Search | Previous : 618-141 | Next : 618-150
Handbook 1997 : Faculty of Science : Mathematics

618-142 Intermediate Mathematics B

Note:

Credit cannot be obtained for both 618-142 and any of 618-101 (1995 Handbook), 618-111 or 618-121, nor for both 618-142 and any of 618-141, 618-161 or 618-162 if 618-142 has already been passed.

Credit Points:

12.5

Coordinator:

Dr J J Koliha

Prerequisite/s:

618-100 (1995 Handbook), or 618-141, or both of 618-161, 618-162, or special permission of the Director of First-year Studies.

Timetable:

Semester 1 and 2

Contact:

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

Objectives:

On completion of this subject, students should:

Comprehend:

  • some of the nature of the different types of numbers they use;

  • the intuitive notion of limits as used in continuity, differentiation and integration;

  • the notion of integral as area;

  • the fundamental ideas in the calculus of functions of several variables.

Have developed:

  • an ability to manipulate complex numbers and to use them to solve problems;

  • skills in approximation and estimation;

  • the skills to solve problems involving contours of surfaces;

  • skills to find extrema of functions and to find volumes using differentiation and integration.

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 importance of the general concept of a vector.

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), Mean Value Theorem and applications, Newton's Method for root-finding, approximate integration, Taylor Polynomials. Multivariable calculus: Functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; coordinate transformations, Jacobi matrix and determinant; Hessian matrix, maxima and minima of functions of several variables; introduction to double and triple integrals and applications.

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.
Search | Previous : 618-141 | Next : 618-150
Handbook 1997 : Faculty of Science : Mathematics 
Status:                   OFFICIAL 1997
Last Modified:            Wednesday March 12 3:36 pm
SGML to HTML Conversion:  Information Technology Services
Authorised by:            Academic Registrar
Email Enquiries:          Course_Information@registrar.unimelb.edu.au
Copyright © University of Melbourne 1997.