CHBE 553: Mathematical Operations in Chemical Engineering

Instructor Information
Instructor: James J. Feng
Email: jfeng_AT_chbe_DOT_ubc_DOT_ca
Offices: CHBE 209 (Phone 822-8875)
Office hours: by appointment
Course Information
Mon. Wed. 10:30 am - 12:00 pm, Location: CEME 1212

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. Note the freely downloadable, open-source MATLAB clone Octave.

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
Sections Additional
Assignments Comments
1. Solution of Algebraic Equations
(6 hours)

Root finding for nonlinear equations: Newton's method Example 1: code
Example 1: plot
Assignment 1
Due: Sept 16 at 2 pm
Solution 1
Linear systems: direct and iterative methods
Example 2.3

Nonlinear systems of equations: Newton's method Notes_1.3.pdf
Assignment 2
Due: Sept 23 at 2 pm
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: Oct. 7 at 2 pm
3. Interpolation & Approximation
(3 hours)
Polynomial interpolation (Lagrange formula) Notes_Polyn_Interp.pdf
Cubic splines Notes_Cubic_Spln.pdf
Assignment 4
Due: Oct 14 at 2 pm
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

Due: Oct 21 at 2 pm

Roundoff errors in finite differencing Notes_Roundoff.pdf
Newton-Cotes and Romberg's methods Notes_NumIntg.pdf
Gaussian quadrature Notes_G_Quad.pdf
Assignment 6
Due: Oct 28 at 2 pm
Multiple integrals
5. Ordinary Differential Equations
(6 hours)
Linear 1st order ODE's
IVP.'s: Euler's method, Runge-Kutta, Predictor-Corrector

BVP's: shooting and finite-difference methods
Assignment 7
Due: Nov 4 at 2 pm
Parameter estimation for ODE models
Exercise 7a

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

Fortran code
Hyperbolic equations Hyperb_PDE_Notes.pdf
  Example on wave propagation
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)