CHEN E4010 Mathematical Methods in Chemical Engineering
Syllabus and Lectures Schedule – Fall 2024
Welcome!
CHEN E4010 Mathematical Methods in Chemical Engineering is a rigorous course that is an important component of the foundations of your graduate education in chemical engineering. I love math's inherent beauty and awesome power to solve practical problems in almost any field. In this course, you will be able to appreciate this in the context of chemical engineering problems.
1. CHEN E4010 Math Methods in Chemical Engineering - 3.0 pts
Prerequisites: CHEN E3120 and E4230, or equivalent, or instructor's permission. Mathematical description of chemical engineering problems and the application of selected methods for their solution. General modeling principles, including model hierarchies. Linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients. Partial differential equations in Cartesian and curvilinear coordinates for the solution of chemical engineering problems. (http://www.columbia.edu/cu/bulletin/uwb/)
4. Textbook and Materials (required and supplemental):
a. Textbook (Required): Rice, Richard G. and Duong D. Do Applied Mathematics and Modeling for Chemical Engineers 2nd Edition, New York, Wiley 2012. ISBN-13: 978- 1118024720 | ISBN-10: 1118024729
(Suggested):
Francis B. Hildebrand, Advanced Calculus for Applications, 2nd Edition, Prentice-Hall
(1976). ISBN-13: 978-0130111890 | ISBN-10: 0130111899
b. Materials(required):
1. CHEN E4010 CourseWork's web site https://courseworks2.columbia.edu/welcome/
c. Materials (supplemental)
1. Reference books and internet sites
Abramowitz, Milton and Irene A. Stegun, Handbook of Mathematical Functions with th
Formulas, Graphs, and Mathematical Tables, New York: Dover, 1965 9 printing.
Billo, E. Joseph, Excel for Scientists and Engineers, Numerical Methods, Hoboken, NJ: Wiley, 2007
Fogler, H. Scott, Elements of Chemical Reaction Engineering 4th Edition (3rd Printing), New York: Prentice Hall, 2006
Fong, C.F. Chan Man, D. De Kee and P.N. Kaloni, Advanced Mathematics for Applied and Pure Sciences, Canada: Gordon Breach Science Publishers, 1997.
(http://cuit.columbia.edu/mathematica-students accessed Jan 5, 2017)
(http://www.mathworksheetsgo.com/trigonometry-calculators/inverse-cosine- calculator.php accessed Jan 5, 2017)
(http:// http://integrals.wolfram.com/index.jsp accessed Jan 5, 2017)
Aris, Rutherford, Vectors, Tensors, and the Basic Equations of Fluid Mechanics. New York: Dover Publications Inc. 1962.
Stewart, James, Calculus Concepts and Contexts, New York: Brooks/Cole Publishing. 1998, P402 -408, Section 5.6 Integration by parts
Strang, Gilbert, Introduction to Linear Algebra, Wellesley-Cambridge Press and SIAM, Fifth Edition (2016). An excellent introduction to the subject.
Zill, Dennis G. and Warren S. Wright, Advanced Engineering Mathematics, Burlington, MA: Jones and Bartlett Learning LLC, 2014. Engineering mathematics textbook.
2. Other supplemental material, notes, and problems will be posted on the CourseWorks web page and updated throughout the course.
5. Course Objectives:
a) Be able to mathematically describe chemical engineering problems and the application of selected methods for their solution.
b) Apply general modeling principles, including model hierarchies.
c) Solve linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients.
d) Solve partial differential equations in Cartesian and curvilinear coordinates to solve chemical engineering problems.
e) Hopefully, to learn to love and admire mathematics for its inherent beauty and almost magical power in solving practical problems.
6. Classroom Procedures:
a) What you should bring to class: A calculator, writing implement, a notebook, textbook, and computer laptop as desired.
b) What not to bring to class: Anything that could disturb others around you. Anything that would distract you or others from the guest speaker, such as but not limited to a plate of food, computer games, any device that makes sounds, coursework from another class, social media connecting devices, etc.
c) Be on time for class and actively participate. Being on time for class means you are seated, ready to take notes, solve problems, listen to lectures, and take other classroom instructions before the start time. You are also expected not to chat and be distracted. This standard is adopted to provide the best class experience possible. Class participation is part of your grade. You must be in class and seated, ready to go at the start time. If you are found to be a distraction, you may be asked to leave.
d) Web Site. The website for this class contains important administrative and scheduling information and is located at the Columbia Course Works website: https://courseworks.columbia.edu/welcome/; I will update the site with lecture slides and links to articles and resources as appropriate.
7. Course Grade: The final grade in this course will be based on points awarded according to the following system:
a. Final grade: 50 % midterms (two midterms, 25% each) + 50 % Final exam
b. Rules for Exams: All exams are closed books and closed notes. You are not allowed to use any books or notes of any sort during the exams, except for a “crib sheet” (one page, 8.5 x 11 inches, for midterms, and two pages for the final exam) as a concise set of notes used for quick reference. You are not allowed to use cell phones, calculators, computers, or any device that allows for data storage during the exams.
c. Final Exam: This is like the midterms, except it will be two hours long and covers all aspects of the course.
8. Homework: Homework problems will be assigned, and completion dates suggested. However, homework will not be collected or graded. You are ultimately responsible for knowing all aspects of the problems. To help you learn, homework solutions will be made available through the TA one week after the homework has been posted. Copying solutions will not help you learn the material and is against Columbia University's Policy. (http://bulletin.engineering.columbia.edu/policy-conduct-and-discipline). The re-distribution of the homework solutions in CHEN E4010 is not authorized. The TA has office hours should you need assistance or clarification with the homework or exams. While the homework in the math methods course is not graded, the homework is still an assignment for a student in the course and is assigned to help your learning. In all exams, at least one question from the homework will be asked. This can be seen as an incentive to do the homework regularly and diligently.