Undergraduate Course: Dynamics and Vector Calculus (PHYS08043)
|School||School of Physics and Astronomy
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 8 (Year 2 Undergraduate)
||Availability||Available to all students
|Summary||This 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.
Dynamics (20 lectures)
Part 1 - Introduction to Dynamics. Newton's laws. Ordinary Differential Equations. Energy and momentum conservation.
Variable mass problems. Rocket equation. (6)
Part 2 - Simple harmonic motion. Solution of 2nd order differential equations. Damped SHM. Forced SHM. Resonance.
Coupled oscillations. Normal modes. (6)
Part 3 - Central forces. Angular momentum conservation.
Orbits. Kepler's Laws. Two-body problem. Centre of Mass system. Hard-body scattering. Rutherford scattering.
Non-inertial frames. Centrifugal & Coriolis forces. (8)
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)
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
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
|Assessment (Further Info)
|Additional Information (Assessment)
||Hours & Minutes
|Main Exam Diet S2 (April/May)||3:00|
|Resit Exam Diet (August)||3:00|
On completion of this course, the 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.
|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 the first halves of:
``Classical Mechanics,'' R. Douglas Gregory, Cambridge University Press (2006)
``Classical Mechanics," J.R. Taylor, USB (2005)
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)
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).
|Graduate Attributes and Skills
|Course organiser||Prof Romeel Dave
Tel: (0131 6)68 8352
|Course secretary||Ms Louise McCarte
Tel: 0131 668 8403