Undergraduate Course: Dynamics and Vector Calculus (PHYS08043)
|School||School of Physics and Astronomy
||College||College of Science and Engineering
||Availability||Available to all students
|Credit level (Normal year taken)||SCQF Level 8 (Year 2 Undergraduate)
|Home subject area||Undergraduate (School of Physics and Astronomy)
||Other subject area||None
||Taught in Gaelic?||No
|Course description||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.
Information for Visiting Students
|Displayed in Visiting Students Prospectus?||No
Course Delivery Information
|Delivery period: 2013/14 Semester 2, Available to all students (SV1)
||Learn enabled: No
|Course Start Date
|Breakdown of 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
|Breakdown of Assessment Methods (Further Info)
||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.
||Dynamics (20 lectures)
- Introduction to Dynamics. Ordinary Differential Equations (2)
- Newtonian dynamics. Reference frames. Projectiles. (2)
- Momentum. Variable mass problems. Rocket equation. (1)
- Simple harmonic motion. Harmonic oscillator. Damped SHM. Forced SHM. (4)
- Second order differential equations. Solution by series. (2)
- Conservation laws. Conservative forces. Conservation of energy and momentum. (1)
- Central forces. Potential. Angular Momentum. Orbits. (3)
- Inverse square forces. Gravity. Kepler┐s laws. (2)
- Coupled oscillators. Normal modes. Compound pendula. (3)
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)
We will not closely follow any book, but it is recommended that you use books in parallel to the lectures. In particular:
``Classical Mechanics,'' R. Douglas Gregory, Cambridge University Press.
``Analytical Mechanics," Fowles/Cassiday, Sounders College Publishing.
``Mathematical Methods for Physics and Engineering'', K. F. Riley, M. P. Hobson, S. J. Bence, Cambridge University Press.
``Foundation Mathematics'', K. F. Riley, M. P. Hobson, Cambridge University Press.
``Mathematical Methods in the Physical Sciences,'' Mary L. Boas, Published by John Wiley and Sons, Inc.
The Vector Calculus part of the course will not use any particular textbook. The first seven listed below are standard texts; Spiegel contains many examples and problems:
KF Riley and MP Hobson, Essential Mathematical Methods for the Physical Sciences (Cambridge University Press)
(also useful for Junior Honours)
KF Riley and MP Hobson, Foundation Mathematics for the Physical Sciences (CUP)
(not so good for JH)
KF Riley, MP Hobson and SJ Bence, Mathematical Methods for Physics and Engineering, (CUP).
(This is an older but more comprehensive version of the books above.)
DE Bourne and PC Kendall, Vector Analysis and Cartesian Tensors, (Chapman and Hall).
PC Matthews, Vector Calculus, (Springer).
(Also useful for Junior Honours Symmetries of classical Mechanics)
ML Boas, Mathematical Methods in the Physical Sciences, (Wiley).
GB Arfken and HJ Weber, Mathematical Methods for Physicists, (Academic Press).
MR Spiegel, Vector Analysis, (Schaum, McGraw-Hill).
Any Mathematical Methods book that you are comfortable with.
|Course organiser||Dr Brian Pendleton
Tel: (0131 6)50 5241
|Course secretary||Miss Jillian Bainbridge
Tel: (0131 6)50 7218
© Copyright 2013 The University of Edinburgh - 13 January 2014 4:59 am