Module manager: Professor A.P. Fordy
Email: allan@maths.leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2009/10
MATH1050 and MATH1055 or equivalent.
| MATH1382 | Fundamentals of Particle Dynamics |
| MATH1400 | Modelling with Differential Equations |
This module is approved as an Elective
The study of what causes objects to move, and how they move (or stand still !) is the subject of this module. The natural language to describe such motions is that of ordinary differential equations, and the module starts with a discussion of the classification and methods of solutions of such equations. The laws describing the motion of objects are developed: the same laws apply whether the motion is that of a motor car, a parachute jumper, or a spacecraft. Mathematical models for each of these examples are considered, together with several others, use being made of the vector geometry studied in module MATH1055.
To introduce the basic concepts of single particle mechanics and to develop the relevant theory of differential equations.
On completion of this module, students should be able to:
(a) solve first order differential equations of various types such as separable, homogenous, linear, and to apply initial conditions to the general solution;
(b) formulate the equations of motion for particles in one and two dimensions and solve these equations of motion in simple cases;
(c) solve second order linear differential equations with constant coefficients by finding complementary functions and particular integrals;
(d) obtain the energy equation for one dimensional particle motion under the action of a conservative force.
Introduction to the theory of differential equations. Introduction ot mechanics: modelling one and two-dimensional motion using ODEs.
1. Classification of ODEs; methods of solution of 1st order ODEs (separable, homogenous and linear).
2. Introduction to mechanics: Newton's laws, forces, gravitation and weight.
3. One dimensional motion: including constant gravity, air resistance etc.
4. Solution of second order ODEs (linear with constant coefficients): Oscillation of a spring / mass system; SHM, damped and forced oscillations, beats and resonance.
5. Energy methods: KE and work done, conservative forces and PE.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Workshop | 5 | 1 | 5 |
| Lecture | 22 | 1 | 22 |
| Tutorial | 5 | 1 | 5 |
| Private study hours | 67 | ||
| Total Contact hours | 32 | ||
| Total hours (100hr per 10 credits) | 99 | ||
Regular example sheets and in-class quizzes.
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 20 |
| Total percentage (Assessment Coursework) | 20 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 0 Mins | 80 |
| Total percentage (Assessment Exams) | 80 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 7/16/2010
Errors, omissions, failed links etc should be notified to the Catalogue Team