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https:/www.coursehero.com/file/10564309/Midterm-1-Exam/
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https:/www.coursehero.com/file/10564309/Midterm-1-Exam/
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Problem 1. Let f(x)=1+3x2-2x3
(i)
(ii)
(iii)
(iv)
Find the x-intercept of f
Find the y-intercept of f
Find the intervals on which f(x) is increasing and decreasing
Find the local max and min values of f(x); use both first and second derivative
tables
(v)
Lecture 2: The Bisection Method
Gui-Bo Ye
Chapter 1. Pre-requisite, will be reviewed when necessary
Chapter 2. More focused on Computer Science, skipped
Chapter 3. Rootnding: Solution of nonlinear equations in one variable
Denition 1. Given a function f (
Lecture 5: Secant Method and Newton method
Gui-Bo Ye
1
Secant Method
Purpose: Find a root of f (x).
Algorithm: Given x0 , x1 , generate xn+1 = xn f (xn )
xn xn1
f (xn )f (xn1 ) , n
= 1, 2, . . .
Secant method is even faster and simpler than the Bisection
Lecture 3: The Bisection Method (Continue)
Gui-Bo Ye
1
Overview:The Bisection Method
Purpose: Find a number such that f () = 0.
Assumption: 1) f (x) is continuous on [a, b]; 2) f (a)f (b) < 0
Algorithm:
1) Set [a1 , b1 ] = [a, b], c1 =
2) If
bn an
2
a1 +b
Lecture 6: Error Analysis for Newton Method
Gui-Bo Ye
We learned three dierent algorithms for nding a root of f (x): Bisection, Secant and Newton.
Secant: xn+1 = xn f (xn )
Newton: xn+1 = xn
xn xn1
f (xn )f (xn1 )
f (xn )
f (xn )
We have studied the err
22M:072 Elementary Numerical Analysis
Homework 5
Due date: Oct. 2, Friday before the class begins
No late homework is permitted.
You have to answer all the questions.
You dont need to show your code until specied.
If you are specied to show your matla
22M:072 Elementary Numerical Analysis
Homework 3
Due date: September 18, Friday before the class begins
No late homework is permitted.
You have to answer all the questions.
You dont need to show your code until specied.
If you are specied to show your
22M:072:231 Elementary Numerical Analysis
Homework 4
Due date: Sept 25, Friday before class begins
No late homework is permitted.
You have to answer all the questions.
You dont need to show your code until specied.
If you are specied to show your matl
22M:072 Elementary Numerical Analysis
Homework 1
Due date: September 4, Friday before the class begins
No late homework is permitted.
You have to answer all the questions.
You dont need to show your code until specied.
If you are specied to show your
22M:072 Elementary Numerical Analysis
Homework 2
Due date: September 11, Friday before class begins
No late homework is permitted.
You have to answer all the questions.
You dont need to show your code until specied.
If you are specied to show your mat