Mathematical Methods

Module title	Mathematical Methods
Module code	INT1202
Academic year	2023/4
Credits	30
Module staff

Duration: Term	1	2	3
Duration: Weeks	11	11

Number students taking module (anticipated)	20

Module description

During your mathematics degree, you will be solving problems and proving theories in several branches of mathematics. Inevitably you need to be able to calculate. That is what gives the mathematics its great power. This module brings emphasis on the techniques rather than the applications of the techniques. You 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. In particular, it develops methods that underpin the second year modules MTH2003 Differential Equations and MTH2004 Vector Calculus and Applications.

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

Geometry: lines; planes; conic sections.

Functions: single- and multivariate; limits; continuity; intermediate value theorem.

Complex numbers

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 activities and teaching methods (given in hours of study time)

Scheduled Learning and Teaching Activities	Guided independent study	Placement / study abroad
120	180

Details of learning activities and teaching methods

Category	Hours of study time	Description
Scheduled Learning & Teaching activities	66	Lectures
Scheduled learning and teaching activities	44	Small group lessons
Scheduled learning and teaching activities	10	Tutorials
Guided Independent Learning	180	Lecture and assessment preparation, wider reading, completing exercises

Formative assessment

Form of assessment	Size of the assessment (eg length / duration)	ILOs assessed	Feedback method
Exercise sheets	10 x 10 Hours	All	Annotated scripts with oral feedback from tutor
Online Quizzes	10 x 30 minutes	All	Via online tool Numbas

Summative assessment (% of credit)

Coursework	Written exams	Practical exams
10	90

Details of summative assessment

Form of assessment	% of credit	Size of the assessment (eg length / duration)	ILOs assessed	Feedback method
Written Exam A - Closed book (Jan)	45	2 Hours	All	Via SRS
Written Exam B - Closed book (May)	45	2 Hours	All	Via SRS
Mid-term Test 1	5	40 Minutes	All	Via SRS
Mid-term Test 2	5	40 Minutes	All	Via SRS
	0
	0

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
Written exam closed book	Ref/Def exam	All	During next examination period
Mid-term test 1 &/or 2	Mid-term test	All	During next examination period

Re-assessment notes

Deferral– if you miss an assessment for reasons judged legitimate by the Mitigation Committee, the applicable assessment will normally be deferred. Reassessment will be by written exam and/or test in the deferred element only, and the mark will be uncapped. For candidates who defer refer one or both of the mid-term tests, the reassessment will be by a single mid-term test.

Referral– if you have failed the module overall (i.e. a final overall module mark of less than 40%) you will be required to take a referral exam. Only your performance in this exam will count towards your final module grade. A grade of 40% will be awarded if the examination is passed.

Indicative learning resources - Basic reading

Core Text:

Author	Title	Edition	Publisher	Year	ISBN
Thomas, G, Weir, M, Hass, J	Thomas' Calculus	14th	Pearson	2020	978-1292253220

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

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

Key words search

Calculus; geometry; sequences; series; limits; convergence; divergence; differentiation; integration; differential equations; conic sections; functions; continuity; vectors; matrices; Gaussian elimination; eigenvalues; eigenvectors.

Credit value	30
Module ECTS	15
Module pre-requisites	None
Module co-requisites	None
NQF level (module)	4
Available as distance learning?	No
Origin date	14/08/2017
Last revision date	19/06/2023