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ENCH620

Methods of Engineering Analysis

Fall 2002

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This file will be updated as needed during the semester.

Table of Contents

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Class Syllabus

Class Syllabus contains information on textbooks, gradings, etc. Be sure you understand the Policy on Academic Integrity within the Chemical Engineering Department.

Schedule
WeekDateTopics
1 9/03Holiday (Labor Day)
9/05Syllabus, What is a function? Mathcad Review.
2 9/09Function approximation (Taylor's polynomial, Lagrange polynomial, Chebychev points)
9/11Numerical integration by trapezoidal rule, Review of vectors/matrices, Linear algebraic equations Ax=b, Gaussian elimination, matrix inverse
3 9/16Nonlinear algebraic equations, f(x)=0, successive approximations, Newton's Method
9/18Multidimensional Newton's method, polynomial roots
4 9/23Linear regression
9/25Nonlinear regression
5 9/30Vector analysis, scalar product, angle
10/02Orthogonality, (Gram-Schmidts)
6 10/07Exam #1
10/09Vector projection (regression & function approximation, approximation of solution to ODE, method of weighted residuals)
7 10/14Linear Transform
10/16Eigenvalue-eigenvector
8 10/21Application of eigenvalue-eigenvector (regression)
10/23Application of eigenvalue-eigenvector ODE, kinetics)
9 10/28Application of eigenvalue-eigenvector (Local stability analysis)
10/30Stability analysis & Trajectories
10 11/04Exam #2
11/06AIChE National Meeting Week (no class)
11 11/11Review of Differential Equations
11/13Runge-Kutta
12 11/18Static Optmization /w Equality Constraints or Inequality Constraints
11/20Dynamic Optimization
13 11/25Dynamic Optimization
11/27Perturbation Methods (Regular)
14 12/02Perturbation Methods (Singular)
12/04Perturbation Methods (Singular)
15 12/09Perturbation Methods (Singular)
12/11Semeter Review
_.o8o.________ We Are Here Now! ________.o8o._
16 12/16Final Examination (Monday 5:30am-7:30pm)
 

Homework Statements & Solutions

DueHomeworkSolutions (Computer Files)
9/09Homework #1  
9/16Homework #2  
9/25Homework #3  
10/02Homework #4  
10/09Homework #5  
10/16Homework #6  
10/23Homework #7  
10/30Homework #8  
11/06Homework #9  
11/13Homework #10  
11/20Homework #11  
11/27Homework #12  
12/04Homework #13  
12/11Homework #14  
   
  
 

Class Handouts & Lecture Notes

DateHandouts
Week #1
9/03, 9/05
Week #2
9/09, 9/11
Week #3
9/16, 9/18
  • f(x)=0
  • Introduction to Successive Approximation (with Square Root Example)
  • Implementation of Bisection Method (sin(x)=a*x Example)
  • Implementation of Newton's Method (sin(x)=a*x Example)
  • Nonlinear Algebraic Equation f(x)=0 by Newton's Method, Demonstrate Combining Two Real Equations into One Complex Equation.
  • Implementation of Newton's Method (Multidimensional f(x)=0)
  • Example of f(x)=0 (Diffusion-Reaction via Finite Element)
Week #4
9/23, 9/25
  • Regression
  • Multivariate Regression Series (Part 1, Linear Least Squares Regression)
  • Multivariate Regression Series (Part 2, Multiple Least Squares Regression)
  • Nonlinear Regression by Gauss-Newton's Method: Exponential Decay Example.
  • Nonlinear Regression and Function Minimization by the Steepest Descent Method: Exponential Decay Example.
Week #5
9/30, 10/02
  • Vector Analysis
  • Linear Vector Space
  • Scalar Product
  • Vectors/Functions and Angles between them
Week #6
10/07, 10/09
Week #7
10/14, 10/16
  • Linear Transformation
  • Rotation Matrix in 3D Cartesian Coordinates
  • Eigenvalue-Eigenvector
    • Snapshot of Mathcad Screen (Whole worksheet, may be too large for browser) (eigen.gif)
    • Snapshot of Mathcad Screen (Part 1, Theory) (eigena.gif)
    • Snapshot of Mathcad Screen (Part 2, Calculation) (eigenb.gif)
    • Mathcad File (eigen.mcd)
Week #8
10/21, 10/23
Week #9
10/28, 10/30
Week #10
11/04, 11/06
Week #11
11/11, 11/13
  • Review of Ordinary Differential Equation
  • The following deals with two major algorithms in the numerical solution of ODEs: Euler and Runge-Kutta. See my ENCH250 web page on ODE Initial Value Problem and ODE Boundary Value Problem for examples of numerical ODE solution in various packages (Fortran, Basic, Matlab, Mathcad, Excel).
  • Implementation of Euler's Method for Solving ODE (Predator-Prey Example)
  • Implementation of Euler's Method for Solving ODE (Lorenz Attractor Example) -- with Movie Clip
  • Implementation of Runge-Kutta 4th-Order Method (Nonisothermal CSTR Example) -- Including Multiple I.C.s
  • Multiple I.C.s with "rkfixed -- Non-isothermal Reactor -- Works only in Mathcad v6 or higher.
Week #12
11/18, 11/20
Week #13
11/25, 11/27
  • Regular Perturbation Method: Diffusion-Reaction
  • Singular Perturbation Method: Boundary Layer & Matching
Week #14
12/02, 12/04
  • Singular Perturbation Method: Location of Boundary Layer
  • Singular Perturbation Method: Matching of Terms in O(e) from O(1)
Week #15
12/09, 12/11
  • Singular Perturbation Method: Michaelis-Menten Kinetics
  • Semester Review
Week #16
12/16
 

List of Students
Click here to match names with faces for the entire class. (Warning: it may take a while on a slower machine because there are many pictures to display.)

Last NameFirst/Middle NameE-MailPicture
100X100

200X200
?, Brandi  
Bolisay, Linden De Venecia lbolisay@wam.umd.edu
Cipriano, Bani csbhc@glue.umd.edu
Davies, Tanner Scott daviests@wam.umd.edu
Dutta, Bhaskar bhaskard@wam.umd.edu
Namatovu, Halima hnamat1@umbc.edu
Kanani, Harin H kanani@wam.umd.edu
Ko, Bongsub Samuel samko@wam.umd.edu
Lewandowski, Angela Teresa atl3h@yahoo.com
MacNeel, Nicole Yvonne nymacneel@aol.com
Edobor, Osaretin oedobor@wam.umd.edu
Parikh, Rinku Pankaj rpparikh@wam.umd.edu
Powell, Victor Robert worthy@wam.umd.edu
Schwalm, Henry Jason jasonschwalm@hotmail.com
Subramani, Aruna Devi adsub@wam.umd.edu
Suchak, Kinjal Suresh kinjal@glue.umd.edu
Wang, Yechun yechun@glue.umd.edu
Yang, Ta-I taiyang@wam.umd.edu
Ye, Yuesheng yey@wam.umd.edu
David, Allan Emerson aedavid@wam.umd.edu

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Methods of Engineering Analysis (ENCH620)
Forward comments to:
Nam Sun Wang
Department of Chemical Engineering
University of Maryland
College Park, MD 20742-2111
301-405-1910 (voice)
301-314-9126 (FAX)
e-mail: nsw@eng.umd.edu ©2002 by Nam Sun Wang
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