An introductory paragraph, as the opening of a conventional essay, composition, or report, is designed to grab people's attention. It informs readers about the topic and why they should care about it but also adds enough intrigue to get them to continue to read. In short, the opening paragraph is your chance to make a great first impression. 9 synonyms of introduction from the Merriam-Webster Thesaurus, plus 8 related words, definitions, and antonyms. Find another word for introduction. Introduction: a short section (as of a book) that leads to or explains the main part.

Connecting with strangers over email is never easy. And writing one that actually gets a response is even harder.

It all starts with an introduction. There are various ways you can introduce yourself over email – it just depends on the level of connection you may or may not already have with a contact, or the business situation in which you’re reaching out.

Top tips for getting a response to an introductory email:

1. Write a compelling subject line
2. Make the first line about the recipient
3. Explain your reason for reaching out
4. Identify the value you will provide
5. Include a call-to-action, if appropriate
6. Show your appreciation for their time

Whether or not your email gets opened – and responded to – depends on how effective its content is. Here are five templates for some of the most common scenarios you’ll encounter to help you simplify the process, so you can focus on more pressing business activities.
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5 Introduction Email Templates Samples

1. Cold introduction template

Goal: You want to connect with someone who doesn’t know you or your business.

Why it works: It focuses on them and how you will solve their pain point.

Cold outreach emails are messages you send to someone you don’t know, and with whom you have no other point of contact. They’re usually done to kickstart a lead generation campaign, to expand a contact list, or to reach new audiences.

But it’s tricky to get a response to a cold introduction email. It’s critical that you get to the point quickly. Let the recipient know how you found their name and contact details, who you are, and how you’ll help them, then back it up with evidence of how you’ve helped similar companies in the past.

Subject Line: [Contact’s name], can I take two minutes of your time?

Hi [contact’s first name],

I found your name [define specific source], and [personalized compliment].

We are [why you are a credible source] and we understand [identify a pain point]. Over the past year and a half, we’ve worked with [name two or three similar companies], and have helped them achieve [identify your number-one benefit]. I know that we can help [contact’s company name] too.

If this is on your agenda, then I’d love to schedule a brief 5-minute phone call to discuss how we can help you. I’m available at [x, y and z times]. Do any of these work for you?

If you’re not addressing this issue right now, or you don’t feel we’d be a good fit for you, I completely understand. Thanks for your time.

Regards,

[Your name]

2. Follow-up introduction

Goal: You want to reconnect with someone you’ve already met in person.

Introduction Definition

Why it works: You’ve already met, giving you a basis from which to expand on your key offering.

If you’ve met someone in person at an event or have been personally introduced by a mutual contact, then it’s a good idea to follow up with an email. You’ve already been formally introduced, so this email is a refresher. It will provide your new contact with your details and also give you the opportunity to both deepen your connection and emphasize how your offering can help.

Subject Line: [First name], it was great to meet you at [event]

Dear [first name],

I’m so glad we had a chance to meet at [event].

I understand from [mutual connection] that you [identify their pain point]. Over the past year, we’ve worked with [name two or three similar companies] and have helped them achieve [identify your number-one benefit]. I know we could help [recipient’s company name] too.

If this is on your agenda at the moment then I’d love to schedule a brief 10-minute phone call to discuss how we can help you. I’m free [x, y and z times]. Do any of these work for you?

If this isn’t something you’d be interested in at the moment, then I completely understand. Thank you for taking the time to read this, and again, I enjoyed meeting you.

Regards,

[Your name]

Additional Reading:How to Introduce Yourself in an Email

3. Referral introduction

Goal: You want to reach out to someone with whom you have a mutual connection.

Why it works: Bringing in your mutual connection gives you weight as a recommended and trustworthy source.

This is an email you’ll send to someone a mutual connection has referred you to. This is probably the simplest path toward making a new connection that there is – people are more likely to be convinced by a recommendation (albeit implicit) than if they receive a cold email out of the blue.

