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# Engineering 1020: Introduction to Programming

.title[
  .lecture[Lecture \2\:]
  .title[Functions]
  
  
]

.footer[[/lecture/2/](/lecture/2/)]

---

# Last time:

## Expressions

_Values_ and _operations_ that _evaluate_ to a _value_

---

# Values

### Literals:

* integer literals (e.g., `42`)
* _floating-point_ (real-valued) literals (e.g., `3.14`)
* _string_ literals (e.g., `'hello'`)
* _Boolean_ (logical) literals (e.g., `True`)

### Variables

---

# Variables

### Named values

_Actually, it's slightly more complicated than that, but..._

???

We'll talk more about variables in later lectures when we talk about how to
**create** them.
For now we will just focus on **using** them.

```python
>>> from math import *
>>> pi
3.141592653589793
>>> 2j * pi
6.283185307179586j
```

```python
r1 + r2
```

---

# Operations

### Arithmetic operators

* addition, substraction, multiplication, division (both kinds)
* exponentiation

---

# Today:
--
 more operators!

.floatleft[
### Values

* literals ✅
* variables ✅
]

.floatleft[
### Operators

* arithmetic ✅
* function calls
* logical operators (**next week**)
]

---

# Function calls

There's lots we _will_ say about functions, but for now...

### What are mathematical functions?

e.g., $\sin(x)$

### Calling Python functions:

```python
>>> from math import *
>>> sin(pi)
1.2246467991473532e-16
```

???

Again, this is **close** to 0 but not **exactly** so!

---

# Math vs programming

### Functions are like math functions, but also not!

Recall: $e^{jx} = \cos x + j \sin x$

Given:
$$f(t) = 8x + j \sin \frac{t}{2} + 1 + \cos \frac{t}{2}$$

Can we simplify $f(t)$?  
???

We can simplify to:

$$f(t) = 8x + e^{\frac{t}{2} j} + 1$$

Can we solve for $x$?

???

In **mathematics**, we can re-arrange things pretty arbitrarily, e.g.,

$$
x = \frac{f(t) - j \sin \frac{t}{2} - 1 - \cos \frac{t}{2}}{8}
$$

But not in **programming**!

---

# Machine model

.center[
<img src="../images/functions/machine-model/cos.png" height="140"/>
]

???

In programming, we should instead think of a function as a machine for
producing output when given input.

.center[
<img src="../images/functions/machine-model/cos-1.png" height="140"/>
]

.center[
<img src="../images/functions/machine-model/cos-half.png" height="140"/>
]

---

# Multiple inputs

### Can have more than one input:

.floatleft[
<img src="../images/functions/machine-model/f-12.png" height="200"/>
]

### Corresponding Python code:

```python
Python 3.9.1

>>> f(1, 2)
1
```

### We'll talk about how to _make_ functions later

???

For now, this will let us **use** functions.

---

# Some functions

Some functions that we can use right now:

.floatleft[
#### General&nbsp;&nbsp;

.floatleft[
#### Trigonometry&ast;&nbsp;&nbsp;

| |
|-|
| `sin` | `asin`
| `cos` | `acos`
| `tan` | `atan`
]

.footnote[
&ast; Type `from math import *` before using mathematical functions
]

.floatleft[
#### Other math&ast;

???

Using these simple functions, you should now be able to write Python expressions
to address math and science problems in your other Engineering One courses.
So, when calculating something by hand, why not _also_ try writing the answer as
a Python expression to help practice programming too?
Then you can put your other course work to work for you in multiple ways!

---

# More operator precedence

.floatleft[
| Operator      | Description      |
|---------------|------------------|
| `()` | Parentheses
| `x(args...)` | Function call
| `**` | Expon.
| `+x`, `-x`, `~x` | Unary
| `*`, `/`, `//`, `%` | Mult.
| `+`, `-` | Add.
]

## ... and more to come next week

---
class: big, middle

(here endeth the lesson)