This document provides an overview of calculus concepts including: 1) It introduces the four major concepts of calculus - limits, derivatives, definite integrals, and indefinite integrals. 2) It explains that the foundation of calculus is the concept of a limit, and covers limits by definition, delta-epsilon definition, graphs, numerical tables, and algebra. 3) It discusses differential calculus and the mathematics of change, including the derivative, related rates, and rules for finding derivatives. 4) It covers integral calculus including areas, volumes, the differences between indefinite and definite integrals, and methods for solving differential equations.

1. The Year in Review What the heck is Calculus?

2. One of the supreme creations of human thought

3. One of the biggest controversies in history

4. The Culmination of K-12 mathematics Calculus Trigonometry Elementary Functions Geometry Algebra Arithmetic

8. Do you Sir Know the Foundation For All of Calculus?

10. Limits by definition

11. Limits by Delta - Epsilon definition

12. Limits by graph

13. Limits by numerical table

14. Limits by algebra

15. Limits involving

16. Intermediate Value Theorem

18. Differential Calculus The mathematics of change Physical Meaning Instantaneous rate of change

19. Slope of the tangent line at a point. Graphical Meaning

20. Do you Sir Know the definition of The Derivative ?

21. Derivative

23. If y = Displacement Then y’ = Velocity And y’’ = Acceleration

24. How’s My Deriving?

25. Power Rule for derivatives Function Notation: Operator Notation:

28. Related Rates

29. y = C + AsinB(x – D) y ‘ = ABcosB(x – D)

31. The Squeeze Theorem

32. If y = e x , then y’ = e x If y = b x , then y’ = b x · ln b

33. If y = ln x, then

34. I PITY DA FOO’ WHO CAN’T FIND DA DERIVATIVE !!!

35. Integral Calculus Areas and Volumes

36. Counting Squares

37. Archimedes Method of Exhaustion

38. Trapezoidal Rule

39. Do you sir, Know the difference between An indefinite integral And A definite integral?

40. Antiderivatives of y’ = x 2 Bring the Whole Indefinite Integral Family! Indefinite Integral A Family of Curves With a given Derivative

41. Definite Integral is a Number

43. Solving Differential Equations and Slope Fields

45. Sweetheart, Check out this definition ! Definite Integral;

46. Rolle’s Theorem The Mean Value Theorem Is just Rolle’s Theorem Rotated

49. What were those Properties Of Integrals?

50. Definite Integrals Allow us to find The area between curves

51. Naked Math Real World

55. Volumes of Revolution The Disk Method

57. An Illuminating Volume

58. This stuff isn’t so hard! In fact …