Registry
Module Specifications
Archived Version 2012  2013
 
Description 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  
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; 2D linear transformations and complex numbers; Review of (basic) abstract linear abgebra, vector spaces, subspaces, basis, dimension, etc; 2. Introduction to multivariate and vectorvalued functions; complex functions; vector fields; 3. Vectorvalued functions and spacecurves, arclength, velocity & tangent vectors, acceleration, curvature; 4. Differentiation in multidimensions, linear approximation of multivariate 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. 2D Vector Analysis: div and curl of vector fields, line integrals, work, circulation and flux, Green; 7. Vector Analysis in 3D, surface integrals, divergence and Stokes' theorems; 8. Boundaryvalue PDE problems and their solution, including the method of separation of variables.  
 
Indicative Reading List
 
Other Resources None  
Programme or List of Programmes  
Archives: 
