This module builds on the learner's previous knowledge and understanding of differential and integral calculus. New techniques and applications of differentiation are included. The learner is also introduced to the theory and applications of vectors and matrices.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1
Differentiate parametrically, implicitly, partially and solve related rates of change problems.
LO2
Apply vector algebra methods to problems involving forces and moments of forces.
LO3
Integrate by parts and by inverse trigonometric substitution; and apply integration methods to various applied problems.
LO4
Solve and analyse simultaneous equations using matrix algebra methods.
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).
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
Co-requisites
No Co Requisites listed
Module Content & Assessment
Indicative Content
Differentiation
Related rates of change. Differentiation of implicit functions and parametric functions. Partial differentiation.
Vector Algebra
Magnitude and direction. Component form in two and three dimensions. Addition and subtraction of vectors: triangle and parallelogram laws. Scalar product, vector product. Application to resolution of forces, work done, moments.
Integration
Techniques of integration including integration by parts and inverse trigonometric substitution. Applications of definite integrals: work done by variable force, expanding gas; centroid of a plane area; volume, mass and centre of gravity of solid of revolution.
Matrix Algebra
Definitions and notation. Addition, subtraction, multiplication of matrices. Determinants. Matrix inversion. Application to the solution of simultaneous linear equations. Cramer's rule. The singular case, inconsistent equations.
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
Short Answer Questions
Written Assessment - Differentiation
1
15.0
Week 4
Short Answer Questions
Written Assessment - Vectors
2
15.0
Week 8
End of Module Formal Examination
Assessment Type
Assessment Description
Outcome addressed
% of total
Assessment Date
Formal Exam
End-of-Semester Final Examination
1,2,3,4
70.0
End-of-Semester
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
Theory
3.0
Every Week
3.00
Tutorial
Problem Solving
1.0
Every Week
1.00
Independent & Directed Learning (Non-contact)
Review of lecture material
1.0
Every Week
1.00
Independent & Directed Learning (Non-contact)
Completion of exercise sheets
2.0
Every Week
2.00
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
Lecture
Theory
2.5
Every Week
2.50
Tutorial
Problem Solving
1.0
Every Second Week
0.50
Independent & Directed Learning (Non-contact)
Review of lecture material
2.0
Every Week
2.00
Independent & Directed Learning (Non-contact)
Completion of exercise sheets
2.0
Every Week
2.00
Total Hours
7.50
Total Weekly Learner Workload
7.00
Total Weekly Contact Hours
3.00
Module Resources
Recommended Book Resources
John Bird 2010, Higher Engineering Mathematics [ISBN: 978-1856177672]