The Area Problem What is the area of the shape Formulas Simple shapes have simple formulas How can we find formulas for more complicated shapes The Area Problem What is the area of the shape ID: 800907
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Slide1
Introduction to Calculus
Slide2The Area Problem
What is the area of the shape?
Slide3Formulas
Simple shapes have simple formulas
How can we find formulas for more complicated shapes?
Slide4The Area Problem
What is the area of the shape?
Slide5Ellipse
Slide6Cubic
Slide7Root
Slide8Application
Slide9Volume
https://www.desmos.com/calculator/5wh1tyjbxv
Slide10The Slope Problem
What is the slope of this line?
Slide11The Slope Problem
What is the slope of this line…
Slide12The Slope Problem
Slope doesn’t really make sense for curves
But we can find something similar…
Slide13The Slope Problem
This is called the tangent line
It just “touches” the curve
Slide14Application
Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm
3
/s. How fast is the radius of the balloon increasing when the diameter is 50 cm?
Slide15Slide16The “divide by zero” problem
If we have the
function
We can simplify it to:
Slide17The “divide by zero” problem
Slide18The “divide by zero” problem
Slide19The Proof Problem
1+2+3 = 6
8+9+10 = 27
101+102+103 = 306
Is this always true?
Slide20The Proof Problem
We want to investigate the “area”, “slope”, and “divide by zero” problems
Slide21Check this out
Key in the first three digits of your phone number (exclude area code)
Multiply by 80
Add 1
Multiply by 250
Add the last 4 digits of your phone number
Add the last 4 digits of your phone number againSubtract 250Divide the number by 2
Slide22Course problem
What is the length of this line?
Slide23Course problem
What is the length of this line?
Slide24Course Outline
Instructor:
Jehu Peters
Email:
jehu.peters@7oaks.org
Required Text: James Stewart, Calculus 8th Edition. Thomson Brooks/Cole. Grading: 60% Final Exam: Friday, June 2, 2017. Check with instructor to confirm final exam room and time.30% Tests: Feb 24, March 24, April 28, May 26 10% Assignments
Slide25Tip: The Forgetting Curve
Slide26Notes
No Calculators
Hand in assignments on time
Choose a “notes buddy”
No make up tests
Slide27Course Outline
First class:
February 8, 2016
Last class:
June 30, 2016
Withdrawal Date: May 20, 2016
Slide28Grades
Tentative Grading System:
A+ 93 – 100
A 85 – 92
A- 80 – 84
B+ 75 – 79
B 69 – 74C+ 63 – 68C 55 – 62D 50 – 54F 0 – 49
Slide29Expectation
You will be expected to:
Review the day’s notes
Attempt homework problems (
2 hours
)
There will be homework checks… You will have 2 days from the time each problem set is assignedComplete assignmentsWatch supplementary videos
Slide30Website
themathbehindthemagic.wordpress.com/calculus/
I will post videos, notes, and handouts
You are expected to check the website regularly
Example:
https://youtu.be/3ZhUdleD1lQ
Slide31Slide32WolframAlpha.com
This website will help you check your answers
Slide33Desmos
Great Graphing Calculator
Slide34Tip
The Illusion of Competence
Reading a “solution” although it may make sense, is not the same as mastering a
problem
Slide35Remind 101 Instructions
Enter this number
: (204) 808-8974
Text this message
: @
uwcalculus
Slide36Course Calendar
Monday
Tuesday
Wednesday
Thursday
Friday
Feb
6 – 10
Introduction / Review
Introduction, course overview
Algebra Review notes
Factoring
Sign Diagram
Proof primer
Limits: Properties and Evaluate
Limits: By Factoring
Limits: one sided
One-sided limits
Feb
13 – 17
Limits
One-sided limits
Squeeze theorem
Trig Limits
Identities
More Trig limits
Continuity
Limits at Infinity
Slide37Questions?
Slide38