Ideally, you’ll ensure that your mutual contact makes the initial email connection, cc’ing you both. Then, you can pick up the email thread from there.

However, if you can’t make that happen, try this template. Note that it’s quite similar to the follow-up email above, with a few differences.

Subject line: Hi [first name], [mutual contact] would like to connect us

Dear [first name],

I’m reaching out because [mutual connection] (copied into this email) suggested that we connect.

I understand from [mutual connection] that you [identify their pain point]. You might be interested to know that we’ve recently been working with [name two or three similar companies] and have helped them achieve [identify a key benefit]. Perhaps we could help [their company name] too.

If this is on your agenda at the moment, then I’d love to schedule a brief phone call to discuss how we can help you. I’m available [x, y and z times]. Do any of these work for you?

I appreciate the time you took to read this.

Regards,

[Your name]

4. An event-triggered introduction email

Goal: To use a behavior on your website to trigger an automated email to introduce yourself.

Why it works: You know that the target is interested in you, based on their interaction with your website. This email introduction builds on that, and can be more direct.

An event-triggered introduction email is a message that’s sent to a person who has visited a certain page on your site, or taken a certain action, like filling out a form or clicking on a “Contact me” button.

Although this email will be automated, it’s important that you make it as personalized and personable as possible.

Subject Line: Congratulations! What’s next?

Dear [prospect’s first name],

Congratulations on signing up to [newsletter/podcast etc]. You’ve taken the first step in achieving [identify a key benefit/offering]. Over the next few days you should expect [outline what correspondence comes next].

Attached is some additional information that you might find interesting.

If you’d like to chat more about how we can meet your needs, I’d love to schedule a brief phone call. I’m free [x, y and z times]. Do any of these work for you?

I look forward to hearing from you.

Regards,

[Your name]

5. Expertise introduction

Goal: To connect with an influencer with whom you have no prior contact.

Why it works: You emphasize your mutual passion and demonstrate what they’ll get in return.

Influencer marketing is a go-to tactic for businesses wanting to expand their exposure online. And while it can be daunting to reach out cold to influencers in your field, there are ways of finding a mutual connection.

But because you’re reaching out to a stranger to ask for something, it should be treated a bit like a cold sales email. The key is to be as brief as you can, get to the point quickly, and demonstrate what they can expect to receive in return.

Subject Line: [Influencer’s first name], I’d like to interview you for my podcast

Dear [influencer’s first name],

I am a big fan of [what they do], and [compliment or reason why you respect them].

I am [your one-sentence bio]. I know my audience on [name of podcast] would love to hear what you have to say, too, since we all share a passion for [your common area of interest].

In return for your participation, I would [benefit for them].

I’d love to schedule a brief phone call to discuss this further, if you’re interested. When would be a good time to chat?

I look forward to hearing from you.

[Your name]

It’s not always easy to introduce yourself over email, or to know the most effective way to do so. Depending on the situation that requires an intro, you need to consider what your goal is and how you craft your message to achieve that goal.

That’s why it’s helpful to follow a template, either one of the above, or one you’ve crafted yourself. It will help you save time and also ensure that you’re giving your message the best chance of getting the response you need.ADD_THIS_TEXT

Calculus is all about changes.

'Wait a minute ...'

'Well in the last minute we went 1.2 km, so we are going:'

1.2 km per minute x 60 minutes in an hour = 72 km/h

'No, Sam! Not our average for the last minute, or even the last second, I want to know our speed RIGHT NOW.'

'OK, let us measure it up here ... at this road sign... NOW!'

'OK, we were AT the sign for zero seconds, and the distance was ... zero meters!'

The speed is 0m / 0s = 0/0 = I Don't Know!

Introduction Paragraph

'I can't calculate it, Alex! I need to know some distance over some time, and you are saying the time should be zero? Can't be done.'

That is pretty amazing ... you'd think it is easy to work out the speed of a car at any point in time, but it isn't.

