# Mathematics

## ECM1708 - Dynamics (2015)

MODULE TITLE CREDIT VALUE Dynamics 15 ECM1708 Prof John Thuburn (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 weeks 0
 Number of Students Taking Module (anticipated) 189
DESCRIPTION - summary of the module content

This module teaches you how to use the mathematical theories of calculus and vectors and matrices to model and understand real physical systems. It starts with projectiles and energy equations to tie in with the A level material, and then moves onto more complicated problems such as motion of a particle in a potential landscape, damped and driven oscillators, coupled oscillators, and  nonlinear dynamics of interacting species (predator-prey models).

Prerequisite module: ECM1705 or equivalent

Corequisite module:ECM1701

AIMS - intentions of the module

The module aims to introduce you to Newtonian dynamics and its applications; to show you the use of calculus and vectors in the modelling of physical systems; to introduce you to applied mathematics as a tool for investigating natural phenomena. As examples, you will explore the consequences of physical laws, as well as the behaviour of physical systems from projectiles and rockets to planetary motion.

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 demonstrate understanding of basic classical mechanics, and of the modelling of simple mechanical and dynamical systems.
Discipline Specific Skills and Knowledge:
2 understand the physical world, how it may be modelled, and how mathematical machinery such as vectors and calculus may be used to analyse these models.
Personal and Key Transferable/ Employment Skills and  Knowledge:
3 reason about physical systems using abstract ideas and models and communicate reasoning effectively in writing;
4 use learning resources appropriately;
5 show self management and time management skills.

SYLLABUS PLAN - summary of the structure and academic content of the module

- basic concepts: modelling; point particles, space, time, velocity, acceleration; Newton's laws;

- projectiles: gravity; trajectories; envelope of trajectories;

- simple harmonic motion: elasticity, Hooke's law; strings and springs; equilibria and oscillations;

- energy: kinetic energy and gravitational potential energy; elastic potential energy; motion under general potentials, equilibria, stability and small oscillations;

- oscillations: damping, forcing and resonance; coupled oscillations; normal coordinates;

- nonlinear systems: first order systems; phase plane; classification of equilibria in linear systems; linearisation about equilibria in nonlinear systems; examples of predator-prey models;

- planetary motion: motion in plane polar coordinates; velocity and acceleration; central forces and angular momentum.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 49 101 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 33 Lectures Scheduled learning and teaching activities 5 Seminar class Scheduled learning and teaching activities 11 Tutorials Guided independent study 101 Guided independent study

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
Three exercises 30 hours 1-5 Seminar classes and tutorials

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 20 80
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 80 2 hours 1-3,5 In line with CEMPS policy
Coursework – problem sheets 20 30 hours 1-5 Seminar classes and tutorials

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

ELE – http://vle.exeter.ac.uk