Mathematical Mathematical Methods in Chemical Engineering University of Colorado – Department of Chemical Engineering CHEN 5740 – Spring 2001
Instructor: Christine Hrenya Office: 130 ECCH Office Office phone: phone: 492-768 492-7689 9 E-mail:
[email protected] Office Hours: Hours: Monday 4:30-6: 4:30-6:00 00 PM and Wednesday Wednesday 4:30-6:00 4:30-6:00 PM TA:
None. If there are questions on course material, please contact Christine Hrenya via e-mail, office hours, or individual appointment. You can also stop by the office without an appointment, but I may have to postpone if that time is inconvenient.
Handouts: At the beginning of each class, detailed handouts covering the day’s material will be
passed out to each student. These notes will will be the primary resource for course material. At the end of the semester, each student will will be assessed copying charges for these handouts. Total cost per student is expected to be about $20. Text:
Rice, R. G. and D. D. Do, Applied Mathematics and Modeling for Chemical Engineers, John Wiley & Sons, New York, 1995. This text is optional, but it is recommended.
Email:
A course e-mail list has been established, and all students are required to subscribe. To do so, send an e-mail message to
[email protected] with the following contents in the body of the message: subscribe chen-5740 full-name-of-student
Learning Goals
To formulate chemical engineering problems in mathematical terms by employing the appropriate microscopic and macroscopic balances. To determine and apply the appropriate analytical methods used to solve the resulting governing equations, namely linear and nonlinear algebraic equations, ordinary differential equations, and partial partial differential equations. To assess when numerical methods are needed for the solution of governing equations, and to solve them accordingly using mathematical software packages. To identify and interpret the differences between model predictions and experimental expe rimental results. Learning Activities
Lectures – meet every Tuesday and Thursday at 11:00 – 12:15 in ECCH 1B58
Homework Assignments will be handed out one week before the due date and are due at the beginning of class. Late homeworks will not be accepted since the solutions will be available in a hanging file (outside of the Chem. Eng. office) the day which the homeworks are due. Roughly 10 homework assignments will be passed out during the semester. Although the total points of various homework sets may vary, all will be normalized and weighted equally at the end of the course. Collaboration on homework assignments is allowed, but direct copying from any source is not permitted. If it is believed that a homework set has been graded unfairly, please resubmit within one week for re-grade of entire assignment. •
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Project The final assignment will take the form of a small project, with students working in groups of 2-3 people. This project will be twofold in nature. First, the group will be responsible for solving a (nontrivial) system of equations found in the literature using an appropriate numerical technique. Second, the group will be responsible for developing a “review problem” for the exam, along with its solution; the topic for this problem will be assigned by the instructor. A compilation of these review problems will be given to students before the final exam. Further details and guidelines on the project will be passed out during the semester. •
Exams The exams will be given during a 2-hour period outside of the scheduled class time. All exams will be composed of two sections. The first section will be closed-book, and should take roughly 1/4 of the total exam time. For the second portion of the exam, a one-sided 8 ½ x 11 crib sheet will be allowed. No make-up exams will be given. If there is an extreme emergency, contact me before exam date for permission to be excused. If excused, the final exam grade will be used in place of the missed exam. If the final exam is excused, the grade on the previous exams will be averaged and used in place of the final exam. If more than one exam is missed, an incomplete/fail will be given for the course. If it is believed that an exam has been graded unfairly, please resubmit within one week for re-grade of entire exam. •
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Grading
Final course grades will not be curved. Instead, the grade will be determined based on the distribution and scale shown below, with plus and minus grades assigned for scores near the cutoffs: Homework Exam 1 Exam 2 Project Final Exam
30% 15% 15% 15% 25%
A B C D F
85-100 75-85 60-75 50-60 0-50
References (* denotes the texts that are on reserve at the Engineering Library) A list of useful references is given below, some of which are on reserve at the Engineering Library throughout the semester. These references can be checked out for 2 hours at a time, and cannot be held overnight. I have a copy of those books which are not on reserve at the library, and will lend them out for several hours upon request. *Finlayson, B. A., Nonlinear Analysis in Chemical Engineering, McGraw-Hill, New York, 1980. nd
Hildebrand, F. B., Advanced Calculus for Applications, 2 Cliffs, NJ, 1976.
Edition, Prentice-Hall, Englewood
*Jenson, V. G. and G. V. Jeffreys, Mathematical Methods in Chemical Engineering, Academic Press, New York, 1963. th
*Kreyszig, E., Advanced Engineering Mathematics, 6 Edition, John Wiley & Sons, 1988. *O’Neil, P. V., Advanced Engineering Mathematics, 2nd Edition, Wadsworth, Belmont, 1991.
*Rice, R. G. and D. D. Do, Applied Mathematics and Modeling for Chemical Engineers, John Wiley & Sons, New York, 1995. Strang, G., Introduction to Applied Mathematics, Wellesle y-Cambridge Press,Wellesley, MA, 1986. *Strang, G., Linear Algebra and its Applications, Harcourt, Brace, Jovanovich Publishers, San Diego, 1988. *Varma, A. and M. Morbidelli, Mathematical Methods in Chemical Enginee ring, Oxford University Press, New York, 1997. *Wylie, C. R. and L. C. Barrett, Advanced Engineering Mathematics, 6th Edition, Mc-Graw-Hill, New York, 1995.
Tentative Course Schedule and Outline Mathematical Methods in Chemical Engineering
CHEN 5740 – Spring 2001 Date
Week
Topic
Jan. 16 Jan. 18
1 1
Introduction to Course Problem Formulation & Dimensionless Analysis
Jan. 23
2
1. Algebraic Equations
Jan. 25 Jan. 30
2 3
Feb. 1
3
Feb. 6, 8
4
Page
1.1 Linear Systems 1.2 Nonlinear Equations and Systems 1.3 Numerical Methods 2. Ordinary Differential Equations (ODEs)
2.1 First Order ODEs Linear Nonlinear 2.2 Higher Order ODEs Linear “non-series” techniques series solutions Nonlinear “non-perturbation” techniques perturbation techniques 2.3 Sytems of ODEs 2.4 Numerical Methods - IVP •
Feb. 13, 15, 20 5-6 Feb. 22, 27, Mar. 1 6-7
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Mar. 6 Mar. 8, 13
8 8-9
Mar. 15 Mar. 20, 22 Apr. 3 Apr. 5 Apr. 10, 12, 17 Apr. 19, 24, 26
9 10 11 11 12-13 13-14
May 1
15
May 3 _____________
15 _____
3. Partial Differential Equations (PDEs)
3.1 Numerical Methods - BVP 3.2 Method of Characteristics 3.3 Similarity Solutions 3.4 Separation of Variables 3.5 Integral Transform LaPlace Transforms Fourier Transforms Review (optimistic) or Catch-Up (pessimistic) ________________________________________ _____
Mar. 27, 29
NO CLASS – SPRING BREAK
Mar. 8 Apr. 19 May 8
EXAM #1 (6:30 – 8:30 PM – 1B58) EXAM #2 (6:30 – 8:30 PM – 1B58) FINAL EXAM (10:30 – 1:00 PM)
