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Welcome to Calculus & Vectors!. How do figure skaters use physics to be so awesome? . Wayward Wednesday. Jason Brown. Syllabus!. Course Website!. http:// www.anneketiman.com /teaching/. What is Calculus?. In a team of three: What is calculus? What is calculus used for? .

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Presentation Transcript
slide1
Welcome to

Calculus & Vectors!

slide4

Course Website!

http://www.anneketiman.com/teaching/

slide5

What is Calculus?

In a team of three:

What is calculus?

What is calculus used for?

slide6

What is Calculus?

We can start to figure that out by answering, “What do we do in calculus?”

1. Find tangent slopes

2. Find areas

Inherently connected

slide7

Tangents and Secants

What is a tangent?

A line that connects two points on a curve

A line that just barely touches a curve

An average rate of change

An instantaneous rate of change

slide8

Tangents and Secants

What is a tangent?

A line that connects two points on a curve

A line that just barely touches a curve

An average rate of change

An instantaneous rate of change

slide9

Tangents and Secants

What is a secant?

A line that connects two points on a curve

A line that just barely touches a curve

An average rate of change

An instantaneous rate of change

slide10

Tangents and Secants

What is a secant?

A line that connects two points on a curve

A line that just barely touches a curve

An average rate of change

An instantaneous rate of change

slide11

Tangents and Secants

Tangent = instantaneous rate of change

Secant = average rate of change

slide13

Apply it!

If we tracked Jason Brown’s position as a function of time, we might see something like this:

Time (s)

Position (m)

Graph it!

What is Brown’s average velocity between 0 and 4s? 1 and 3s?

0

1

4

7

8

7.5

5

0

1

2

3

4

5

6

slide14

Apply it!

If we tracked Jason Brown’s position as a function of time, we might see something like this:

Time (s)

Position (m)

Graph Brown’s approximate instantaneous velocity as a function of time

0

1

4

7

8

7.5

5

0

1

2

3

4

5

6

slide16

Sign out your Textbook!

Page 9

The basics: #2a(i), 3a, 4a

The good stuff: #13, 14

Homework