Archive for year: 2019

A Logistic Differential Equation (LDE) is an ordinary differential Equation whose solution is a logistic function.

LDE(logistic differential equation) include two positive parameters –

i) Growth parameter (growth rate)k: This parameter   plays a role similar to that of r in exponential differential equation.

ii) Carrying capacity (M):The carrying capacity of an organism in a given environment is defined to be the maximum population of that organism that the environment can sustain indefinitely.

Logistic Differential Equations

There is  no difference between linear approximation and linearization. These are just two different ways to say the same thing.

Linear approximation is an important application of differential calculus.

Differential calculus  has numerous applications , from finding critical values  to finding maximum  and minimum values , checking concavity, rate of change measures,  linearization  , optimization and many more.

I find these topics very interesting  and i bet you too will find them interesting  once you get the concepts. Here i’m sharing a link where you can find useful notes  on these topics. Some are added already  and some are being added  at regular intervals.

Don’t forget to share your experience  and your valuable suggestions to improve  this service. Thanks !

Polar coordinate system is a plane with Pole(point O) and polar axis  which is horizontal axis from point O. Any point P in this plane is assigned polar coordinates represented as P(r, theta)

we measure theta as positive when moving counterclockwise and negative when moving clockwise.

If r > 0, then P is on the terminal side of  theta . If r < 0, then P is on the terminal side of   (theta + pi).

 

An algebraic expression containing two terms is called binomial expression. The general form of the binomial expression is (x+a) and the expansion of (x+a)^n, where n is a natural number, is called binomial theorem. It gives a formula for the expansion of the powers of binomial expression.
The coefficients in the binomial expansion follow a specific pattern known as Pascal’s triangle.
Following are some important features of Pascal’s triangle.
-Each row is bounded by 1 on both sides.
-Any entry except first and last, is the sum of two entries in preceding row , one on the immediate left and other on immediate right.
Some important conclusions from the Binomial Theorem:
Total number of terms in binomial expansion is n+1.
The coefficients of terms equidistant from the beginning and end are equal. These coefficients are known as binomial coefficients.
The terms in the expansion of (x-a)^n are alternatively positive and negative first being positive always.
The coefficient of x^r in (r+1)th term in the expansion of (x+a)^n is (_r^n)C.
For more help on this topic, please visit..https://celestialtutors.com/topic/pascals-triangle-and-binomial-theorem-2/