Undergraduate Course: Dynamics and Vector Calculus (PHYS08043)
Course Outline
School  School of Physics and Astronomy 
College  College of Science and Engineering 
Course type  Standard 
Availability  Available to all students 
Credit level (Normal year taken)  SCQF Level 8 (Year 2 Undergraduate) 
Credits  20 
Home subject area  Undergraduate (School of Physics and Astronomy) 
Other subject area  None 
Course website 
None 
Taught in Gaelic?  No 
Course description  This course is designed for all prehonours 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. 
Information for Visiting Students
Prerequisites  None 
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 110:
Dynamics M & Th 1112 Vector Calculus Tu & F 1112
Workshops in Weeks 211:
Dynamics M 1416 & W 911 (choose one)
Vector Calculus Tu & Th 1416 (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 problemsolving.

Assessment Information
20% Coursework
80% Exams 
Special Arrangements
None 
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.
Noninertial frames. Centrifugal & Coriolis forces. (5)
Part 4  Twobody 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, McGrawHill). 
Study Abroad 
Not entered 
Study Pattern 
Not entered 
Keywords  DVC 
Contacts
Course organiser  Prof Stephen Playfer
Tel: (0131 6)50 5275
Email: S.Playfer@ed.ac.uk 
Course secretary  Mrs Bonnie Macmillan
Tel: (0131 6)50 5905
Email: Bonnie.MacMillan@ed.ac.uk 

