# Mathematics

## MTH1002 - Mathematical Methods (2018)

MODULE TITLE CREDIT VALUE Mathematical Methods 30 MTH1002 Dr Pascal Philipp (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 11 0
 Number of Students Taking Module (anticipated) 325
DESCRIPTION - summary of the module content

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, geometry and the fundamentals of vectors and matrix algebra.

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.

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 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 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

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 0 100
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam - Closed book (Jan) 30 2 hours All Via SRS
Written exam - Closed book (May) 70 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
All above Written exam (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

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