
In differential calculus, related rates problems involve finding a rate that a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time.

The most common way to approach related rates problems is the following:

  1. Identify the known variables, including rates of change and the rate of change that is to be found. (Drawing a picture or representation of the problem can help to keep everything in order)
  2. Construct an equation relating the quantities whose rates of change are known to the quantity whose rate of change is to be found.
  3. Differentiate both sides of the equation with respect to time (or other rate of change).
  4. Substitute the known rates of change and the known quantities into the equation.
  5. Solve for the wanted rate of change.

Errors in this procedure are often caused by plugging in the known values for the variables before (rather than after) finding the derivative with respect to time. Doing so will yield an incorrect result.





add comment ( 6 views )   |  permalink   |  related link   |   ( 3 / 5 )


| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Next> Last>>