M ATH 155
C HAPTER 3
Reminder. The definite integral was introduced to compute area. It is defined by the rule
b
Z
f (x)dx = lim
N
a
N
X
f (xk )(x).
k=1
P
The sum N
k=1 f (xk )(x) gives the area of a
M ATH 155
C HAPTER 1
Although calculus is was developed in the 17th century, its roots go back
much further in time. One precursor of calculus is the special number
3.14159265358979323846264338327950
M ATH 155
C HAPTER 2
Question. What is the surface area of Greenland?
A. 500,000 km2
B. 1,000,000 km2
C. 2,000,000 km2
D. 4,000,000 km2
E. 8,000,000 km2
C.
2,000,000 km2
Note: This is a significant pa
MATH 155 - D100
A SSIGNMENT #7
Instructor Questions #7
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MATH 155 - D100
Midterm 2 Study Package
This is meant to give you a sense of how long you should spend on each question.
If a question is worth N points, you should solve it in about N minutes (note
MATH 155 - D100
A SSIGNMENT #9
Instructor Questions #9
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MATH 155 - D100
A SSIGNMENT #6
Instructor Questions #6
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M ATH 155
C HAPTER 3
Review/Preview
1. We have defined the integral of a function in an attempt to formalize the
calculation of areas of regions in the planean applied problem.
2. Next we will develop
M ATH 155
C HAPTER 1
Carl Friedrich Gau
Gauss is one of the all time great mathematicians. In fact, many historians
regard him as the greatest of all time. His impact on present day mathematics is ext
M ATH 155
C HAPTER 2
Question. Which statement best describes the mathematical concept of area
for sets in the plane?
A. Every set in the plane has an area which is easy to calculate.
B. Every set in
6.1.2 Riemann Integrals
1. Quote. “Mathematics, rightly Viewed, possesses not only truth,
but supreme beauty”
(Betrand Russell, 1872—1970)
2. A more general formulation of area.
Ingredients: A functio
6.3.1 Areas
1. Quote. It is not worth an intelligent mans time to be in the majority.
By definition, there are already enough people to do that.
(G.H. Hardy)
2. Goal: To find the area between two curv
7.1.2 The Substitution Rule for Definite Integrals
1. Quote. In the depth of winter I finally learned that there was
in me an invincible summer.
(Albert Camus, 1913-1960, French philosopher)
2. Substi
6.3.2 Cummulative Change and 6.3.3 Average Values
1. Quote. The real danger is not that computers will begin to
think like men, but that men will begin to think like computers
(Sydney J. Harris, Ameri
6.2.3 The Fundamental Theorem of Calculus (Part II)
1. Quote.Each problem that I solved became a rule, which served
afterwards to solve other problems
(Rene Decartes, 1596-1650)
2. The Fundamental The
6.1.3 Properties of the Riemann Integral
1. Quote. No human investigation can be called real science if it cannot
be demonstrated mathematically
(Leonardo da Vinci (1452-1519)
2. Two Special Propertie
7.1.1 The Substitution Rule for Indefinite Integrals
1. Quote. Persuasion is often more effectual than force.
(Aesop, Greek fabulist, 6th century BC)
2. Problem. Find
Z
2
2xex dx
3. Hint. What if we t
6.2.1 The Fundamental Theorem of Calculus (Part 1) and
6.2.2 Antiderivatives and Indefinite Integrals
1. Quote. If you cant run, then walk. And if you cant walk,
then crawl. Do what you have to do. Ju
M ATH 155
C HAPTER 1
Question: Which of the following infinite series sums to
2
?
6
A.
1
1
+ 21 + 13 + 14 + 51 + . . .
(reciprocals of positive integers)
B.
1
2
+ 31 + 15 + 17 +
(reciprocals of primes
M ATH 155
9.2.5
C HAPTER 9
Leslie Matrices
Goal: Obtain a more accurate population model by taking age into account.
Leslies Model.
Focus on the female population only, and divide into
groups based on
MATH 155 - D100
A SSIGNMENT #8
Instructor Questions #8
Directions: Print double sided, write your solutions to both questions directly on this page, place immediately after cover page and staple toge
Math 155 - D100 Midterm 2 - Version 3
Simon Fraser University, Department of Mathematics
March 16, 2016
Namelprintedl 55 HM/'5 .
(Familv Name) (Gwen Name)
Student Number
SF U email
Signature : 7
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