Handbook 1996 : Faculty of Engineering (Volume 4 page 86)
First Year Engineering subject : Next:640-005 | Prev:618-181 | Search | Help

1. First Year Engineering, Faculty of Engineering (v4, p86) : Next:640-005 | Prev:618-181
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618-182 Mathematics 1S

Credit points: 14.2

Coordinator: Prof. A. J. Guttmann, Ms. C. Mangelsdorf.

Prerequisite: Mathematics 618-181

Contact: 52 hours of lectures (4 a week) and 26 thours of utorials (2 a week) (Semster two)

Objectives:

On completion of this subject students should:

Comprehend:

• some of the nature of the different types of numbers they use
• the intuitive nature 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
• the mathematical formulation of physical problems and their solution using differential equations

Have developed:

• an ability to manipulate complex numbers and to use them to solve problems
• an ability to use differential calculus to solve extremal problems
• an ability to compute a wide range of integrals
• an ability to use integration to compute area, length and volume
• an ability to solve arbitrary systems of simultaneous linear equations
• skills to apply differential equation techniques to simple problems

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

Content:

Foundations: sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus: functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vectors and linear equations: vectors in three-dimensional space, dot and cross products, triple products, determinants; linear dependence; equations of lines and planes, geometrical applications; bases and coordinates, dimension; row reduction, rank, inverse solution of linear equations, geometrical interpretation. Systems of differential equations: systems of first order differential equations; linear systems; eigenvalues and eigenvectors; solutions for distinct, repeated and complex eigenvalues, inhomogeneous systems; application to phase plane; equilibrium points and their stability; second order systems, application to systems of mechanical or electrical oscillators; longitudinal and transverse oscillators.

Assessment:

Up to 35 pages of written assignments, up to four hours of end-of-semester written examinations (one hour of which will be a written examination on differential equations) and in addition class tests totalling not more than 1.5 hours.

First Year Engineering subject : Next:640-005 | Prev:618-181 | Search | Help
Handbook 1996 : Faculty of Engineering (Volume 4 page 86)

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.