Handbook 1996 : Faculty of Science (Volume 4 page 206)
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618-111 Mathematics 1A(Advanced)

Note: Students may not gain credit for both 618-111 and any of 618-101 (1995 Handbook), 618-121, 618-142, nor for any of 618-141, 618-161, 618-162 if 618-111 has already been passed.

Credit points: 12.5

Coordinator: Dr J R J Groves

Prerequisite: Invitation by the Head of Department.

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

Timetable: First semester

Objectives:

On completion of this subject, students should:

Comprehend:

• some of the nature of the different types of numbers they use;
• the notion of limits as used in continuity, differentiation and integration;
• the notion of integral as area;
• the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
• the theoretical treatment of systems of simultaneous linear equations.

Have developed:

• an ability to construct simple proofs;
• an ability to manipulate complex numbers and to use them to solve problems;
• an ability to compute a wide range of integrals;
• an ability to use integration to compute areas, arc lengths and volumes;
• an ability to solve arbitrary systems of simultaneous linear equations.

Appreciate:

• the role of proof and logical reasoning in mathematics;
• the use of complex numbers;
• the role of limits in both the differential and integral calculus;
• the practical uses of calculus;
• the use of the ideas of linear algebra in dealing with the solution of simultaneous linear equations.

Content:

Foundations: integers, mathematical induction; topics in elementary number theory; real numbers. Complex numbers including the complex exponential. Topics in elementary geometry. Calculus: functions of one real variable, limits, continuity, derivatives; introduction to Riemann integration, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc lengths, volumes and surface areas of solids of revolution. Vectors and linear equations: vectors in three-dimensional space, dot and cross products; geometrical applications; linear dependence, bases and coordinates, dimension. Solution of simultaneous linear equations, row-reduction, rank, computation of inverses, determinants.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

Mathematics subject : Next:618-112 | Search | Help
Handbook 1996 : Faculty of Science (Volume 4 page 206)

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.