**INTEGRAL (1/x) dx**

*Perform integration by parts:*

let

**u = 1/x , dv = dx du = -1/x2 dx , v = x**

Then obtain:

**INTEGRAL (1/x) dx = (1/x)*x - INTEGRAL x (-1/x2) dx**

**= 1 + INTEGRAL (1/x) dx**

which implies that

**0 = 1.**

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## Thursday, July 16, 2009

###
ONE EQUALS ZERO

###
USES OF LAPLACE TRANSFORMS

**PIERRE SIMON LAPLACE**

**Here's an example**** ** **:**

Suppose we have a function of time, such as cos(w*t). With the Laplace transform, we can convert this to a function of frequency, which is

**cos(w*t) ----L{}-----> w / (s^2 + w^2)**

###
THE PROOF 1 + 1 = 0

**1****+1** **= 1+ sqrt (1)**

= 1+ sqrt [(-1) (-1)]

= 1+ [sqrt (-1) * sqrt (-1)]

= 1+ [i * i]

= 1+ (-1 )

= 1 -1

= 0
###
MATH INVOLVED IN ELECTRICAL AND ELECTRONIC ENGINEERING

**In general, it is not possible to do EE without math. **

**Each abstract mathematical theorem somehow** **finds its use in EE**.

## About Me

## Labels

"LIKE THE CREST OF A PEACOCK , SO IS MATHEMATICS AT THE HEAD OF ALL KNOWLEDGE"

Consider the following integral:

**INTEGRAL (1/x) dx**

*Perform integration by parts:*

let**u = 1/x , dv = dx du = -1/x2 dx , v = x **

Then obtain:

**INTEGRAL (1/x) dx = (1/x)*x - INTEGRAL x (-1/x2) dx**

**= 1 + INTEGRAL (1/x) dx**

which implies that**0 = 1. **

let

Then obtain:

which implies that

**The Laplace transform is a simple way of converting functions in one domain to functions of another domain**.

Suppose we have a function of time, such as cos(w*t). With the Laplace transform, we can convert this to a function of frequency, which is

**This is useful for a very simple reason**: it makes solving differential equations much easier.

- The development of the logarithm was considered the most important development in studying astronomy. In much the same way, the
**Laplace transform makes it much easier to solve differential equations.**

- Since the Laplace transform of a derivative becomes a multiple of the domain variable, the Laplace transform turns a complicated n-th order differential equation to a corresponding nth degree polynomial. Since polynomials are much easier to solve, we would rather deal with them. This occurs all the time.

- In brief, the
**Laplace transform is really just a shortcut for complex calculations**. It may seem troublesome, but it bypasses some of the most difficult mathematics.

- Laplace transform is a technique mainly utilized in engineering purposes for system modeling in which a large differential equation must be solved.

- The Laplace transform can also be used to solve differential equations and is used extensively in electrical engineering.

- Laplace Transform is used in electrical circuits for the analysis of linear time-invariant systems

Labels:
APPLICATIONS OF MATHEMATICS,
LAPLACE,
LAPLACE TRANSFORM,
RFEL LIFE APPLICATIONS OF LAPLACE,
USES OF LAPLACE RANSFORM

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= 1+ sqrt [(-1) (-1)]

= 1+ [sqrt (-1) * sqrt (-1)]

= 1+ [i * i]

= 1+ (-1 )

= 1 -1

= 0

- There's really a lot of math involved in electrical and electronicengineering.
**How much you do depends on what area of EE (shorthand for electrical and electronic engineer) you do.**

**For example**, there's a lot more abstract math in communication theory and signal processing, and many more**very direct calculation differential equations in circuit theory and systems****design.**

**Circuit theory****at its simplest form is really differential equations, which is basically solving equations involving derivatives**, so you need some**CALCULUS****and****ALGEBRA and TRIGONOMETRY**are fundamental to understanding it. Every basic circuit element (resistor, capacitor, inductor) has arelated current-voltage relation determined by its impedance. This iswhere**COMPLEX NUMBERS**come in.

**If we move on to the****theory of "how" electromagnetism works, we haveMaxwell's equations**. These pretty much form the basis for EE.**They are written in both integral and derivative forms and involve vectors.**So, suddenly, we also have**VECTOR CALCULUS**.

- If we move to
**Communication Theory/Information Theory**, a mathematician named**Claude Shannon**developed a mathematical theory to explain various quantities related to how to communicate between devices.**Communication Theory is used everywhere, from RADAR, to****telephones, to devices within computers. The underlying theory requires at least CALCULUS , some LINEAR ALGEBRA , some MEASURE THEORY, etc**.

**Even wavelets, which have revolutionized signal processing, were discovered by mathematicians early in the 20th century, but not used by engineers until 20 years ago**.

Labels:
APPLICATIONS OF MATHEMATICS

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