Mathematics Mathematics

in Electricity

in Electricity

By: HAZADOUS GEMS4

By: HAZADOUS GEMS4

Mat

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Mathematics in Electronics

Mathematics in Electronics

Electrical Engineering usually include

Electrical Engineering usually include

CalculusCalculus (single and

(single and multivariablemultivariable), ),

Complex Analysis

Complex Analysis, , Differential Equations

Differential Equations (both ordinary

(both ordinary

and partial), Linear Algebra and

and partial), Linear Algebra and

Probability. Fourier Analysis and Z-

Probability. Fourier Analysis and Z-

Transforms are also subjects which are

Transforms are also subjects which are

usually included in electrical

usually included in electrical

engineering programs.

engineering programs.

Of these subjects, Calculus and

Of these subjects, Calculus and

Differential equations are usually

Differential equations are usually

prerequisites for the Physics courses

prerequisites for the Physics courses

required in most electrical

required in most electrical

engineering programs (mainly

engineering programs (mainly

Mechanics, Electromagnetism &

Mechanics, Electromagnetism &

Semiconductor Physics). Complex

Semiconductor Physics). Complex

Analysis has direct applications in

Analysis has direct applications in

Circuit Analysis, while Fourier Analysis

Circuit Analysis, while Fourier Analysis

is needed for all Signals & Systems

is needed for all Signals & Systems

courses, as are Linear Algebra and Z-

courses, as are Linear Algebra and Z-

Transform.Transform.

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Intr

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Intr

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Numbers can take different forms:

Numbers can take different forms:

Whole numbers: 1, 20, 300, 4,000, 5,000

Whole numbers: 1, 20, 300, 4,000, 5,000

Decimals: 0.80, 1.25, 0.75, 1.15

Decimals: 0.80, 1.25, 0.75, 1.15

Fractions: 1/2, 1/4, 5 8, 4 3 ⁄ ⁄

Fractions: 1/2, 1/4, 5 8, 4 3 ⁄ ⁄

Percentages: 80%, 125%, 250%, 500%

Percentages: 80%, 125%, 250%, 500%

You’ll need to be able to convert these

You’ll need to be able to convert these

numbers from one form to another and

numbers from one form to another and

back again, because all of these

back again, because all of these

number forms are part of electrical

number forms are part of electrical

work and electrical calculations.

work and electrical calculations.

You’ll also need to be able to do some

You’ll also need to be able to do some

basic algebra. Many people have a

basic algebra. Many people have a

fear of algebra, but as you work

fear of algebra, but as you work

through the material here you’ll see

through the material here you’ll see

there’s nothing to fear.

there’s nothing to fear.

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Whole numbers are

Whole numbers are exactly what the term

exactly what the term implies. These numbers

implies. These numbers

don’t contain any

don’t contain any fractions, decimals, or

fractions, decimals, or percentages. Another

percentages. Another name for whole numbers

name for whole numbers

is “integers.”

is “integers.”

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The decimal method is

The decimal method is

used to display numbers

used to display numbers

other than whole

other than whole numbers, fractions, or

numbers, fractions, or percentages such as,

percentages such as, 0.80, 1.25, 1.732, and so

0.80, 1.25, 1.732, and so

on. on.

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A fraction represents part of a whole

A fraction represents part of a whole

number. If you use a calculator for

number. If you use a calculator for

adding, subtracting, multiplying, or

adding, subtracting, multiplying, or

dividing, you need to convert the

dividing, you need to convert the

fraction to a decimal or whole number.

fraction to a decimal or whole number.

To change a fraction to a decimal or

To change a fraction to a decimal or

whole number, divide the numerator

whole number, divide the numerator

(the top number) by the denominator

(the top number) by the denominator

(the bottom number).

(the bottom number). Examples Examples 1 6 = one divided by six = 0.166

⁄1 6 = one divided by six = 0.166

⁄ 2 5 = two divided by five = 0.40

⁄2 5 = two divided by five = 0.40

⁄ 3 6 = three divided by six = 0.50

⁄3 6 = three divided by six = 0.50

⁄ 5 4 = five divided by four = 1.25

⁄5 4 = five divided by four = 1.25

⁄ 7 2 = seven divided by two = 3.50

⁄7 2 = seven divided by two = 3.50

⁄

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When a number needs

When a number needs

to be changed by

to be changed by multiplying it by a

multiplying it by a percentage, the

percentage, the percentage is called a

percentage is called a multiplier. The first step

multiplier. The first step

is to convert the

is to convert the percentage to a decimal,

percentage to a decimal,

then multiply the

then multiply the original number by the

original number by the

decimal value.

decimal value.

