1. Circular Measure HCI Cheers Ivan (11)| Jeremy (02) 4O1 Copyright © 2010 HCICheers Pte Ltd. All Rights Reserved. For Educational Purposes only In conjunction with… Ω β α π κ μ λ ξ θ Binomial Theorem + - x ÷ )¯¯¯ Differentiation Integration Trigonometry

2. Introduction –Pascal’s Triangle –Thus, Binomial Theorem n=0 n=1 n=2 n=3 n=4 1 + 5 + 10 + 10 + 5 + 1 1 + 6 + 15 + 20 + 15 + 6 + 1

3. Binomial Theorem 1. Where When 2. Binomial Theorem

4. Binomial Theorem (Advanced) Binomial Theorem

5. Binomial Theorem (Advanced) –Newton's generalized binomial theorem –Around 1665, Isaac Newton generalized the formula to allow real exponents other than nonnegative integers. In this generalization, the finite sum is replaced by an infinite series. –In order to do this one needs to factor out (n−k)! from numerator & denominator in that formula, and replacing n by r which now stands for an arbitrary number, one can define: –Where is the Pochhammer symbol here standing for a falling factorial. Binomial Theorem

6. Binomial Theorem (Advanced) Binomial Theorem

7. Video Presentation (Part1) Binomial Theorem

8. Video Presentation (Part2) Binomial Theorem

9. Video Presentation (Part3) Binomial Theorem

10. Circular Measure Formula Circular Measure

11. Circular Measure Formula Circular Measure

12. Video Presentation (Part1) Circular Measure

13. Video Presentation (Part2) Circular Measure

14. Video Presentation (Part3) Circular Measure

15. Trigonometrical Functions Differentiation

16. Diffusing Chain Rule Differentiation of Exponential Functions Differentiation

17. Laws of Logarithim

18. Video Presentation (Part1) Differentiation

19. Video Presentation (Part2) Differentiation

20. Video Presentation (Part3) Differentiation

21. Indefinite Integrals Integration

22. Definite Integrals Integration

23. Integration of Trigonometric Functions Integration

24. Integration of Exponential Functions Integration of Logarithmic Functions Integration

25. Video Presentation (Part1) Integration

26. Video Presentation (Part2) Integration

27. Video Presentation (Part3) Integration

28. Cheers Differentiation - Power Rule

29. Cheers Differentiation - Chain Rule

30. Cheers Differentiation - Product Rule

31. Cheers Differentiation - Quotient Rule

32. Cheers Differentiation - Trigonometrical Functions

33. Cheers Differentiation - Trigonometrical Functions

34. Cheers Differentiation - Diffusing Chain Rule

35. Cheers Differentiation - Differentiation of Exponential Functions Derivatives of Natural Logarithmic Functions

36. Cheers Differentiation - Indefinite Integrals

37. Cheers Differentiation - Integration of Trigonometric Functions

38. Cheers Differentiation - Integration of Trigonometric Functions

39. Cheers Differentiation - Integration of Exponential Functions

40. Cheers Differentiation - Integration of Logarithmic Functions

41. Cheers Differentiation - Visit Our Additional Online Website To Find Out More http://hcicheers.wikispaces.com/

42. Bibliography http://www.wikipedia.org –http://en.wikipedia.org/wiki/Binomial_theoremhttp://en.wikipedia.org/wiki/Binomial_theorem –http://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Derivative –http://en.wikipedia.org/wiki/Integralhttp://en.wikipedia.org/wiki/Integral –http://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Trigonometry http://www.youtube.com Guide Notes Spark Notes Past Formulas Copyright © 2010 HCICheers Pte Ltd. All Rights Reserved. For Educational Purposes only

43. Thank you! End of Presentation Copyright © 2010 HCICheers Pte Ltd. All Rights Reserved. For Educational Purposes only