Even the speedometer of a car just shows us an average of how fast we were going for the last (very short) amount of time.

How About Getting Real Close

But our story is not finished yet!

Sam and Alex get out of the car, because they have arrived on location. Sam is about to do a stunt:

Sam uses this simplified formula to find the distance fallen:

d = 5t²

• d = distance fallen, in meters
• t = time from jump, in seconds

(Note: the formula is a simpler version of how fast things fall under gravity: d = ½gt²)

Example: at 1 second Sam has fallen

d = 5t² = 5 × 1² = 5 m

But how fast is that? Speed is distance over time:

Speed = distancetime

So at 1 second:

Speed = 5 m1 second = 5 m/s

'BUT', says Alex, 'again that is an average speed, since you started the jump, ... I want to know the speed at exactly 1 second, so I can set up the camera properly.'

Well ... at exactly 1 second the speed is:

Speed = 5 − 5 m1 − 1 s = 0 m0 s = ???

So again Sam has a problem.

Think about it ... how do we figure out a speed at an exact instant in time?

What is the distance? What is the time difference?

They are both zero, giving us nothing to calculate with!

But Sam has an idea ... invent a time so short it won't matter.

Sam won't even give it a value, and will just call it 'Δt' (called 'delta t').

So Sam works out the difference in distance between t and t+Δt

At 1 second Sam has fallen

5t² = 5 × (1)² = 5 m

At (1+Δt) seconds Sam has fallen

5t² = 5 × (1+Δt)² m

We can expand(1+Δt)²:

So at (1+Δt) seconds Sam has fallen

In Summary:

So between 1 second and (1+Δt) seconds we get:

Change in distance over time:

So the speed is 10 + 5Δt m/s, and Sam thinks about that Δt value ... he wants Δt to be so small it won't matter ... so he imagines it shrinking towards zero and he gets:

Speed = 10 m/s

Wow! Sam got an answer!

Sam: 'I will be falling at exactly 10 m/s'

Alex: 'I thought you said you couldn't calculate it?'

Sam: 'That was before I used Calculus!'

Yes, indeed, that was Calculus.

The word Calculus comes from Latin meaning 'small stone'.

· Differential Calculus cuts something into small pieces to find how it changes.

· Integral Calculus joins (integrates) the small pieces together to find how much there is.

Sam used Differential Calculus to cut time and distance into such small pieces that a pure answer came out.

And Differential Calculus and Integral Calculus are like inverses of each other, similar to how multiplication and division are inverses, but that is something for us to discover later!

So ... was Sam's result just luck? Does it work for other things?

Let's try doing this for the function y = x³

This will be similar to the previous example, but we will just use a slope on a graph, no one has to jump for this one!

Example: What is the slope of the function y = x³ at x=1 ?

We can expand (1+Δx)³ to 1 + 3Δx + 3(Δx)² + (Δx)³, and we get:

y = 1 + 3Δx + 3(Δx)² + (Δx)³

And the difference between the y values from x = 1 to x = 1+Δx is:

Introduction Paragraph Examples

Now we can calculate slope:

Once again, as Δx shrinks towards zero we are left with:

Slope = 3

And here we see the graph of y = x³

The slope is continually changing, but at the
point (1, 1) we can draw a line tangent to the curve

and find the slope there really is 3.

(Count the squares if you want!)

Question for you: what is the slope at the point (2, 8)?

Try It Yourself!

Go to the Slope of a Function page, put in the formula 'x^3', then try to find the slope at the point (1, 1).

Zoom in closer and closer and see what value the slope is heading towards.

Conclusion

Introduction To Sociology

Calculus is about changes.

Differential calculus cuts something into small pieces to find how it changes.

• Learn more at Introduction to Derivatives

Introduction To Algorithms

Integral calculus joins (integrates) the small pieces together to find how much there is.

Introduction Synonym

• Learn more at Introduction to Integration