Shortly I will have consecutive postings on:

1. Generalized Functions

2. Distributional/ weak Derivatives

3. Function Spaces in particular Sobolev Spaces

This block/module will be for calculus lessons:

I will post rudiments of calculus in the following order:

Sets-Functions

Limits-Continuity

Differentiation-Techniques of Differentiations-Applications of Differentiation in different areas.

Antiderivative or Integration

Techniques of Integrations-Applications of Integrations.

Knowing all these concepts will give a student a good momentum to learn mathematics at universities and colleges. Threfore stay tune for the fun.

Definite Integral :

lim ∑_{k=0}ⁿ =∫_{a}^{b}

n→∞

E

J

C

S

M

SHINING & SPARKLING MATHEMATICAL IMAGES -- BY DEJENIE ALEMAYEHU LAKEW, PH.D.

Think for the moment why computers do perfectly with minimal possibility of errors, doing what we intend them to do: computers in flights, hospitals, banks, cars, etc. ? Because their language - the way they receive input data, process information and communicate their results to us is through the only language of no ambiguity -- *Mathematic*s. Had it been one of the languages of man that computers use, I can imagine how many tragedies have been committed from flights, hospitals, cars, etc, where computers are used, since the advent of computers and their usage for man.

As a matter of fact we sometimes say, the *mathematics* we write in human languages informal, while the one we do in abstractions using possible symbols of *mathematics* formal. Here the formal descriptions of the mathematics we do are not bound to misinterpretations and thereby getting different results - which in most cases are wrong results. But the formal ones always precise, not open to distortions which when happen reflected on the negative and un intended results. Almost all destructions that occurred through out the history of humankind in dealing with each other and reading nature are due to misrepresentation, misreading, misunderstanding, miscommunication and thereby getting un intended results and their aftermath.

Then what better language of precision can somebody of a common sense imagine than *Mathematics *?

~* Dejenie Alemayehu Lakew, Ph.D.*

Two Fundamental Theorems of Calculus

Few of the basic rules of differentiation

Integration by parts

Length of an arc C: graph of **ψ **on [a,b]

Volume of a solid of revolution **of a plane domain enclosed by graph of ****ψ** on [a,b]

CALCULUS -

GATEWAY TO MATHEMATICS

Mathematics Problems Corner: