Queen's School of Computing

CISC-271* Scientific Computing

Most Recent Author: Randy Ellis
Last Revised: September 2015

Calendar Description

Introduction to scientific computing: algorithm design, error analysis, ill-conditioning. Linear equations. Least-squares fitting. Non-linear equations. Effective use of library programs, with discussion of their limitations and some aspects of their design and implementation.

Prerequisites: CISC 101/3.0 or CISC-121/3.0; (MATH-112/3.0 or MATH 111/6.0 or MATH-110/6.0) and MATH 121/6.0 or equivalents.

Exclusions: MATH 272/3.0, PHYS 313/3.0.
Learning Hours 120 (36L;84P)


Mathematical problems arise is all fields of science and engineering. Often a continuous mathematical model is difficult or impossible to solve analytically and numerical methods must be used to obtain approximate solutions. Numerous software libraries and applications have been developed to relieve the practitioner from the subtle complexities that arise in the implementation of these numerical solutions. This course introduces common numerical algorithms, how they work, their shortcomings, and how to use them effectively. MATLAB, a widely used mathematical software package, provides students with a platform to experiment with the use of state-of-the-art numerical routines. It is is also used as a programming environment for implementing some of the algorithms studied.

This course is required in BMCO.

Introduction to MATLAB, Representations of floating-point numbers, Taylor series approximations, representational error sources.

Bisection method, Newton's method, secant method; properties of these methods.

Linear Systems:
Gaussian elimination, pivoting, error analysis, important matrix decompositions, eigenvalues, principal-component analysis.

Polynomials, piecewise polynomials, cubic splines.

Functional approximation:
Least-squares approximations, error analysis.

Newton-Cotes integration, Gaussian quadrature, adaptive integration, error analysis.
Recent Textbooks
  • G. Recktenwald, Numerical Methods with MATLAB, Prentice Hall, 2000.

  • C. B. Moler, Numerical Computing with MATLAB, SIAM, 2004.

  • S. C. Chapra, Applied Numerical Methods with MATLAB, McGraw-Hill, 2006.

  • E. Twizell: Numerical Methods with Applications in the Biomedical Sciences, Prentice-Hall, 1988.

  • J. Easterby, Numerical Methods, with Applications in the Biomedical Sciences, Bioinformatics.1989; 5: 77.

  • S. Dunn, A. Constantinides, and P. Moghe: Numerical methods in Biomedical Engineering, Elsevier Academic Press, 2005.