Courses:

Numerical Methods Applied to Chemical Engineering >> Content Detail



Syllabus



Syllabus

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A list of topics by lecture is available in the calendar listed below.



Purpose


  • To ensure you are aware of the wide range of easily accessible numerical methods that will be useful in your thesis research, at practice school, and in your career.
  • To make you confident to look up additional methods when you need them.
  • To help you become familiar with MATLAB® and other convenient numerical software, and with simple programming/debugging techniques.
  • To give you some understanding of how the algorithms work and to help you understand why numerical algorithms sometimes give unexpected results.


Topics


This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment.



Prerequisite


Solid undergraduate preparation including but not limited to Calculus (18.01, 18.02), Differential Equations (18.03), Linear Algebra (18.06), Thermodynamics (5.60, 10.213), Fluid Mechanics (10.301), Chemical Kinetics and Reactor Design (10.37).



Texts




Required Text


Amazon logo Beers, Kenneth J. Numerical Methods for Chemical Engineering: Applications in MATLAB®. New York, NY: Cambridge University Press, November 2006. ISBN: 9780521859714.



Recommended Texts


Other easier-to-read but less comprehensive texts that are helpful:

For short, clear synopses of methods for many types of problems:

Amazon logo Press, William H. Numerical Recipes in C: The Art of Scientific Computing. New York, NY: Cambridge University Press, 1988. ISBN: 9780521354653.
Comes in various editions.

For simple methods and a good introduction to using MATLAB®:

Amazon logo Recktenwald, Gerald W. Introduction to Numerical Methods with MATLAB®: Implementations and Applications. Upper Saddle River, NJ: Prentice-Hall, 2000. ISBN: 9780201308600.

For a more concise coverage of many topics discussed in Beers's text:

Amazon logo Heath, Michael T. Scientific Computing: An Introductory Survey. 2nd ed. New York, NY: McGraw-Hill Companies, Inc., 2002. ISBN: 9780072399103.



Homework Guidelines


You will submit your solution electronically. The due date is 9am on Wednesday, although submissions after that time will be marked as late and (at least for this first homework) accepted on the same day. If you have difficulty working with the computer systems, please consult the TAs.

Write a Microsoft® Word® document with the title username_HW1.doc, where username is your MIT e-mail name (for example, for [email protected], it would be sample_email_address_ihtfp_HW1.doc). In this document, describe how you solved each problem, and include as figures any graphs that you wish to present. Like any piece of technical writing, you must find a balance between being concise and providing sufficient detail that an educated reader can follow your reasoning and methods. The Microsoft® equation editor is available for typing any equations.

If in a particular problem you are asked to write a MATLAB® program, gather all necessary code into a single .m file and submit it electronically as well (we may wish to run it). Use the file name username_HW1_PX.m for the program for problem X. In your Microsoft® Word® document, clearly note the name of any program that you submit, and describe how it may be used to perform the calculation for the problem; for example, describe what you should provide as input, how the results are stored, etc.

Do all analysis and data visualization within your MATLAB® program - do not export your results to another program such as Microsoft® Excel® for plotting. It is not necessary and makes it difficult for us to reproduce (and assess) your results.

You are free to discuss and consult with your colleagues, but everyone must submit his or her own programs and solution. You may not simply copy the program of another, or jointly write the same program. This would defeat the purpose of the class, which is to provide you with personal experience in scientific computing.



Grading



ACTIVITIESPERCENTAGES
Homework (best 10 out of 11 assignments)30%
Two quizzes30%
Final exam40%



Recommended Citation


For any use or distribution of these materials, please cite as follows:

William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].



Calendar


The calendar below provides information on the course's lecture (L) and quiz (Q) sessions.


SES #TOPICSKEY DATES
L1Using MATLAB® to evaluate and plot expressions
L2Solving systems of linear equations
L3

Matrix factorization

Modularization

L4When algorithms run into problems: Numerical error, ill-conditioning, and tolerancesProblem set 1 due: MATLAB®
L5Introduction to systems of nonlinear equations
L6Modern methods for solving nonlinear equations
L7Introduction to eigenvalues and eigenvectorsProblem set 2 due: Systems of equations
L8Constructing and using the eigenvector basis
L9Function space vs. real space methods for partial differential equations (PDEs)Problem set 3 due: Eigenvalues, linear algebra
L10Function space
L11

Numerical calculation of eigenvalues and eigenvectors

Singular value decomposition (SVD)

Problem set 4 due: Eigenvectors
Q1Quiz 1
L12Ordinary differential equation - initial value problems (ODE-IVP) and numerical integration
L13

Stiffness

MATLAB® ordinary differential equation (ODE) solvers

Problem set 5 due: SVD, integrals
L14

Implicit ordinary differential equation (ODE) solvers

Shooting

L15

Differential algebraic equations (DAEs)

Introduction: Optimization

L16Unconstrained optimizationProblem set 6 due: ODE, DAE
L17Constrained optimization
L18

Optimization

Sensitivity analysis

Introduction: Boundary value problems (BVPs)

L19Boundary value problems (BVPs) lecture 2Problem set 7 due: Optimization intro BVPs
L20Boundary value problems (BVPs) lecture 3: Finite differences, method of lines, and finite elements
L21TA tutorial on BVPs, FEMLAB®
L22Introduction: Models vs. DataProblem set 8 due: BVPs
L23Models vs. Data lecture 2: Bayesian view
L24Uncertainties in model predictions
L25Conclude models vs. dataProblem set 9 due: Models vs. Data
L26TA led review
Q2Quiz 2
L27

Models vs. Data recapitulation

Monte Carlo and molecular dynamics

L28Guest lecture on Monte Carlo / molecular dynamics: Frederick Bernardin
L29

Global optimization

Multiple minima

L30

Modeling intrinsically stochastic processes

Multiscale modeling

L31Fluctuation-dissipation theoremProblem set 10 due: Monte Carlo
L32Kinetic Monte Carlo and turbulence modeling
L33

Operator splitting

Strang splitting

L34

Fourier transforms

Fast fourier transform (FFT)

Problem set 11 due: Stochastic processes
L35Summary: Problem solving
L36TA led final review

 








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