dv/dt.com

NOTES

Newton first law of motion states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of a net external force. This is normally taken as the definition of Inertia. Net force on a body is determined by adding up all external forces. ZERO net force would essentially mean that all the external forces cancel each other out.Thus in absence of net external force, the object will maintain a constant velocity. If that velocity is zero, then the object remains at rest.

Following presents the definition of Newton's first law of motion on NASA webpage

Above diagram presents example of an airplane, a ball, a model rocket and a kite to describe newton's first law of motion.

Following are some videos on differential calculus taken from MIT courseware webpage. They are worth a look:

Derivative of sin x and cos x
Product Rule and Quotient Rule
Chains f(g(x)) and the Chain Rule
Limits and Continuous Functions
Inverse Funtions f ^-1 (y) and the Logarithm x = ln y
Derivatives of ln y and sin ^-1 (y)
Growth Rate and Log Graphs
Linear Approximation/Newton's Method
Power Series/Euler's Great Formula
Differential Equations of Motion
Differential Equations of Growth
Six Functions, Six Rules, and Six Theorems

Following are links for some videos for high school students to understand calculus. These videos are created as part of MIT Courseware and is worth a look:

Introduction to calculus
Big Picture of Calculus
Big Picture: Derivatives
Max and Min and Second Derivative
The Exponential Function
Big Picture: Integrals

NOTES

According to Wikipedia, following is how derivative is defined:

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity (conversely, integrating a car's velocity over time yields the distance traveled).

Mathematically speaking, above can be represented as following:

If Y changes with x, Y can be termed as function of x.

Thus, Y = f(x)

The process of determining the change of Y with respect to change in x is termed as Differentiation. This is represented using letter DELTA or d.

Change of Y with respect to x could be measured as following:

(Y2 - Y1)/(X2 - X1)
OR
DELTA (Y) / DELTA (x)
OR
dY/dx

Following is an animation depicting atom and their fundamental particles except morons..:)