Unit information: Mechanics 1 in 2013/14

Unit name	Mechanics 1
Unit code	MATH11009
Credit points	10
Level of study	C/4
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Professor. Wiggins
Open unit status	Not open
Pre-requisites	Normally, an A at A-level mathematics or equivalent.
Co-requisites	Calculus 1, Linear Algebra and Geometry
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Prerequisites: calculus, elementary vector calculus, elementary linear algebra. Contents: kinematics; Newton's equations; motion in one dimension; ballistic motion; constrained motion; friction; conservation of energy and momentum for one particle and for a particle system; two-body problem; central force problem; the Kepler problem; oscillations; driven oscillations.

Aims:

• To introduce the basic principles and laws of classical mechanics.

• To develop mathematical tools of kinematics and dynamics.

• To illustrate the ideas of mechanics by applying them to certain classical problems.

Syllabus

• Basic concepts of mechanics. Space, time, coordinates.

• Trajectory, velocity and acceleration.

• Newton's laws and the concept of force.

• Equation of motion, examples in 1D.

• Momentum. Impulse. Conservation of momentum.

• Angular momentum, torque, pendulum.

• Kinetic energy. Work done, power. Path-independence, potential energy, conservative forces.

• Oscillations and phase plane analysis

• Two-body problem and polar coordinates.

Relation to Other Units

This unit is an essential part of the Year 1 core curriculum. It uses the methods of Linear Algebra and Geometry and Calculus 1 (and partially some methods systematically taught later in Calculus 2), as well as introduces some techniques of the analysis of Ordinary Differential Equations, taught in Year 2.

Intended Learning Outcomes

• To create a solid foundation for understanding of basic principles of Mechanics and some of its classical problems.

• To be able to use Calculus and Linear Algebra to approach these problems.

• To open ways to further study of Applied Mathematics

Transferable Skills:

Mechanics 1 is a pre-requisite for studying any further mathematical physics. Even if you plan to further specialise in Pure Mathematics or Statistics, Mechanics will provide you with a rich source of mathematical techniques and intuition for advancing in your studies.

Teaching Information

Lectures, homework, problem-solving and tutorials. Motivation and independent reading.

Assessment Information

The final assessment mark for Mechanics 1 is calculated from a standard rubric 1½ -hour written examination in May/June with two sections.

• Section A (worth 40%) consists of 5 short mandatory questions.

• Section B (worth 60%) consists of 3 long questions of which the best 2 will count.

Calculators are NOT permitted in this examination.

Reading and References

There is no one standard text for the course. Online notes will be available. There are many excellent texts for this subject. The following books are suggested:

• An Introduction to Mechanics, D. Kleppner & Robert J. Kolenkow, McGraw-Hill, 1973

• Analytical Mechanics, G.R. Fowles & G.L. Cassiday, 6th ed. Saunders College Publishing (1993)

This book covers the same ground as Kleppner and Kolenkow, except for special relativity.

• Mechanics (Berkeley Course), Charles Kittel, Walter D. Knight, & Malvin A. Ruderman.

This is a good physics book with less emphasis on maths than Kleppner and Kolenkow.

• Mechanics P. Smith, and R.C. Smith. Chichester : Wiley, 1990.