1. MAT 4725 Numerical Analysis Section 2.1 The Bisection Method http://myhome.spu.edu/lauw

2. HW Non-Team HW NO talking to anyone NO Google or advises from aliens

3. Improvement

4. MCM Teams Any progress?

5. Homework Download the homework Read 2.2 (Burden) You may skip all the proofs unless specified

6. Preview Find the solutions of an equation in one variable. Repeatly cut the intervals that contain the solution in half.

7. Population Model 1 Why?

8. Population Model 2 Why?

9. Population Model 2

12. In general We want to find the solutions of a equation in one variable.

13. IVT

14. IVT: Special Case

15. The Bisection Method Idea

16. Theorem 2.1

17. Thus, the method always converges to a solution

18. Algorithm 2.1 Pseudo code (descriptions) of the algorithm will be given. Easy to translate it into a program

19. Algorithm 2.1

20. Example 1

21. Example 2 Theoretical Computations

22. Classwork 1 Write a program to implement the bisection algorithm.

23. Remark #1

24. Remark #2 Bisect:=proc(f, aa, bb, tol, N0) local i, p, a, b, FA, FP; a:=aa; b:=bb; The values of the parameters passed into a procedure cannot be changed

25. Remark #3 Use return() to stop the program

26. Homework From now on… Use the Maple program in your classwork to do all the computations Use Maple to plot all the graphs