1. MAT 4725 Numerical Analysis Section 1.4 Loops with “do” statements http://myhome.spu.edu/lauw

2. Homework Download homework from the web Read 2.1.4 while-do loop 1.6.1 documentations 1.6.2 format printing Quiz on 1.6.2, we will not lecture on that section

3. Preview Monotonic Sequence Theorem (Stewart, section 12.1) Introduce the first type of repetition statements – the for loop Allow a specific section of code to be executed a number of times Introduces simple arrays

4. Definition A sequence {a n } is bounded above if  M such that a n  M  n A sequence {a n } is bounded below if  m such that a n  m  n

5. Monotonic Sequence Theorem The following sequences are convergent Increasing and bounded above Decreasing and bounded below

6. Example Show that the sequence defined by is convergent and find its limit.

7. Example From homework 01, we know

9. Zeng Section 1.4 Please listen to the explanations before you type in the program. It takes one minute to explain.

10. Example 1 Print the square of the first 10 positive integers What is the task being repeated?

11. Example 1

12. 1210 14100

13. Example 1 > sq(); 1 4 9

14. Structure of the for loop

16. Example 2 Print the square of the first 10 positive odd integers

17. Example 2

18. > sq2(); 1 9 25

19. Example 3 Print the square of the first n positive integers

20. Example 3 Print the square of the first n positive integers Introduces array and seq Note that these commands are not necessary here

21. Example 3

23. > sq3(2); 1, 4 > sq3(5); 1, 4, 9, 16, 25

24. Example 4 Fibonacci sequence is defined by

25. Example 4 Write a program that generate the first n+1 terms of the Fibonacci sequence F 0,F 1,…,F n

26. Example 4

27. What happen if we do not initialize F?

28. Example 4 Why there is no print statement?

29. Example 4

30. Example 5 Write a program, for the input of x and n, to approximate the value of sin(x) by the first sum of the first n+1 terms in the Taylor series.

31. Example 5