Search : Index : Faculty of Science : Mathematics and Statistics
Prev 620-202 Statistics
Next 620-221 Real and Complex Analysis

 620-211 Mathematics 2 (Advanced)

Note

  1. Students may gain credit for only one of 620-112, 620-122, 620-200, 620-211.

  2. In some cases (for example, students from the MUPHAS Mathematics program), direct entry into this subject may be possible.

  3. High-achieving students from [98]620-142 should ask the Head of Department about taking this subject as an alternative to 620-200.

Credit Points

12.5

Coordinator

Dr I Aitchison

Prerequisites

620-111 or invitation by the Head of Department.

Semester

1 (view timetable)

Contact

36 lectures (three per week), 12 tutorial/practice class hours (one per week) and 36 hours problem solving

Subject Description

This subject gives a sophisticated treatment of core material in single- and multi-variable calculus and linear algebra. This advanced perspective is especially suited to students planning higher-level studies in Mathematics and Statistics.

Sequences and series: convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra: vector spaces in general, axioms, linear independence, basis sets, dimension, Rn and Cn; inner products in real and complex spaces; linear transformations, matrix of a linear transformation, change of basis; eigenvectors and eigenvalues, diagonalisation of real symmetric matrices, applications, including applications to geometry; symmetry groups of matrices of R2 and R3. 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.

Assessment

Up to 24 pages of written assignments and a 3-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.

Search : Index : Faculty of Science : Mathematics and Statistics
Prev 620-202 Statistics
Next 620-221 Real and Complex Analysis
 
Status:                   Official 1999
Last Modified:            Tuesday October 20 11:53
SGML to HTML Conversion:  Information Technology Services
Authorised by:            Academic Registrar
Email Enquiries:          Course_Information@registrar.unimelb.edu.au