Study information

# Mathematical Methods - 2024 entry

MODULE TITLE CREDIT VALUE Mathematical Methods 30 MTH1002 Prof Layal Hakim (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 11 0
 Number of Students Taking Module (anticipated) 200
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. In particular, it develops methods that underpin the modules MTH2003 Differential Equations and MTH2004 Vector Calculus and Applications.

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;

-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 AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 76 224
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 Studying additional recordings complementing lectures and reading material, examples sheets and revision

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
Online quizzes 10 x 30 minutes All Via online tool Numbas

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 0 100 0
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) 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

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 (45%, 2hr) All August Ref/Def Period
Written Exam B - Closed Book Written Exam B (45%, 2hr) All August Ref/Def Period
Mid-Term Test 1 &/or 2  Mid-Term Test (5% and/or  5%) All August Ref/Def Period

RE-ASSESSMENT NOTES

Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only.  For deferred candidates, the module mark will be uncapped.

Referrals: Reassessment will be by a written exam (worth 50% of the module mark) for each term where the mark for the term is less than 40%. As it is a referral, the module mark 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