Description
Mathematical Methods
| Module title | Mathematical Methods |
|---|---|
| Module code | INT1202 |
| Academic year | 2018/9 |
| Credits | 30 |
| Module staff |
| Duration: Term | 1 | 2 | 3 |
|---|---|---|---|
| Duration: Weeks | 11 | 11 |
| Number students taking module (anticipated) | 20 |
|---|
Description - summary of the module content
Module description
This module will introduce you to key mathematical tools and techniques essential to your further studies. This will include differential and integral calculus, computing limits and convergence of sequences and series, real and complex geometry and the fundamentals of vectors and matrix algebra.
Module aims - intentions of the module
This module aims to develop your skills and techniques in calculus, geometry and algebra. It is primarily focused on developing methods and skills for accurate manipulation of the mathematical objects that form the basis of much of an undergraduate course in mathematics. Whilst the main emphasis of the module will be on practical methods and problem solving, all results will be stated formally and each sub-topic will be reviewed from a mathematically rigorous standpoint. The techniques developed in this course will be essential to much of your undergraduate degree programme, particularly the second-year streams of Analysis, Differential Equations & Vector Calculus, and Mathematical Modelling. This module is equivalent to MTH1002 and students will join MTH1002 for lectures.
Intended Learning Outcomes (ILOs)
ILO: Module-specific skills
On successfully completing the module you will be able to...
- 1. Explain how techniques in differential and integral calculus are underpinned by formal rigour
- 2. Apply techniques in geometry and algebra to explore three dimensional analytic geometry
- 3. Perform accurate manipulations in algebra and calculus of several variables using a variety of standard techniques
- 4. Solve some specific classes of ordinary differential equations
ILO: Discipline-specific skills
On successfully completing the module you will be able to...
- 5. Demonstrate a basic knowledge of functions, sequences, series, limits and differential and integral calculus necessary for progression to successful further studies in the mathematical sciences
ILO: Personal and key skills
On successfully completing the module you will be able to...
- 6. Reason using abstract ideas, and formulate and solve problems and communicate reasoning and solutions effectively in writing
- 7. Use learning resources appropriately
- 8. Exhibit self-management and time-management skills
Syllabus plan
Syllabus plan
Geometry: lines; planes; conic sections.
Functions: single- and multivariate; limits; continuity; intermediate value theorem.
Sequences: algebra of limits; L'Hopital's rule.
Series: convergence/divergence tests; power series.
Differential calculus: simple and partial derivatives; Leibniz' rule; chain rule; Taylor approximation; implicit differentiation; minima and maxima.
Integral calculus: substitution; integration by parts; multiple integrals; applications.
Differential equations: linear and separable ordinary DEs; basic partial DEs.
Vectors, matrices: Gaussian elimination; transformations; eigenvalues/eigenvectors.
Learning and teaching
Learning activities and teaching methods (given in hours of study time)
| Scheduled Learning and Teaching Activities | Guided independent study | Placement / study abroad |
|---|---|---|
| 106 | 194 |
Details of learning activities and teaching methods
| Category | Hours of study time | Description |
|---|---|---|
| Scheduled Learning & Teaching activities | 66 | Lectures |
| Scheduled learning and teaching activities | 40 | Small group lessons |
| Guided independent study | 194 | Lecture and assessment preparation, wider reading, completing exercises. |
Assessment
Formative assessment
| Form of assessment | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
|---|---|---|---|
| Exercise sheets | 10x10 Hours | All ILOs | Annotated scripts with oral feedback from tutor |
Summative assessment (% of credit)
| Coursework | Written exams | Practical exams |
|---|---|---|
| 0 | 100 | 0 |
Details of summative assessment
| Form of assessment | % of credit | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
|---|---|---|---|---|
| Written exam - Closed book (Jan) | 30 | 2 hours | All ILOs | Via SRS |
| Written exam - Closed book (May) | 70 | 2 Hours | All ILOs | Via SRS |
Re-assessment
Details of re-assessment (where required by referral or deferral)
| Original form of assessment | Form of re-assessment | ILOs re-assessed | Timescale for re-assessment |
|---|---|---|---|
| As above | Written examination (100%) | All | During next examination period |
Re-assessment notes
Referred and deferred assessment will normally be by examination. The module mark is calculated solely from the mark on the referred/deferred exam. For referred candidates, this mark is capped at 40%.
Resources
Indicative learning resources - Basic reading
Core Text:
|
Author |
Title |
Edition |
Publisher |
Year |
ISBN |
|
Thomas, G, Weir, M, Hass, J |
Thomas' Calculus |
13th |
Pearson |
2016 |
978-1292089799 |
Additional RecommendedReading for this module:
|
Author |
Title |
Edition |
Publisher |
Year |
ISBN |
|
Tan, Soo T |
Calculus |
International edition |
Brooks/Cole Cengage Learning |
2010 |
978-0495832294 |
|
Tan, T Soo |
Calculus Early Transcendentals |
International edition |
Brooks Cole/Cengage learning |
2010 |
978-1439045992 |
|
Extended Reading: |
|
|
|
|
|
|
Stewart J. |
Calculus |
5th |
Brooks/Cole |
2003 |
000-0-534-27408-0 |
|
McGregor C., Nimmo J. & Stothers W. |
Fundamentals of University Mathematics |
2nd |
Horwood, Chichester |
2000 |
000-1-898-56310-1 |
Indicative learning resources - Web based and electronic resources
Module has an active ELE page
| Credit value | 30 |
|---|---|
| Module ECTS | 15 |
| NQF level (module) | 4 |
| Available as distance learning? | No |
| Origin date | 14/08/2017 |