Short Title:  Mathematics 4 

Full Title:  Mathematics 4 

Field of Study:  Mechanics and metal work 

Reviewed By:  FIONA CRANLEY 

Module Author:  ANTHONY TANSEY 

Module Description:  The first aim of Mathematics 4 is to further develop the broad range of standard
mathematical techniques in linear algebra, analysis and calculus assimilated in
Mathematics 2. The second aim is to enable the student to apply these
mathematical techniques to the solution of bounded engineering problems. 

Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Find partial derivatives of functions of several variables. 
LO2 
Use partial derivatives to find the gradient of a scalar field and the divergence and curl of a vector field. [POa, POb, POd, POg] 
LO3 
Obtain definite and indefinite integrals of functions using standard integration
methods. [POa, POb] 
LO4 
Apply integration methods to solving engineering problems. [POa, POb,POd] 
LO5 
Obtain eigenvalues and eigenvectors of 2 × 2 and simple 3 × 3 matrices.
[POa, POb, POd] 
LO6 
Solve nonlinear equations using appropriate techniques and software and to
understand their limitations. [POa, POb, POd] 
Prerequisite learning 

Corequisite Modules
 2234  MATH H1018  Mathematics 1  2750  MATH H1019  Mathematics 2 
Module Content & Assessment
Content (The percentage workload breakdown is inidcative and subject to change) 
% 
Introduction to functions of several variables: (6 hrs) Evaluation of functions of several variables. Plotting. Partial differentiation. Vector fields. Divergence and curl of a vector Field.

12.00% 
Vector Calculus Scalar fields, vector fields. Calculate the gradient of a scalar field and the divergence and curl of a vector field.

19.00% 
Integration: (13 hrs) Integration methods: Definite and Indefinite Using substitution. Further Substitutions. Integration by Parts. Improper Integrals. Partial fractions

25.00% 
Applications (9 hrs) Applications of integration: Solving practical problems using integration.

17.00% 
Eigenvalues and Eigenvectors: (6 hrs) Eigenvectors and Eigenvalues

12.00% 
Solution of Non Linear Equations: (8 hrs) Graphical exploration to locate approximate roots. Iterative point estimation and interval reduction methods. Convergence of iterative methods. Use of appropriate software to solve nonlinear equations.

15.00% 
Assessment Breakdown  % 
Course Work  30.00% 
End of Module Formal Examination  70.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Other 
Assignment in the visualization of functions in 3D using appropriate software and the use symbolic of mathematics software. (Using for example MATLAB). 

10.00 
Week 4 
Other 
High threshold test in methods and application of integral calculus and sequences and series. 

10.00 
Week 7 
Other 
Assignment in the application of point estimation and interval reduction methods to the solution of nonlinear equations. (Using for example Excel/MATLAB). 

10.00 
Week 10 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 

70.00 
EndofSemester 
IT Tallaght 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 
No Description 
3.00 
Every Week 
3.00 
Lab 
Computer packages, problem solving 
1.00 
Every Week 
1.00 
Independent Learning 
No Description 
4.00 
Every Week 
4.00 
Total Weekly Learner Workload 
8.00 
Total Weekly Contact Hours 
4.00 
Workload: Part Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
No Description 
2.00 
Every Week 
2.00 
Lab 
Computer packages, problem solving 
5.00 
Week 13 
0.38 
Independent Learning Time 
No Description 
6.00 
Every Week 
6.00 
Total Weekly Learner Workload 
8.38 
Total Weekly Contact Hours 
2.38 
Module ResourcesRequired Book Resources 

 Glyn James... [et al.] 2001, Modern engineering mathematics, Prentice Hall [ISBN: ISBN: 0130183199]
 Recommended Book Resources 

 Howard Anton, Chris Rorres 2000, Elementary linear algebra, Wiley New York [ISBN: ISBN: 0471170526]
 H Anton 2002, Contemporary Linear Algebra MATLAB Technology Resource Manual, John Wiley and Sons
 K. A. Stroud; with additions by Dexter J. Booth 2001, Engineering mathematics, Palgrave Basingstoke [ISBN: ISBN: 0333919394]
 Anthony Croft, Robert Davison, Martin Hargreaves 2000, Engineering mathematics, A Foundation for Electronic, Electrical, Communications and Systems Engineers, Prentice Hall [ISBN: ISBN 0130268585]
 This module does not have any article/paper resources 

This module does not have any other resources 

Module Delivered in
