1.9 ARTICLES

What are articles?

Articles are words that identify a noun as being specific or unspecific. Consider the following examples:

Example : After the long day, the cup of tea tasted particularly good.

By using the article THE, we’ve shown that it was one specific day that was long and one specific cup of tea that tasted good.

Example : After a long day, a cup of tea tastes particularly good.

By using the article A, we’ve created a general statement, implying that any cup of tea would taste good after any long day.

English has two types of articles: definite and indefinite. Let’s discuss them now in more detail.

The definite article

The definite article is the word "THE".It limits the meaning of a noun to one particular thing.

Example :“Are you going to the party this weekend?” 

The definite article tells you that your friend is referring to a specific party that both of you already know about. The definite article can be used with singular, plural, or uncountable nouns.

The indefinite article

The indefinite article takes two forms. It’s the word "A" when it precedes a word that begins with a consonant. It’s the word "AN" when it precedes a word that begins with a vowel. The indefinite article indicates that a noun refers to a general idea or category of a thing rather than a specific thing. 

Example 1: You might ask your friend, “Should I bring a gift to the party?” 

Your friend will understand that you are not asking about a specific type of gift or a specific item. 

Example 2: Your sister tells, “I am going to bring an apple pie,” 

The indefinite article indicates that she is not talking about a particular apple pie. she probably doesn’t even have any pie yet. 

Note :The indefinite article appears only with singular nouns. 

Exceptions: using a or an

There are a few exceptions to the general rule of using a before words that start with consonants and an before words that begin with vowels. The first letter of the word honor, for example, is a consonant, but it’s unpronounced. Despite its spelling, the word honor begins with a vowel sound. Therefore, we use an. Consider the example sentence below for an illustration of this concept.

Incorrect: My mother is a honest woman.

Correct : My mother is an honest woman.

Similarly, when the first letter of a word is a vowel but is pronounced with a consonant sound, use a, as in the sample sentence below:

Incorrect: She is an United States senator.

Correct : She is a United States senator.

This holds true for acronyms and initialisms too: an LCD display, a UK-based company, an HR department, a URL.

An article before an adjective

Sometimes an article modifies a noun that is also modified by an adjective. The usual word order is article + adjective + noun. If the article is indefinite, use a or an based on the word that immediately follows it. Consider the following examples for reference:

Examples: 

Eliza will bring a small gift to Sophie’s party. 

I heard an interesting story yesterday.

Indefinite articles with uncountable nouns

        Uncountable Nouns are nouns that are impossible to count, whether because they name intangible concepts (e.g., information, animal husbandry, wealth), collections of things that are considered as wholes (e.g., jewelry, equipment, the working class), or homogeneous physical substances (e.g., milk, sand, air). Although most of these nouns are singular in form, because they refer to things that can’t be isolated and counted, they never take a or an. Uncountable nouns can be modified by indefinite adjectives like some, however. Consider the examples below for reference:

Incorrect : Please give me a water.

Water is an uncountable noun and should not be used with the indefinite article.

Correct : Please give me some water.

If you describe the water in terms of a countable unit (like a bottle), you can use the indefinite article to modify the unit.

Correct : Please give me a bottle of water.

Incorrect : Please give me an ice.

Correct : Please give me an ice cube.

Correct : Please give me some ice.

Note that depending on the context, some nouns can be countable or uncountable (e.g., hair, noise, time):

Correct : We need a light in this room.

Correct : We need some light in this room.

Omission of articles

Occasionally, articles are omitted altogether before certain nouns. In these cases, the article is implied but not actually present. This implied article is sometimes called a “zero article.” Often, the article is omitted before a noun that refers to an abstract idea. Look at the following examples:

Incorrect : Let’s go out for a dinner tonight.

Correct : Let’s go out for dinner tonight.

Incorrect :The creativity is a valuable quality in children.

Correct : Creativity is a valuable quality in children.

Tip: The words for many languages and nationalities are not preceded by an article. 

Incorrect : I studied the French in high school for four years.

Correct : I studied French in high school for four years.

Tip: Sports and academic subjects do not require articles. 

Incorrect : I like to play the baseball.

Correct : I like to play baseball.

Incorrect : My sister was always good at the math.

Correct : My sister was always good at math.

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                   Engineering Chemistry - I

                                  Unit -IV

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Calculus use in Music Field

 

Music

You may be surprised  to know that the use of calculus is not restricted to engineering or medical science, but can also be applied to music. Some applications include:

Harmonics:

An oscillation created by a damped harmonic is not infinite, as friction and air resistance will dissipate the energy. Calculus is used to anticipate these motions to make the proper adjustments and provide the best musical experience to the listeners.

Differential calculus applications in Medicine field

 

 Medicine :

Calculus can also be applied in medicine. Applications of calculus in medical science include:

Bacterial growth:

Biologists use differential calculus to compute the exact bacterial growth rate in a culture by varying environmental factors such as temperature and food source.   

Patient Diagnosis:

Calculus is crucial in medical tests used for measuring cardiac output, blood flow, and tumor growth. This data is needed to properly assess a patient’s health condition. 

