This course provides an introduction to the mathematical modelling of mechanical phenomena, for example, the motion of a golf ball moving under the influence of gravity. The main mathematical tools used in this course are vector algebra and the analysis of solutions of differential equations. It is an essential course for intending honours students.

2 x lectures per week. Fortnightly tutorials.

None

Mathematics 2A: Multivariable Calculus

Mathematics 2B: Linear Algebra

One degree examination (80%) (1 hour 30 mins); coursework (20%).

It is the default expectation that all courses will offer opportunities for reassessment or deferred assessment. Where it is not possible to offer this in some assessment components, the grade achieved at the first attempt will be counted towards the final course grade, and any exceptions for this course are described below.

[No exceptions]

The aim of this course is to provide an introduction to the kinematics and dynamics of a single point mass particle. Equations of motion are constructed via the application of Newton's laws. The Lagrangian formalism of mechanics is introduced.

By the end of this course, students will be able to:

■ Predict functional dependence based on dimensional analysis.

■ Calculate the tangent vector and arc-length of a parametric curve and sketch such curves; use plane, cylindrical and spherical polar coordinates to describe particle motion; fluently apply the terms velocity, speed, acceleration, displacement and distance travelled to describe the motion of a point particle and connect these concepts to properties of parametric curves.

■ Mathematically model suitable particle mechanics systems using vectors and differential equations as appropriate, and solve the resulting equations to determine the motion of the particle.

■ Define the terms linear momentum, impulse and force and apply these in calculations; given a description of a mechanical system, construct a model of this system and provide predictions of future states of the system.

■ Define and apply the concepts of energy, work and power in given physical situations; compute projectile motion and motion governed by Hooke's Law; use plane polar coordinates to model and solve elementary mechanics systems.

■ Determine appropriate Lagrangians, and derive and solve the equations of motions for simple mechanical systems subject to the principle of least action.

■ State the definitions, results and formulae presented in lectures; apply and adapt these to solve suitable problems.