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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: [email protected] [email protected] [email protected] 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 44 x 3 (b) ye (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