Epidemiology:

Epidemiologists who conduct research on infectious diseases use calculus to discover the spread rate and area where an infection will likely occur. Calculus can also help create a containment plan and investigate the source of an infection.   

Cancer:

Calculus is used to determine the growth or shrinkage and number of cells of a cancerous tumor. Using an exponential function, oncologists analyze the progression or regression of a disease.

Real life Application of calculus

 

What is Calculus?

Calculus means ‘small pebble’ in Latin, and is named after the rocks used by the Romans for counting. Sir Isaac Newton, one of the greatest scientists and mathematicians in history, is credited as the founder of calculus. Over centuries, many mathematicians have contributed to the further development of calculus as a branch of mathematics and physics. 

What does calculus actually do? Well, calculus measures the rate of change that occurs in almost every phenomenon in the universe. There are two branches of calculus, integrals and derivatives. The derivative component of a mathematical function defines the rate of change at a specific point, whereas integrals show the accumulation of discrete values of a function over a range.

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1.8 PREPOSTIONS

 1.8 PREPOSITIONS

What is Preposition?

A Preposition is a word placed before a noun or a pronoun to show in what relation the person or thing denoted by it stands in regard to something else:

Example:

1. There is a cow in the field.
2. He is fond of tea.

What are the types of Preposition?

1. Preposition of Location

'Preposition of Location' specifies the current location of the subject. Prepositions of Location are used when we want to give exact location of an item to the user. Commonly used prepositions of location are in, at, on, inside, etc.

2. Preposition of Time

'Preposition of time' indicates the time at which the action happened. It adds extra information to the verb. Commonly used prepositions of time are in, on, before, after, etc.

3. Preposition of direction/movement

'Preposition of direction' specifies the direction in which the subject is moving. Commonly used prepositions of direction/movement are into, through, across, etc.

EXAMPLE 1

EXAMPLE 2

Differentiation Formulas

 

1.7 FRAMING WH QUESTIONS

 1.7 FRAMING WH QUESTIONS

Wh-questions begin with what, when, where, who, whom, which, whose, why and how. We use them to ask for information. The answer cannot be yes or no:

Warning:

When what, who, which or whose is the subject or part of the subject, we do not use the auxiliary. We use the word order subject + verb:

What fell off the wall? Which horse won?

Who bought this? Whose phone rang?

Compare

Who owns this bag?	Who is the subject of the sentence and this bag is the object. We use no auxiliary verb.
Who do you love most?	Who is the object of the sentence and you is the subject. We use the auxiliary verb do.

 Responding to wh-questions

Wh-questions ask for information and we do not expect a yes-no answer to a wh-question. We expect an answer which gives information:

A:

Where’s the coffee machine? (We expect an answer about the location of the coffee machine.)

B:

It’s in the room next to the reception.

A:

How old is your dog? (We expect an answer about the age of the dog.)

B:

She’s about five. I’m not very sure.

Adding emphasis to wh-questions

We can add emphasis to wh-questions in speaking by stressing the auxiliary verb do. We usually do this when we have not already received the information that we expected from an earlier question, or to show strong interest.

When the wh-word is the object of the sentence, the do auxiliary is stressed to make it more emphatic:

A:

How was your weekend in Edinburgh?

B:

I didn’t go to Edinburgh.

A:

Really. Where did you go?

B:

We decided to go to Glasgow instead.

When the wh-word is the subject of the sentence, we can add the auxiliary do to make it emphatic. We stress do:

A:

Ronald Price lives in that house, doesn’t he?

B:

No. He moved out.

A:

So who does live there? (non-emphatic question: So who lives there?)

B:

Actually, his son is living there now.

See also:

• Intonation and wh-questions

Negative wh-questions

When we ask negative wh-questions, we use the auxiliary verb do when there is no other auxiliary or modal verb, even when the wh-word is the subject of the clause:

Affirmative with no auxiliary	Negative with auxiliary do
Who wants an ice cream?	Who doesn’t want an ice cream?
Which door opened?	Which door didn’t open?

Adding a wh-word at the end of a statement to make a question

Spoken English:

In speaking, we can sometimes turn wh-questions into statement questions:

What’s today’s date? or Today’s date is what?

We do this especially when we are checking information that we have already been given or when we want to quickly check a particular detail. These are less formal than full wh-questions:

A:

So we’re all going to be there at eight?

B:

Right, I’m travelling with Larry.

A:

You’re travelling with who? (more formal: Who are you travelling with?)

B:

With Larry. We’re actually going on our bikes.

A:

Is your sister here too or just your mother?

B:

Just my mother.

A:

And she’s here until when? (more formal: And when is she here until? or even more formal: Until when is she here?)

Prepositions and particles with wh-questions

We can use wh-words and phrases after prepositions in more formal questions:

Where will the money come from?

From where will the money come? (formal)

Spoken English:

In informal styles, especially in speaking, the preposition may be separated and placed at the end of the question clause:

What will I talk to her about?

Who should we send the invitation to? (informal)

Whom should we send the invitation to? (formal)

To whom should we send the invitation? (more formal)

For what reason did she leave him? (formal: preposition + wh-phrase)

When we make questions shorter, we usually put the preposition and its complement together:

A:

We’re all meeting up tonight.

B:

At what time?