Download presentation
Presentation is loading. Please wait.
1
MAT 4725 Numerical Analysis
Section 1.3 Conditional Statements
2
MCM Teams Jonathan, Laura, Leah Ashley, Brittany, Tiff
Andrea, Kristen? Meghan? David? Caro, Delsey, Theresa (sophomore team) Grace??
3
HW Comments Print on one side of the paper only. Line up equal signs
Use “×” for multiplication, not “” Use instead of Start a new page for a new problem
4
Preview Review some facts about sequences
Introduces the conditional statements Allow the flow of control to branch into two or more sections of codes based on the truth values of a control expressions Open Maple
5
Why Sequences? We are going to successively approximate certain “desirable answer”. The approximations form a sequence. Recall “Newton’s Method” in calculus I.
6
Example 1 ,
7
Example 1 , By the Intermediate Value Theorem, there is a root between 1 and 2. How to approximate the value of this root?
8
Idea 1. Choose a point x1 nearby. 2. Find the tangent line at (x1,f(x1)). 3. Find the intersection point x2 with the x-axis. 4. Repeat* Step 2-3 until the desired accuracy is obtained.
9
Example 1 Use Newton’s Method to approximate the root of the equation correct to 6 decimal places.
10
Example 1
11
Calculus III This is a review and a review only.
You are supposed to know these stuff.
12
Finding limits There are 5 tools that you can use to find limit of sequences
13
Tool #1 (Theorem) If and , then
14
Tool #1 (Theorem) If and , then .
15
Remarks In general, if r>0 is a rational number, then
16
Tool #2 Use the Limit Laws
17
Tool #3 (Squeeze Theorem)
If and Then
18
Tool #3 (Squeeze Theorem)
If and Then .
19
Example 4
20
It is important to state the name of the theorem
Remark 1 It is important to state the name of the theorem
21
Remark 1 Typically, you need to find an and cn
22
Tool #4 (Theorem)
23
Tool #4 (Theorem) .
24
Tool #4 (Theorem) .
25
Example 5
26
Remark .
27
Tool #5
28
Example 6
29
Maple I will explain how things work first.
Do not type into Maple program until I tell you to do so. Use worksheet mode, and text input.
30
Review from Last Time name:=proc(variables) #Comments
local local variables; …………………………. print(….); end;
31
Example 1 Consider the piecewise defined function
For each interval, we need a different formula to compute the function values
32
Example 1 Consider the piecewise defined function
For each interval, we need a different formula to compute the function values Q: Input=? , Output=?
33
Example 1 Version 1
34
Example 1 Version 1
35
Structure of the if-block
Statements executed only if the condition is met. Otherwise, the statements will be skipped:
36
Example 1 Version 2
37
Example 1 Version 2 > fun(-2);fun(2); 4 2
38
Structure of the if-block
There are two cases separated by one condition: the condition is met or else:
39
Example 2 We need 3 branches
40
Example 2
41
Example 2 > fun(-3);fun(1);fun(3); -14 3 5e(-1)
42
Structure of the if-block
43
Classwork Team Classwork
44
Homework Download from the web
Do not use other references including Google Read Zeng Section 1.4
Similar presentations
© 2025 SlidePlayer.com Inc.
All rights reserved.