Mathematical Methods in Chemical Engineering

University of Colorado – Department of Chemical EngineeringCHEN 5740 – Spring 2001

Instructor: Christine HrenyaOffice: 130 ECCHOffice phone: 492-7689

E-mail: hrenya@colorado.eduOffice Hours: Monday 4:30-6:00 PM and Wednesday 4:30-6:00 PM

TA: None. If there are questions on course material, please contact Christine Hrenya viae-mail, office hours, or individual appointment. You can also stop by the officewithout 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 bepassed out to each student. These notes will be the primary resource for coursematerial. At the end of the semester, each student will be assessed copying chargesfor 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 ChemicalEngineers, John Wiley & Sons, New York, 1995. This text is optional, but it isrecommended.

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 listproc@lists.colorado.edu with the followingcontents 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 theappropriate microscopic and macroscopic balances. To determine and apply the appropriateanalytical methods used to solve the resulting governing equations, namely linear and nonlinearalgebraic equations, ordinary differential equations, and partial differential equations. To assesswhen numerical methods are needed for the solution of governing equations, and to solve themaccordingly using mathematical software packages. To identify and interpret the differencesbetween model predictions and experimental 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 ahanging 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 thetotal points of various homework sets may vary, all will be normalized and weightedequally at the end of the course.

• Collaboration on homework assignments is allowed, but direct copying from any source isnot permitted. If it is believed that a homework set has been graded unfairly, pleaseresubmit within one week for re-grade of entire assignment.

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 beresponsible for solving a (nontrivial) system of equations found in the literature using anappropriate 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 beassigned by the instructor. A compilation of these review problems will be given tostudents before the final exam. Further details and guidelines on the project will bepassed 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, andshould take roughly 1/4 of the total exam time. For the second portion of the exam, aone-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 beforeexam date for permission to be excused. If excused, the final exam grade will be used inplace of the missed exam. If the final exam is excused, the grade on the previous examswill 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 weekfor re-grade of entire exam.

Grading

Final course grades will not be curved. Instead, the grade will be determined based onthe distribution and scale shown below, with plus and minus grades assigned for scores near thecutoffs:

Homework 30% A 85-100Exam 1 15% B 75-85Exam 2 15% C 60-75Project 15% D 50-60Final Exam 25% F 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 theEngineering Library throughout the semester. These references can be checked out for 2 hours ata time, and cannot be held overnight. I have a copy of those books which are not on reserve atthe library, and will lend them out for several hours upon request.

*Finlayson, B. A., Nonlinear Analysis in Chemical Engineering, McGraw-Hill, New York, 1980.

Hildebrand, F. B., Advanced Calculus for Applications, 2nd Edition, Prentice-Hall, EnglewoodCliffs, NJ, 1976.

*Jenson, V. G. and G. V. Jeffreys, Mathematical Methods in Chemical Engineering, AcademicPress, New York, 1963.

*Kreyszig, E., Advanced Engineering Mathematics, 6th 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, JohnWiley & Sons, New York, 1995.

Strang, G., Introduction to Applied Mathematics, Wellesley-Cambridge Press,Wellesley, MA,1986.

*Strang, G., Linear Algebra and its Applications, Harcourt, Brace, Jovanovich Publishers, SanDiego, 1988.

*Varma, A. and M. Morbidelli, Mathematical Methods in Chemical Engineering, OxfordUniversity 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 EngineeringCHEN 5740 – Spring 2001

Date Week Topic PageJan. 16Jan. 18

Jan. 23

Jan. 25Jan. 30

Feb. 1

Feb. 6, 8

Feb. 13, 15, 20Feb. 22, 27, Mar. 1

Mar. 6Mar. 8, 13

Mar. 15Mar. 20, 22Apr. 3Apr. 5Apr. 10, 12, 17Apr. 19, 24, 26

May 1

May 3_____________

Mar. 27, 29

Mar. 8Apr. 19May 8

11

2

23

3

4

5-66-7

88-9

910111112-1313-14

15

15_____

Introduction to CourseProblem Formulation & Dimensionless Analysis

1. Algebraic Equations1.1 Linear Systems1.2 Nonlinear Equations and Systems1.3 Numerical Methods

2. Ordinary Differential Equations (ODEs)2.1 First Order ODEs

LinearNonlinear

2.2 Higher Order ODEsLinear• “non-series” techniques• series solutionsNonlinear• “non-perturbation” techniques• perturbation techniques

2.3 Sytems of ODEs2.4 Numerical Methods - IVP

3. Partial Differential Equations (PDEs)3.1 Numerical Methods - BVP3.2 Method of Characteristics3.3 Similarity Solutions3.4 Separation of Variables3.5 Integral Transform

LaPlace TransformsFourier Transforms

Review (optimistic) or Catch-Up (pessimistic)________________________________________

NO CLASS – SPRING BREAK

EXAM #1 (6:30 – 8:30 PM – 1B58)EXAM #2 (6:30 – 8:30 PM – 1B58)FINAL EXAM (10:30 – 1:00 PM)

_____