CHBE 230: Computational Methods (Spring 2014)

Instructor Information
Instructor: James J. Feng
Email: jfeng(at)chbe(dot)ubc(dot)ca
Offices: CHBE 209 (Phone 822-8875); MATX 1206 (Phone 822-4936)
Office Hours: by appointment (please e-mail)
Teaching Assistants
Amirhossein Mafi (amafi@chbe etc) and Tenghu Wu (tenghuwu@chbe etc), our graduate TA's, will lead the Wednesday afternoon tutorials, mark your assignments and quizzes, and hold office hours.

TA office hour: every Friday, 4-5 pm, in CHBE 316 (smaller computer room).
Lectures
Mon Wed Fri, 9 - 10 am, Location: CHBE 102
Tutorials: Wed 2 - 4 pm, Location: CHBE 314 + 316

Manhattan: Throughout the term, I will communicate with you through the course's Manhatten website. You will also receive and submit your assignments through this site. I will send you your individual log-in by email.
Textbook
S. E. Chapra: Applied Numerical Methods With MATLAB for Scientists and Engineers.
(3rd edn.) ISBN-10: 0073401102; ISBN-13: 978-0073401102, McGraw-Hill (2011).

MATLAB will be required for our course. The software package is available on all CHBE machines in the computer labs (CHBE 314 and 316). You may also download the freely-distributed Octave, which works essentially as MATLAB. Finally, you could also purchase the MATLAB software or ask our CHBE IT help (help@chbe etc) to install a client on your laptop.
Exams and grading formula

Final Grade = final exam (50%) + midterm (30%) + tutorial & quizzes (10%) + homework (10%)
  • Midterm: Feb 14, 9-10 am in CHBE 102.
  • Final: date and time to be announced, to be written in Computer Rooms.
Policies:
  • Missing a quiz or the midterm results in a score of 0, except with prior consent of the instructor or with a doctor's note. In these latter cases, you will receive no score from the missed quiz or midterm, and its weight will be shifted to the other quizzes or the final exam. If you have a legitimate reason for missing the midterm, for example, your final exam will count for 80% of the grade.
  • Weekly assignments will be posted on the course website on Manhattan. Due dates will be announced later. Late homework will receive no point.
Course Outline
Topics Textbook
Chapters
Approx.
Hours
Content
Description
Introduction to MATLAB and programming
Chapters 2, 3 1 See textbook
Introduction to computation
Chapters 1, 4 3
Engineering examples
Numerical methods
Pseudo-codes
Roundoff and truncation errors
Root finding and optimization
Chapters 5 - 7
4
Incremental search
Bisection
Interpolation
Newton-Raphson
Secant Method
1D optimization: golden-section search
Solution of linear systems
Chapters 8 - 12 7
Direct vs. iterative methods
Gauss elimination, with pivoting
Tridiagonal system - 1D heat equation
LU decomposition
Matrix inverse
Gauss-Seidel iteration
Newton-Raphson for nonlinear systems
Curve fitting
Chapters 14, 15
4
Linear regression
Polynomial regression
Multiple linear regression
Introduction to nonlinear regression
Interpolation
Chapters 17, 18
3
Linear interpolation
Lagrange polynomial
Cubic spline
Numerical Integration & differentiation
Chapters 19 - 21
6
Trapezoidal rule
Simpson's rules
Multiple Integrals
Richardson extrapolation
Romberg Integration
Numerical differentiation: high-order formulas
Differentiation with Richardson extrapolation
Ordinary differential equations Chapters 22, 24
9
Initial value problems
Euler's method
Runge-Kutta methods
Systems of ODE's
Boundary value problems
The shooting method
Finite difference method
Total hours

37