Exam Specifications
Mathematics
Engineering Probability and Statistics
Chemistry
Computers
Ethics and Business Practices
Engineering Economics
Statics and Dynamics
Strength of Materials
Material Properties
Fluid Mechanics
Electricity and Magnetism
Thermodynamics
15%
7%
9%
7%
7%
8%
10%
7%
7%
7%
9%
7%
Prof. Gennaro J. (Jerry) Maffia
Dartmouth College, D.E. 1988
New York University, M.B.A. 1977
After twenty years of industrial experience with large multinational companies,
Dr. Maffia is presently Professor of Chemical Engineering at Manhattan College
and Adjunct Professor of Chemical Engineering at Drexel University. He is also
Professor Emeritus at Widener University.
Dr. Maffia is a member of many professional and honor societies. His research
interests include the development of environmental remediation technologies
bases on water retention properties of unraveled bovine hide collagen.
Dr. Maffia offers training courses throughout the world in topics related to
process engineering
GJM - current
• Professor of Chemical Engineering –
Manhattan College
• Professor Emeritus of Chemical Engineering –
Widener University
• Adjunct Professor of Chemical Engineering –
Drexel University
GJM Collagen Research
1985-1988 Dartmouth College
1988-1992 Verax, Inc.
1992-2010 Collagen Research Group
(Widener U & USDA)
2010-present Manhattan College & USDA
Prof. Gennaro J. (Jerry) Maffia
Education:
Dartmouth College, D.E. 1988
New York University, M.B.A. 1977
Manhattan College, M/Ch.E. 1973
Manhattan College, M/Ch.E. 1972
Prof. Gennaro J. (Jerry) Maffia
Teaching:
Manhattan College, 2010 Drexel University, 1992 Widener University, 1992 - 2010
Short Courses and Training:
various venues, 1993 - 2010
Prof. Gennaro J. (Jerry) Maffia
Major Industrial Experience:
CE Lummus, 1973 -1979
ARCO Chemical, 1979 – 1991
Consulting 1993 – current
(100+ assignments)
Prof. Gennaro J. (Jerry) Maffia
Contact:
gjmaffia@widener.edu
gjm29@drexel.edu
gennaro.maffia@manhattan.edu
Website:
http://quantum.soe.widener.edu:281/gjm.htm
• Founded in 1821, Widener
University is a multi-campus,
independent, metropolitan
university. It offers a studentcentered learning environment
where course work connects to
societal issues. Dynamic teaching,
active scholarship, personal
attention, and experiential
learning are key components of
the Widener experience.
• The university provides a unique
combination of liberal arts and
professional education through
its eight schools and colleges.
2010 Senior Project: Lindsay, Derek, and Elliott
Teppicha Vityanatpaisal and
family with Prof. Maffia at
Widener University graduation
ceremony May, 2010
Teppicha Vityanatpaisal with Prof. Maffia at
Widener University graduation ceremony May, 2010
BEGINNING OF MATHEMATICS
Problem 1
TOPIC:
Units (pg 19,20)
A petroleum fraction has a viscosity of 2.7 cP and a density of 0.77 g/ml
Questions
(a) Please calculate the viscosity in Pa s
(b) Please calculate the viscosity in lbm/(ft h)
(c) Please calculate the kinematic viscosity in ft2/h
(d) Please calculate the kinematic viscosity in m2/s
Problem 2
TOPIC:
Units (pg 19,20)
The production rate of a methanol plant is 200e6 gallons per year;
methanol has a density of 0.79 g/ml
Questions
(a) How many barrels per year are produced?
(b) How many kilograms per year are produced?
(c) How many pounds per year are produced?
(d) How many liters per year are produced?
Problem 3
TOPIC:
Mathematics (page 21)
Given the following equation:
x2 – 5x +6 = 0
Questions
(a) What are the roots of this equation?
(b) Factor the equation into its linear parts.
(c) If some of the signs on the function were reversed as follows what would
be true about the roots of the equation?
x2 + 5x - 6 = 0
Problem 4
TOPIC:
Mathematics (page 21)
Given the following equation:
y = x2 – 5x +6
(a) What is the geometric form of this equation?
(b) What best describes the direction of the shape?
(c) What are the x intercepts?
(d) What is the y intercept?
Problem 5
TOPIC:
Mathematics (page 21)
Given the following equation:
x  3
9
2

