CHBE 553: Mathematical Operations in Chemical Engineering

Instructor Information
Instructor: James J. Feng
Email: james.feng_AT_ubc_DOT_ca
Offices: CHBE 209 (Phone 604-822-8875); MATX 1206 (604-822-4936)
Office hours: by appointment
Course Information
Mon. Wed. 11:30 am - 1:00 pm, Location: CHBE 103 (Mon), ANGU 334 (Wed)

This course requires you to write computer codes and solve problems numerically. In the past, most students have used MATLAB, although some used Fortran and Visual Basic. We will not have time to review programming languages, and you should do it on your own if needed.

Reference Books

W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in Fortran, 2nd edn. Cambridge University Press (1992).

A. Constantinides and N. Mostoufi, Numerical Methods for Chemical Engineers with MATLAB Applications, Prentice-Hall (1999).

D. N. P. Murthy, N. W. Page and E. Y. Rodin, Mathematical Modelling. A Tool for Problem Solving in Engineering, Physical, Biological and Social Sciences, Pergamon Press (1990).

G. I. Barenblatt, Scaling, Cambridge University Press (2003).

G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations, Springer-Verlag (1974).

Assignments and Grade

There will be weekly assignments but no mid-term or final exam.

Final Grade = 50% Assignments + 25% Final Project + 25% Final Presentation
Course Outline
x
Chapters
Sections Additional
Materials
Assignments Comments
1. Solution of Algebraic Equations
(6 hours)

Root finding for nonlinear equations: Newton's method Example 1: code
Example 1: plot
Notes_1.1.pdf
Assignment 1
Due: Jan. 10 in class
Linear systems:direct and iterative methods
Notes_1.2.pdf


Nonlinear systems of equations: Newton's method Notes_1.3.pdf
Assignment 2
Due: Jan 24
 
2. Curve Fitting
(4 hours)


Least square fitting Notes_Least_Sqr.pdf

 
Linear and multiple linear regression Notes_Linear_Reg.pdf

 
Nonlinear regression Notes_Nonlinear_Reg.pdf
Assignment 3
Data file
Due: Jan 31
 
3. Interpolation & Approximation
(3 hours)
Polynomial interpolation (Lagrange formula) Notes_Polyn_Interp.pdf
   
Cubic splines Notes_Cubic_Spln.pdf
Cubic_Supplement.pdf
Assignment 4
Due: Feb 7
 
Interpolation in 2D and 3D Notes_2d_Interp.pdf
   
4. Differentiation & Integration
(5 hours)
Forward, backward and central differencing Notes_Differ.pdf
Formula Sheet
Assignment 5
Diffus.txt

Due: Feb 14

 
Roundoff errors in finite differencing Notes_Roundoff.pdf
   
Newton-Cotes and Romberg's methods Notes_NumIntg.pdf
Romberg Integration code in Fortran
   
Gaussian quadrature Notes_G_Quad.pdf
Assignment 6
Due: Feb 28
 
Multiple integrals
Notes_MultiIntg.pdf
   
5. Ordinary Differential Equations
(6 hours)
Linear 1st order ODE's
Notes_Linear_ODE.pdf
   
IVP.'s: Euler's method, Runge-Kutta, Predictor-Corrector
IVP_ODE_Notes.pdf

 
BVP's: shooting and finite-difference methods
BVP_ODE_Notes.pdf
Assignment 7
Due: Mar 14
 
Parameter estimation for ODE models
GaussNewton_ODE.pdf
Exercise 7a
(Not collected)
Hints: p. 97, Englezos & Kalogerakis (2000) 
6. Partial Differential Equations
(6 hours)
Finite difference methods: generalities PDE_Intro_Notes.pdf
   
Elliptic equations Ellip_PDE_Notes.pdf
   
Parabolic equations Parab_PDE_Notes.pdf
Assignment 8
Due: (Not collected)
Assignment 8 solution:
Outline
Plot
Fortran code
Hyperbolic equations Hyperb_PDE_Notes.pdf
   
7. Mathematical Modeling
(5 hours)
Mathematical modeling: general procedure Modeling_Intro_Notes.pdf
   
Model building, analysis and validation: a case study Modeling_Case_Notes.pdf
   
Similarity and scaling Modeling_Similarity.pdf
   
8. Presentation of Projects
(4 hours)