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EXAMPLEEXAMPLE

Question: An overcurrent

Question: An overcurrent

device (circuit breaker or

device (circuit breaker or

fuse) must be sized no less

fuse) must be sized no less

than 125 percent of the

than 125 percent of the

continuous load. If the load is

continuous load. If the load is

80A, the overcurrent device

80A, the overcurrent device

will have to be sized no

will have to be sized no

smaller than smaller than

. . Figure 1–

Figure 1–

22

(a) 75A (b

) 80A

(a) 75A (b

) 80A

(c) 100A

(d) 125A

(c) 100A

(d) 125A

Answer: (c) 100A

Answer: (c) 100A

Step 1: Convert 125 percent to

Step 1: Convert 125 percent to

a decimal: 1.25

a decimal: 1.25

Step 2: Multiply the value of

Step 2: Multiply the value of

the 80A load by 1.25 = 100A

the 80A load by 1.25 = 100A

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Square Root

Square Root Deriving the square root of a number (√

Deriving the square root of a number (√ nn) is ) is

the opposite of squaring a number. The square

the opposite of squaring a number. The square

root of 36 is a number that, when multiplied by

root of 36 is a number that, when multiplied by

itself, gives the product 36. The √

itself, gives the product 36. The √36 36 equals six, equals six,

because six, multiplied by itself (which can be

because six, multiplied by itself (which can be

written as 62) equals the number 36.

written as 62) equals the number 36.

Because it’s difficult to do this manually, just

Because it’s difficult to do this manually, just

use the square root key of your calculator.

use the square root key of your calculator.

√ √ 33: Following your calculator’s instructions,

: Following your calculator’s instructions,

enter the number 3, then press the square root

enter the number 3, then press the square root

key = 1.732. key = 1.732. √ √ 1,0001,000: enter the number 1,000, then press the

: enter the number 1,000, then press the

square root key = 31.62.

square root key = 31.62.

If your calculator doesn’t have a square root

If your calculator doesn’t have a square root

key, don’t worry about it. For all practical

key, don’t worry about it. For all practical

purposes in using this textbook, the only

purposes in using this textbook, the only

number you need to know the square root of is

number you need to know the square root of is

3. The square root of 3 equals approximately

3. The square root of 3 equals approximately

1.732. 1.732. To add, subtract, multiply, or divide a number

To add, subtract, multiply, or divide a number

by a square root value, determine the decimal

by a square root value, determine the decimal

value and then perform the math function.

value and then perform the math function.

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Introduction to Calculus

Introduction to Calculus

math\calculus.doc

math\calculus.doc 01/16/2002

01/16/2002 This brief Section seeks only

This brief Section seeks only

to provide the reader with a

to provide the reader with a

very brief and general

very brief and general concept of what calculus is

concept of what calculus is

all about.all about. The study of calculus is

The study of calculus is

customarily divided into two

customarily divided into two

parts:parts: Differential calculus

Differential calculus, and,, and,

Integral calculus

Integral calculus..

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DIFFERENTIAL

DIFFERENTIAL

CALCULUS CALCULUS

Differential calculus is

Differential calculus is

concerned with the rate of

concerned with the rate of

changechange of one variable with

of one variable with

respect to another.

respect to another.

Differential calculus is

Differential calculus is

exemplified by the following

exemplified by the following

questions:questions:

What is the best way of

What is the best way of

describing the speed of a car

describing the speed of a car

or the cooling of a hot object?

or the cooling of a hot object?

How does the change of

How does the change of

output current of a transistor

output current of a transistor

amplifier circuit depend upon

amplifier circuit depend upon

the change of the input

the change of the input

current?current?

INTEGRALINTEGRAL

The study of

integration and

its uses, such as

in calculating

areas bounded

by curves,

volumes

bounded by

surfaces, and

solutions to

differential

equations.

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