y  6
2
1
49
(a) What is the geometric form represented by this equation?
(b) What point is the center of the shape?
(c) What is the x intercept?
(b) What is the y intercept?
Problem 6
TOPIC:
Mathematics (page 22)
Using the general form of the conic section equation:
Ax  Bxy  Cy  Dx  Ey  F  0
2
2
What is the shape described in each of the following cases:
(a) B=1, A=1, C=1
(b) B=5, A=1, C=1
(c) B=-2, A=1, C=1
(d) B=0, A=0, C=0
Problem 7
TOPIC:
Mathematics (page 22)
The Haaland equation for the Fanning friction factor is given as:
1
fF

  roughness


 6 .9
D

  k log 10 

Re 
3 .7











 10 


 9 







(a) If k = 3.6 for log base 10 what is the value of k for log base e
(b) If Reynolds Number (Re) is 1e5 and roughness factor is 0.0003 ft,
find the Fanning friction factor for a 35 mm internal diameter
Problem 8
TOPIC:
Mathematics (page 22)
Simplify the following equations by taking the natural logarithm of both sides:
(a)
e  4x
y
3
44 x
3
(b)
ye
(c)
z  4x y
(d)
e e
3
y
4
3e
x
Problem 9
TOPIC:
Mathematics (page 23)
If possible, please perform the indicated operations to simplify
the following complex numbers:
(a) (4+3i)+(3-2i)
(b) (4+3i)-(3-2i)
(c) (4+3i)(3-2i)
(d) (4+3i)/(3-2i)
Problem 10
TOPIC:
Mathematics (page 23)
Given matrices A, B and C please perform the indicated operations:
1
A 
1
2
1
;B  

3
1
(a) A+C
(b) B-C
(c) AB
(d) Determinant (A) = det (A)
1
0
;C  

0
0
0
1 
Problem 11
TOPIC:
Mathematics (page 23,24)
Given matrices A, B and C please perform the indicated operations:
1
A
1
2
1
;B  

3
1
(a) Transpose (B)
(b) 4D
(c) Determinant (C), |C|
(d) Determinant (D), |D|
1
0
;C  

0
0
1
0
0
;
D


1 
 2
1
1 2

0 1
2
Problem 12
TOPIC:
Mathematics (page 24)
Given velocity vectors A, B and C please perform the indicated operations:
A =xi + 5yj - 6xk; B =zi + 3zj – 2xk; C =1xi + 2yj – 3zk
(a) A - C
(b) A+B+C
.
(c) A B
(d) AxB
Problem 13
TOPIC:
Mathematics (page 24)
For (a), (b), and (c) given velocity vectors A, B and C please perform
the indicated operations:
A =xi + 5yj - 6xk; B =zi + 3zj – 2xk; C =1xi + 2yj – 3zk
(a)   C
(b)   C
(c)  2  A  C 
Problem 14
TOPIC:
Mathematics (page 24)
Given velocity vectors A, B and C please perform the indicated operations:
(a)  2  xyz , where x, y and z are all scalars
(b)  2  x 2 y 2 z 2 , where x, y and z are all scalars
Problem 15
TOPIC:
Mathematics (page 25)
Find the next term in each of the following series the following series:
(a) 0,1,1,2,3,5,8,13......
(b) 2,3,4,6,9,13,19.......
(c) 2 , 3 , 5 , 8 , 13 , 21 ........
1 2 3 5 8 13
(d) What is the value of the 67th term in this series
2 3 5 8 13 21
, , , , , ........
1 2 3 5 8 13
Problem 16
TOPIC:
Mathematics (page 25)
Find the first 4 terms in the MacLaurin Series expansion for the following functions:
(a) sin(x)
(b) x sin(x)
(c)
(d)
ex
xex
Problem 17
TOPIC:
Mathematics (page 27)
Please evaluate the following definite integrals:
1
1
(a)

x
1
2
dx
1
(b) 
sin( x )dx
1

(c)
e
1
x
dx
Problem 18
TOPIC:
Mathematics (page 27)
Please evaluate the following definite integrals:
1
(d)
2

sin x dx
1
1

(e)
ln x dx
0 .5
(f)
1
x
 xe dx
0
Problem 19
TOPIC:
Mathematics (page 27)
Please perform the indicated partial differentiations:
(a)

x
(b)
(c)
x

y

z
y ln( z ) 
2
x
2
x
y ln( z ) 
2
y ln( z ) 
END OF MATHEMATICS