Upcoming SlideShare
×

# CRMS Calculus May 31, 2010

1,190 views

Published on

Final Review

Published in: Education, Technology
2 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
1,190
On SlideShare
0
From Embeds
0
Number of Embeds
422
Actions
Shares
0
24
0
Likes
2
Embeds 0
No embeds

No notes for slide

### CRMS Calculus May 31, 2010

1. 1. The Year in Review What the heck is Calculus?
2. 2. One of the supreme creations of human thought
3. 3. One of the biggest controversies in history
4. 4. The Culmination of K-12 mathematics Calculus Trigonometry Elementary Functions Geometry Algebra Arithmetic
5. 5. Course Goals <ul><li>To introduce you to the four major concepts of calculus: </li></ul><ul><ul><li>Limits </li></ul></ul><ul><ul><li>Derivatives </li></ul></ul><ul><ul><li>Definite Integral </li></ul></ul><ul><ul><li>Indefinite Integral </li></ul></ul>
6. 6. For each concept you will … <ul><li>know the precise definition; </li></ul><ul><li>have an intuitive understanding of what the concept means; </li></ul><ul><li>be able to “do” the concept; </li></ul><ul><li>be able to apply it in the real world or mathematical world. </li></ul>
7. 7. You will develop this knowledge by using four multiple representations: <ul><li>Numerical (Table) </li></ul><ul><li>Visual (Graph) </li></ul><ul><li>Algebraic (Function) </li></ul><ul><li>Verbally (and written). </li></ul>
8. 8. Do you Sir Know the Foundation For All of Calculus?
9. 9. The foundation of Calculus is the concept of a limit . <ul><li>1/2, 2/3, 3/4, 4/5, 5/6,... 10/11,... 99/100,... 99999/100000,... </li></ul>
10. 10. Limits by definition
11. 11. Limits by Delta - Epsilon definition
12. 12. Limits by graph
13. 13. Limits by numerical table
14. 14. Limits by algebra
15. 15. Limits involving
16. 16. Intermediate Value Theorem
17. 18. Differential Calculus The mathematics of change Physical Meaning Instantaneous rate of change
18. 19. Slope of the tangent line at a point. Graphical Meaning
19. 20. Do you Sir Know the definition of The Derivative ?
20. 21. Derivative
21. 23. If y = Displacement Then y’ = Velocity And y’’ = Acceleration
22. 24. How’s My Deriving?
23. 25. Power Rule for derivatives Function Notation: Operator Notation:
24. 28. Related Rates
25. 29. y = C + AsinB(x – D) y ‘ = ABcosB(x – D)
26. 31. The Squeeze Theorem
27. 32. If y = e x , then y’ = e x If y = b x , then y’ = b x · ln b
28. 33. If y = ln x, then
29. 34. I PITY DA FOO’ WHO CAN’T FIND DA DERIVATIVE !!!
30. 35. Integral Calculus Areas and Volumes
31. 36. Counting Squares
32. 37. Archimedes Method of Exhaustion
33. 38. Trapezoidal Rule
34. 39. Do you sir, Know the difference between An indefinite integral And A definite integral?
35. 40. Antiderivatives of y’ = x 2 Bring the Whole Indefinite Integral Family! Indefinite Integral A Family of Curves With a given Derivative
36. 41. Definite Integral is a Number
37. 43. Solving Differential Equations and Slope Fields
38. 45. Sweetheart, Check out this definition ! Definite Integral;
39. 46. Rolle’s Theorem The Mean Value Theorem Is just Rolle’s Theorem Rotated
40. 49. What were those Properties Of Integrals?
41. 50. Definite Integrals Allow us to find The area between curves
42. 51. Naked Math Real World
43. 55. Volumes of Revolution The Disk Method
44. 57. An Illuminating Volume
45. 58. This stuff isn’t so hard! In fact …