2. Exam Specifications Mathematics15% Engineering Probability and Statistics7% Chemistry9% Computers7% Ethics and Business Practices7% Engineering Economics8% Statics and Dynamics10% Strength of Materials7% Material Properties7% Fluid Mechanics7% Electricity and Magnetism9% Thermodynamics7%

3. 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

4. GJM - current Professor of Chemical Engineering – Manhattan College Professor Emeritus of Chemical Engineering – Widener University Adjunct Professor of Chemical Engineering – Drexel University

5. GJM Collagen Research 1985-1988 Dartmouth College 1988-1992 Verax, Inc. 1992-2010 Collagen Research Group (Widener U & USDA) 2010-present Manhattan College & USDA

6. 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

7. Prof. Gennaro J. (Jerry) Maffia Teaching: Manhattan College, 2010 - Drexel University, 1992 - Widener University, 1992 - 2010 Short Courses and Training: various venues, 1993 - 2010

8. Prof. Gennaro J. (Jerry) Maffia Major Industrial Experience: CE Lummus, 1973 -1979 ARCO Chemical, 1979 – 1991 Consulting 1993 – current (100+ assignments)

9. 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

11. Founded in 1821, Widener University is a multi-campus, independent, metropolitan university. It offers a student- centered 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.

14. 2010 Senior Project: Lindsay, Derek, and Elliott

15. Teppicha Vityanatpaisal and family with Prof. Maffia at Widener University graduation ceremony May, 2010

16. Teppicha Vityanatpaisal with Prof. Maffia at Widener University graduation ceremony May, 2010

19. BEGINNING OF MATHEMATICS

20. Problem 1TOPIC: 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 ft 2 /h (d)Please calculate the kinematic viscosity in m 2 /s

21. Problem 2TOPIC: 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?

22. Problem 3TOPIC: Mathematics (page 21) Given the following equation: x 2 – 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? x 2 + 5x - 6 = 0

23. Problem 4TOPIC: Mathematics (page 21) Given the following equation: y = x 2 – 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?

24. Problem 5TOPIC: Mathematics (page 21) Given the following equation: (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?

25. Problem 6TOPIC: Mathematics (page 22) Using the general form of the conic section equation: 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

26. Problem 7TOPIC: Mathematics (page 22) The Haaland equation for the Fanning friction factor is given as: (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

27. Problem 8TOPIC: Mathematics (page 22) Simplify the following equations by taking the natural logarithm of both sides: (a) (b) (c) (d)

28. Problem 9TOPIC: 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)

29. Problem 10TOPIC: Mathematics (page 23) Given matrices A, B and C please perform the indicated operations: (a)A+C (b) B-C (c) AB (d) Determinant (A) = det (A)

30. Problem 11TOPIC: Mathematics (page 23,24) Given matrices A, B and C please perform the indicated operations: (a)Transpose (B) (b) 4D (c)Determinant (C), |C| (d)Determinant (D), |D|

31. Problem 12TOPIC: 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

32. Problem 13TOPIC: 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) (b) (c)

33. Problem 14TOPIC: Mathematics (page 24) Given velocity vectors A, B and C please perform the indicated operations: (a) (b)

34. 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) (d)What is the value of the 67 th term in this series

35. 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) e x (d) xe x

36. Problem 17 TOPIC: Mathematics (page 27) Please evaluate the following definite integrals: (a) (b) (c)

37. Problem 18 TOPIC: Mathematics (page 27) Please evaluate the following definite integrals: (d) (e) (f)

38. Problem 19 TOPIC: Mathematics (page 27) Please perform the indicated partial differentiations: (a) (b) (c)

39. END OF MATHEMATICS