# Computational Science

University College Dublin

## Course Description

• ### Course Name

Computational Science

• ### Host University

University College Dublin

• ### Location

Dublin, Ireland

• ### Area of Study

Computer Science, Mathematics

• ### Language Level

Taught In English

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• ECTS Credits

5
• Recommended U.S. Semester Credits
2.5 - 3
• Recommended U.S. Quarter Units
3.75 - 4.5
• ### Overview

Typically, problems in Applied Mathematics are modelled using a set of equations that can be written down but
cannot be solved analytically. In this module we examine numerical methods that can be used to solve such
problems on a desktop computer. Practical computer lab sessions will cover the implementation of these methods
using mathematical software (Matlab). No previous knowledge of computing is assumed. Topics and techniques
discussed include but are not limited to the following list. [Computer architecture:] The Von Neumann model
of a computer, memory hierarchies, the compiler. [Floating-point representation:] Binary and decimal notation,
floating-point arithmetic, the IEEE double precision standard, rounding error. [Elementary programming
constructions:] Loops, logical statements, precedence, array operations, vectorization. [Root-finding for
single-variable functions:] Bracketing and Bisection, Newton?Raphson method. Error and reliability analyses
for the Newton?Raphson method. [Numerical integration:] Midpoint, Trapezoidal and methods.Error analysis.
[Solving ordinary differential equations (ODEs):] Euler Method, Runge?Kutta method. Stability and accuracy
for the Euler method. [Linear systems of equations:] Gaussian elimination, partial pivoting. The condition
number of a matrix: quantifying the idea that amatrix can be ?almost? singular, investigating the consequences
of this idea for the robustness of numerical solutions of linear systems. [Fitting data to polynomials using
the method of least squares.] [Random-number generation using the linear congruential method.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.

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