Handbook 1996 : Faculty of Science (Volume 4 page 209)
Mathematics subject : Next:618-201 | Prev:618-191 | Search | Help
618-200 "Mathematics 2" appears differently in several places - choose the one you want:
1. Mathematics, Faculty of Science (v4, p209) : Next:618-201 | Prev:618-191
3. Geomatics, Faculty of Engineering (v4, p123) : Next:619-100 | Prev:618-142
Note: Students may not gain credit for more than one of 618-200, 618-211, 618-102 (1995 Handbook), 618-112, 618-122.
Credit points: 13.5
Coordinator: Dr J Clark
Prerequisite: One of Mathematics 618-101 (1995 Handbook) or 121 or 142.
Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving.
Timetable: Offered in both semesters
Objectives:
On completion of this subject, students should :Comprehend:
- the basic properties of sequences and series, including Taylor series for functions;
- the concepts of abstract vector spaces and inner product spaces;
- the uses and properties of linear transformations;
- the role of eigenvalues and eigenvectors in the study of such mappings;
- the fundamental ideas in the calculus of functions of several variables.
Have developed:
- an ability to use tests to decide if sequences and series converge or diverge;
- the skills to find coordinates and matrices to represent vectors and linear transformations;
- the ability to change coordinate systems to simplify problems involving vector spaces and linear transformations;
- 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 series in estimation of functions;
- the role of linear algebra to find invariants and bring out the underlying geometry in problems;
- the similarities and differences between functions of one variable and multivariate functions.
Content:
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, dimensionality, Rn and Cn; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, quadrics and conics, rotation matrices, diagonal, real-symmetric and orthogonal matrices. 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; surface areas and volumes of solids of revolution; introduction to double and triple integrals.
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
1. Mathematics, Faculty of Science (v4, p209) : Next:618-201 | Prev:618-191
3. Geomatics, Faculty of Engineering (v4, p123) : Next:619-100 | Prev:618-142
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-212 | Prev:618-162
Note: Students may not gain credit for more than one of 618-200, 618-211, 618-102 (1995 Handbook), 618-112, 618-122.
Credit points: 13.5
Coordinator: Dr J Clark.
Prerequisite: Mathematics 618-101 (1995 Handbook) or 618-121 or 618-142.
Contact: 39 lectures (three each week), 13 1-hour tutorials and 39 hours problem solving.
Timetable: First or second semester.
Objectives:
On completion of this subject, students should :Comprehend:
- the basic properties of sequences and series, including Taylor series for functions;
- the concepts of abstract vector spaces and inner product spaces;
- the uses and properties of linear transformations;
- the role of eigenvalues and eigenvectors in the study of such mappings;
- the fundamental ideas in the calculus of functions of several variables.
Have developed:
- an ability to use tests to decide if sequences and series converge or diverge;
- the skills to find coordinates and matrices to represent vectors and linear transformations;
- the ability to change coordinate systems to simplify problems involving vector spaces and linear transformations;
- 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 series in estimation of functions;
- the role of linear algebra to find invariants and bring out the underlying geometry in problems;
- the similarities and differences between functions of one variable and multivariate functions.
Content:
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, dimensionality, Rn and Cn; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, quadrics and conics, rotation matrices, diagonal, real- symmetric and orthogonal matrices. 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; surface areas and volumes of solids of revolution; introduction to double and triple integrals.
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
* Note that CONTACT, CONTENT, PREREQUISITES, SEMESTER differs from the maintainer's version above. A log of variations is available.
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-212 | Prev:618-162
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
Maintained by: Dept. of Mathematics, Faculty of Science.
Copyright © University of Melbourne 1995,1996.