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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

Undergraduate Course: Dynamics and Vector Calculus (PHYS08043)

Course Outline
SchoolSchool of Physics and Astronomy CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) Credits20
Home subject areaUndergraduate (School of Physics and Astronomy) Other subject areaNone
Course website None Taught in Gaelic?No
Course descriptionThis course is designed for all pre-honours physics students. It covers ordinary differential equations and the techniques of vector calculus, which are used to describe concepts in physics. The course consists of lectures to present new material, and workshops to develop understanding, familiarity and fluency.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: ( Algebra and Calculus (PHYS08041) OR Linear Algebra and Several Variable Calculus (PHYS08042) OR Several Variable Calculus and Differential Equations (MATH08063)) AND ( Classical and Modern Physics (PHYS08044) OR Modern Physics (PHYS08045))
Co-requisites Students MUST also take: Physics of Fields and Matter (PHYS08046)
Prohibited Combinations Students MUST NOT also be taking Introductory Dynamics (PHYS08052)
Other requirements None
Additional Costs None
Information for Visiting Students
Displayed in Visiting Students Prospectus?No
Course Delivery Information
Delivery period: 2014/15 Semester 2, Available to all students (SV1) Learn enabled:  Yes Quota:  None
Web Timetable Web Timetable
Class Delivery Information Lectures in Weeks 1-10:
Dynamics M & Th 11-12 Vector Calculus Tu & F 11-12
Workshops in Weeks 2-11:
Dynamics M 14-16 & W 9-11 (choose one)
Vector Calculus Tu & Th 14-16 (choose one)
Course Start Date 12/01/2015
Breakdown of Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 44, Seminar/Tutorial Hours 40, Summative Assessment Hours 3, Revision Session Hours 4, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 105 )
Additional Notes
Breakdown of Assessment Methods (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)3:00
Resit Exam Diet (August)3:00
Summary of Intended Learning Outcomes
On completion of this course it is intended that student will be able to:
- Explain how aspects of the physical world are appropriately modelled in terms of ordinary differential equations and scalar and vector fields.
- Apply standard methods for solving ordinary differential equations and vector calculus to physics problems.
- Present a solution to physics and mathematics problems in a clear and logical written form.
- Assess whether a solution to a given problem is physically and mathematically reasonable
- Locate and use additional sources of information (to include discussion with peers where appropriate) to facilitate independent problem-solving.
Assessment Information
20% Coursework
80% Exams
Special Arrangements
Additional Information
Academic description Not entered
Syllabus Dynamics (~20 lectures)
Part 1 - Introduction to Dynamics. Ordinary Differential Equations.
Newton's laws. Reference frames. Energy and momentum conservation.
Projectiles. Variable mass problems. Rocket equation. (5)
Part 2 - Simple harmonic motion. Solution of 2nd order differential equations.
Damped SHM. Forced SHM. Coupled oscillations. Normal modes. (5)
Part 3 - Central forces. Angular momentum. Orbits. Kepler's Laws.
Non-inertial frames. Centrifugal & Coriolis forces. (5)
Part 4 - Two-body problem. Centre of Mass system. Scattering.
Rigid bodies. Torque. Moments of inertia. (4)
+ Introduction to Lagrangian dynamics (optional topic, time permitting)

Vector Calculus (20 lectures)
- Introduction to fields. Equipotentials. Scalar and vector fields. (3)
- Gradient. Divergence. Curl. Laplacian operator. Vector operator identities.(4)
- Plane surfaces. Line, surface and volume elements. Line integrals. Surface integrals. Volume integrals. (5)
- Divergence Theorem. Continuity equation. Stokes┐s Theorem. (3)
- Scalar potential. Conservative forces and fields. Poisson┐s equation. Vector potential.(3)
- Curvilinear surfaces. Line, surface, volume elements. Div, grad, curl in polar coordinates.(2)
Transferable skills Not entered
Reading list For the whole of this course the mathematical methods are covered in:
``Mathematical Methods for Physics and Engineering'', K. F. Riley, M. P. Hobson, S. J. Bence, Cambridge University Press (1998)
``Mathematical Methods in the Physical Sciences,'' Mary L. Boas, Published by John Wiley and Sons, Inc.(1966)

The Dynamics part of the course is closest to the material in:
``Classical Mechanics,'' R. Douglas Gregory, Cambridge University Press (2006)
Also useful are:
``Introduction to Classical Mechanics,'' A.P.French & M.G.Ebison (1987)
``Analytical Mechanics," G.R.Fowles & G.L.Cassiday, 7th Edition, Brookes/Cole (2005)
``Classical Mechanics," John R. Taylor, UCB (2005)
The first half of: ``Dynamics and Relativity,'' W.D.McComb, Oxford University Press (1999)
and for SHM: ``Vibrations and Waves,'' A.P.French, CRC Press (1971)

The Vector Calculus part of the course will not use any particular textbook. The first two listed below are standard texts; Spiegel contains many examples and problems:

DE Bourne and PC Kendall, Vector Analysis and Cartesian Tensors, (Chapman and Hall).
PC Matthews, Vector Calculus, (Springer).
MR Spiegel, Vector Analysis, (Schaum, McGraw-Hill).
Study Abroad Not entered
Study Pattern Not entered
Course organiserProf Stephen Playfer
Tel: (0131 6)50 5275
Course secretaryMrs Bonnie Macmillan
Tel: (0131 6)50 5905
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