Mathematics

MTH1002 - Mathematical Methods (2019)

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MODULE TITLEMathematical Methods CREDIT VALUE30
MODULE CODEMTH1002 MODULE CONVENERDr Layal Hakim (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 11 0
Number of Students Taking Module (anticipated) 180
DESCRIPTION - summary of the module content

During your mathematics degree, you will be solving problems and proving theories in several branches of mathematics such as in pure mathematics, in applications to science and engineering, and in statistics. Inevitably you need to be able to calculate. That is what gives the mathematics its great power. This module covers developed bodies of useful techniques as a toolkit of common knowledge. It brings emphasis on the techniques rather than the applications of the techniques. Such techniques will enable you to deepen your familiarity with, and generalise, methods that you have seen at school level mathematics. This module will study topics that include the geometry of conic sections, properties of functions such as continuity and differentiability, differential and integral calculus, limits and convergence of sequences and series including Power Series and Taylor Series. The module also develops the fundamentals of vector and matrix theory, multivariate calculus, and the classification of various types of differential equations as well as analytical methods for solving them. The material in this module provide intuition for, and examples of, many of the mathematical structures that will be discussed in the module MTH1001 Mathematical Structures, and supply a firm understanding of methods required in future modules in the mathematics degree.

 

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 for much of your undergraduate degree programme, particularly the second-year streams of Analysis, Differential Equations & Vector Calculus, and Mathematical Modelling.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

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;

Discipline Specific Skills and Knowledge:

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;

Personal and Key Transferable/ Employment Skills and Knowledge:

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 - summary of the structure and academic content of the module

- 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 & Teaching Activities 76.00 Guided Independent Study 224.00 Placement / Study Abroad
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled Learning and Teaching Activities 66 Lectures
Scheduled Learning and Teaching Activities 10 Tutorials
Guided Independent Study 224 Lecture and assessment preparation, wider reading, completing exercises

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Exercise sheets 10 x 10 hours All Annotated scripts with oral feedback from tutor
Mid-Term Tests 2 x 1 hour All Feedback on marked sheets, class feedback

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 0 Written Exams 100 Practical Exams
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written Exam A - Closed book (Jan) 50 2 hours All Via SRS
Written Exam B - Closed book (May) 50 2 hours All Via SRS

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
Written Exam A - Closed Book Written exam (50%, 2hr) All August Ref/Def Period
Written Exam B - Closed Book Written Exam B (50%, 2hr) All August Ref/Def Period

 

RE-ASSESSMENT NOTES

In the case of module referral, the higher of the original assessment and the reassessment will be recorded for each component mark. In the case of module referral, the final mark for the module reassessment will be capped at 40%..

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Basic reading: Any A-Level on mathematics and further mathematics

ELE: http://vle.exeter.ac.uk

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Finney, R.L., Maurice, D., Weir, M. and Giordano, F.R. Thomas' Calculus based on the original work by George B. Thomas, Jr. 10th or later Addison-Wesley 2003 000-0-321-11636-4 [Library]
Set Stewart, J. Calculus 5th Brooks/Cole 2003 000-0-534-27408-0 [Library]
Set McGregor, C., Nimmo, J. & Stothers, W. Fundamentals of University Mathematics 2nd Horwood, Chichester 2000 000-1-898-56310-1 [Library]
Set Tan, Soo T. Calculus International edition Brooks/Cole Cengage Learning 2010 978-0495832294 [Library]
Set Tan, Soo T. Calculus: Early Transcendentals International edition Brooks Cole/Cengage Learning 2010 978-1439045992 [Library]
CREDIT VALUE 30 ECTS VALUE 15
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) 4 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Tuesday 10 July 2018 LAST REVISION DATE Thursday 14 November 2019
KEY WORDS SEARCH Calculus; geometry; conic sections; functions; continuity; sequences; limits; series; convergence; divergence; differentiation; integration; differential equations; vectors; matrices; Gaussian elimination; eigenvalues; eigenvectors