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Module Specifications

Archived Version 2013 - 2014

Module Title
Module Code

Online Module Resources

NFQ level 8 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

This module provides second year Engineering students with the techniques and skills that they need to solve problems involving multivariate calculus and second order ordinary equations with cosntants coefficients.

Learning Outcomes

1. differentiate and integrate standard functions of several variables
2. define and calculate selected quantities in vector calculus
3. formulate and solve engineering optimization problems
4. solve second order ordinary differentail equations with constant coefficients

Workload Full-time hours per semester
Type Hours Description
Lecture36No Description
Tutorial12No Description
Independent Study77No Description
Total Workload: 125

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Indicative syllabus
Mathematical optimization, Lagrange multipliers. Review of vectors; vector algebra, dot and cross products; lines and planes in space; Cartesian and other coordinate systems; Review of matrix algebra, eigenvectors, determinants; 2-D linear transformations and complex numbers; Review of (basic) abstract linear abgebra, vector spaces, subspaces, basis, dimension, etc; 2. Introduction to multi-variate and vector-valued functions; complex functions; vector fields; 3. Vector-valued functions and space-curves, arc-length, velocity & tangent vectors, acceleration, curvature; 4. Differentiation in multi-dimensions, linear approximation of multi-variate functions, max/min problems chain rule, directional derivatives, gradient vector field, Taylor; 5. Double and triple integrals, areas, moments and centre of mass; substitutions in multiple integrals; 6. 2-D Vector Analysis: div and curl of vector fields, line integrals, work, circulation and flux, Green; 7. Vector Analysis in 3-D, surface integrals, divergence and Stokes' theorems; 8. Boundary-value PDE problems and their solution, including the method of separation of variables.

Assessment Breakdown
Continuous Assessment% Examination Weight%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Reassessment Requirement
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
Indicative Reading List

  • Croft, Davidson and Hargreaves: 0, Engineering Mathematics,
Other Resources

Programme or List of Programmes