Fundamental Equations

HW:
Derive the fundamental equations from their calculus expressions
a=dv/dt   for constant acceleration/non constant acceleration
v=dx/dt   for constant velocity/non constant velocity
 



What is dv/dx?
Write a statement explaining the physics and the related quantities.
Write using the process illustrated to write an equation for v in terms of x.

Graphical Analysis

Note:

There are two ways to approach the solution to a graphical problem.

• use Graphical Analysis
• Define the stated function and use Calculus to determine quantities

In all cases the 2 solutions must agree mathematically and physically!!!

IDEAS: Definite and Indefinite Integrals----->In both cases the integral can only allow you to calculate the change from one condition to another

• Indefinite
• No bounds defined/Starting condition or intercept is unknown  +C
• Definite 
• Bounds Defined starting conditions known 

Graphical Analysis

SAMPLE PROBLEM

•  
• Try the problem above!!!
• Work through the solution.
• Discuss on Blog copy solution with proper heading into composition notebook with full title

Day 3 Fundamental Theorem of Calculus

Day 3
Agenda Book
Blog
Calendar
Infinite Campus

Activity:
Fundamental Theorem of Calculus
Discuss and analyze Graphically
Position 
Velocity (Proof for instantaneous vs. Avg)(FINISH FOR HW)
Acceleration
SLOPE
Intercept
Area 

Objective:
                 You should be able to Define Describe Differentiate and Relate  the above quantities from both a Physical and mathematical standpoint.

Key Skill: be able to apply the fundamental theorem of calculus to a novel situation 


What is wrong with the proof below: