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MATH7015 - Numerical Methods 1

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Title:Numerical Methods 1
Long Title:Numerical Methods 1
Module Code:MATH7015
 
Duration:1 Semester
Credits: 5
NFQ Level:Intermediate
Field of Study: Mathematics
Valid From: Semester 1 - 2016/17 ( September 2016 )
Module Delivered in 4 programme(s)
Module Coordinator: David Goulding
Module Author: AINE NI SHE
Module Description: This is a first course in numerical techniques, introducing the student to problem solving and algorithms.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Use numerical techniques to solve non-linear equations.
LO2 Quantify numerical errors and ensure numerical methods are convergent and stable.
LO3 Apply both direct and iterative methods in the solution of physical problems.
LO4 Analyse and use numerical algorithms for both integration and differentiation.
LO5 Derive and apply numerical algorithms for interpolation.
Pre-requisite learning
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list.
No incompatible modules listed
Co-requisite Modules
No Co-requisite modules listed
Requirements

This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.

No requirements listed
 

Module Content & Assessment

Indicative Content
Number Systems and Errors
Representation of real numbers. Floating point arithmetic. Basic concepts of numerical errors: absolute, relative, inherent, truncation, roundoff. Error propagation.
Solution of Non-Linear Equations
Iterative methods. Regula-Falsi, Bisection, Secant method, Newton-Raphson. Fixed Point Iteration including: Zeroes (real or complex) of polynomial equations. Synthetic division.
Systems of equations
Elimination methods; Gaussian elimination, pivoting, strategies, ill-conditioned systems. Tridiagonal systems. Iterative methods, Guass-Seidel, Gauss-Jacobi, relaxation methods.
Approximation
Discrete Least square approximation. Orthogonal Polynomials & Least Squares Approximation.
Interpolation
Polynomial forms. Interpolation polynomial. Lagrange form, Newton form (divided difference tables), Newton Gregory forms (difference tables). Piecewise polynomials. Splines.
Numerical Integration & Differentiation
Newton-Cotes formulae. Mid-point, trapezoidal, Simpson’s, Romberg Integration. Gaussian quadrature. Difference operators. Numerical differentiation.
Assessment Breakdown%
Course Work100.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Practical/Skills Evaluation Based on weekly 2-hour Laboratory sessions 1,4 25.0 Week 6
Short Answer Questions Written assessment 1,4 25.0 Week 7
Practical/Skills Evaluation Based on weekly 2-hour Laboratory sessions 2,3,5 25.0 Week 11
Short Answer Questions Written assessment 2,3,5 25.0 Week 12
No End of Module Formal Examination
Reassessment Requirement
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.

The institute reserves the right to alter the nature and timings of assessment

 

Module Workload

Workload: Full Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture Lecture 2.0 Every Week 2.00
Lab Computer laboratory 2.0 Every Week 2.00
Independent & Directed Learning (Non-contact) Independent study 3.0 Every Week 3.00
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Independent & Directed Learning (Non-contact) Independent study 3.0 Every Week 3.00
Lecture Lecture 2.0 Every Week 2.00
Lab Computer laboratory 2.0 Every Week 2.00
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
 

Module Resources

Recommended Book Resources
  • S.C.Chapra 2014, Numerical Methods for Engineers, 7th Ed., McGraw-Hill [ISBN: 978-007339792]
  • S.C. Chapra 2012, Applied Numerical Methods with MATLAB for Engineers and Scientists, 3rd Ed., TMH [ISBN: 978-125902743]
This module does not have any article/paper resources
This module does not have any other resources
 

Module Delivered in

Programme Code Programme Semester Delivery
CR_EMECH_8 Bachelor of Engineering (Honours) in Mechanical Engineering 3 Mandatory
CR_CSTRU_8 Bachelor of Engineering (Honours) in Structural Engineering 3 Elective
CR_CCEEE_9 Master of Engineering in Civil Engineering (Environment and Energy) 3 Elective
CR_CSTEN_9 Master of Engineering in Structural Engineering 3 Elective

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