Welcome to Calculus & Vectors!

1. Welcome to Calculus & Vectors!

2. How do figure skaters use physics to be so awesome? Wayward Wednesday Jason Brown

3. Syllabus!

4. Course Website! http://www.anneketiman.com/teaching/

5. What is Calculus? In a team of three: What is calculus? What is calculus used for?

6. 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

7. 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

8. 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

9. 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

10. 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

11. Tangents and Secants Tangent = instantaneous rate of change Secant = average rate of change

12. How are slope, average rate of change, and instantaneous rates of change connected? Investigate Page 5 - 6

13. 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

14. 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

15. Graphing Instantaneous Rate of Change

16. Sign out your Textbook! Page 9 The basics: #2a(i), 3a, 4a The good stuff: #13, 14 Homework