1a) Write Vx3y(a: < y + 5) in English. Assume a, y are real numbers.
For a. x *Hnew: exisls a y sudn +ha+
1b) Determine whether or not p > q E ~p V q with a truth table.
2) Given sets A = cfw_a,b,d, f, B = cfw_a,b,c,d,e,f,g, and C = cfw_a
Review Exam III
A graph with 21 edges has 7 vertices of degree 1, 3 of degree 2, 7 of degree 3 and the
rest of degree 4. How many vertices in graph?
Can the following degree structure occur in a simple graph? If so, draw a
representation. If not, ex
1. Prove by induction that
1 2 3
(n + 2)
+ 2 + 3 + . + n = 2
for n P
2 2 2
b) 11! + 2 2! + . + n n! = (n + 1)! 1 for n P
c) (1 + x)n 1 + nx for n P x a real number, x 1
2. How many 4 digit numbers can be formed using the digits 2
H D 1/00
/- German 330 ALL Cob/la sz MED/T /
LW : g;
gamma [9A Mb
. THvste, ML 41 Venn 13- 4ng #
(Afarseclian oqc all gas is n"w1:j)m8rm ( me a
4) (Maw, C = id
('13'497)? "(1 cfw_55/183
cfw_41:5 A cfw_max: cfw_53 ,.
Project 1 MAD 3401 (Numerical Analysis)
1) Write a program to ﬁnd an approximation to the solution to the equation
_ 11:4 — 3952 — 3 = o
lying in [1,2] that is accurate to within 10‘6 using
a) The bisection method
b) The ﬁxed—point iteration m
I -1 ”1K ‘3
5" + cw) , sum 6 10m) View)
1 (J \
f /(K+l) “(09(%«
Final Exam: MAD 3401 (Numerical Analysis)
Exercise 1: (20 points)
Let f(x) = ez+ln(x+1)+cosx. Find the Lagrange polynomial P that interpolates f
at $0 20.5, 231 = 1 and x2 = 1.5. Appr
NUMERICAL ANALYSIS PROJECT #1
Approximation to the Solution of an Equation
Dr. Theodore Tachim Medjo
Graphs Error 1 Exercise #1
Notice the Y axis is the ERROR and the X axis is the amount of ITERATIONS. The
Coordinator: Dr. Theodore Tachim Medjo,
Office: DM 413B
Text: Numerical Analysis (8th edition), RL. Burden and J.D Faires.
The 7th and 6th editions contain the same materials as the 8th edition.
Office Hours: TR: 2:00pm-3:00
- sin x
- csc2 x
sec x tan x
- csc x cot x
xn+1/(n+1) + c
ax/ln a + c
ex + c
ln |x| + c
- cos x + c
sin x + c
Section 2.1 Sets and Elements
1) List the elements from each set
a. A=cfw_ x: x is an odd integer, 5 " 93
b. B=cfw_ x: x is a perfect square, x 225
c. C= cfw_ y: y is a positive integer, y is a multiple of 3
d. D=cfw_ x: x is positive
EXAM #1 Review
1) List the elements of a given set.
A=cfw_ x: x is a perfect square, -16 # 16
E=cfw_ x: x is an integer such that # $ = 3.1
2) Translate symbolic compound statement into words.
Let P represent the statement It is Tuesday and le
Section 3.2 & 3.3
Permutations & Combinations
1) A restaurant offers nine different desserts, which it serves with coffee, decaffeinated coffee, tea, milk, or
hot chocolate. In how many different ways can one order a dessert and a d
Consider the following statements: x > 3, x = y + 3, x + y = z
The truth value of these statements has no meaning without specifying the values of x, y, z.
However, we can make propositions out of such statements.
Section 3.2 Permutations
The Fundamental Counting
The Fundamental Counting Principle
Suppose a procedure consists of n stages. At the first stage there are there are !" choices, at
the second stage ther
SETS AND LOGIC
SECTION 2.1 : SETS AND
A set is a well-defined collection of objects. The objects in a set are called the elements or
members of the set.
Note: By well-defined we mean there is a rule that enables us to deter
Section 4.1 Finite Probability
1) An experiment results in one of the following points: , , , , or .
a) Find P( ) if P( ) = .1 , P(
= .2 , P( ) = .1, and P( ) = .1.
b) Find P( ) if P( ) = P( ), P(
= .1, P( ) = .2, and P( ) = .1.
Chapter 5: Relations and Functions
Section 5.1 Relations
An ordered pair consists of two elements, one of which is designated the first element and the
other the second element. We write such a pair as (a, b).
Equality: Two ordered p