Handbook 1996 : Faculty of Science (Volume 4 page 207)
Mathematics subject : Next:618-141 | Prev:618-131 | Search | Help

1. Mathematics, Faculty of Science (v4, p207) : Next:618-141 | Prev:618-131
2. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-141 | Prev:618-130

618-132 Applied Mathematics (Advanced)

Note:

1. Students may not gain credit for both 618-132 and 618-130.
2. Students who have obtained a result of H3 or better in 618-101 (1995 Handbook) or 618-121 may ask for permission to enter 618-132.

Credit points: 12.5

Coordinator: Professor L R White

Prerequisite: 618-111 or by invitation by the Head of Department (See Note 2 below).

Corequisite: 618-112 or 618-122.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving.

Timetable: Second semester

Objectives:

On completion of this subject, students should:

Comprehend:

• the classification and principles governing the solution of the basic first and second order differential equations;
• the range of calculus skills and techniques necessary for the solution of these differential equations, and the solution methods applicable to each type;
• the mathematical formulation of physical problems and their solution via the above techniques;
• the principles of Newtonian mechanics and its application in single particle and simple rigid body motions and in coupled vibrating systems.

Have developed:

• the ability to classify and solve the basic differential equations of first and second order; the integral and differential calculus skills to achieve these solutions with accuracy and confidence;
• a sound understanding of the action of forces in mechanical systems and the translation of that understanding into mathematical formulation of physical problems.

Appreciate:

• the power of differential equation modelling in advancing an understanding of complex physical processes from a wide variety of real world phenomena.

Content:

Differential equations: first-order differential equations (linear via integrating factors, separable and homogeneous) and applications; linear differential equations with constant coefficients, particular integrals and complementary functions. Mechanics: kinematics; Newton's laws, projectiles, constrained motion of a particle; systems of particles; motion of a rigid body; impulse problems. Systems of differential equations: systems of linear differential equations with constant coefficients, applications of matrix methods, stability; equilibrium and stability of conservative systems, small oscillations; first-order autonomous nonlinear systems and the phase plane.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Mathematics subject : Next:618-141 | Prev:618-131 | Search | Help
Handbook 1996 : Faculty of Science (Volume 4 page 207)

Status:          Official 1996
Date created:    Oct  9 1995
Last modified:   Oct  9 1995
Authorised by:   Academic Registrar
Email enquiries: Course_Information@registrar.unimelb.edu.au

Copyright © University of Melbourne 1995,1996.