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Area/Catalogue
MATH 1069

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Course Level
Undergraduate

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Offered Externally
No

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Course ID
154440

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Unit Value
4.5

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University-wide elective course
No

Course owner

Course owner
School of Information Technology and Mathematical Sciences

Course aim

To develop fundamental concepts in linear algebra and in calculus. To demonstrate links between linear algebra and analysis by the use of infinite series.

Course content

Introduction to Analysis using Infinite Series
Numerical sequences, examples, definition and properties of limit, including lim inf and lim sup; Numerical series, examples (including geometric, harmonic, telescoping, and p-series). Convergence tests. Absolute and conditional convergence; Power series: Motivation, formula for coefficients, radius of convergence, examples. Term-by-term integration and differentiation. Power series of the exponential, sine, cosine, logarithm. Uniform convergence. Abel’s theorem. Applications.

Linear Algebra of general vector spaces.
Definition and basic properties of vector spaces; examples; Inner products; Cauchy-Schwarz inequality; Subspaces; Definition of dimension; Finite vector spaces and bases; The isomorphism theorem; Linear Transformations. Basic definitions: rank, null space, etc. The fundamental theorem; Special transformations: projections, orthogonal transformation, symmetric transformations, stochastic matrices; Spectral theorem for symmetric matrices; Matrix functions: matrix exponential, power series.

Textbook(s)

Edwards, CH & Penney DE 2008, Calculus Early Transcendentals, , 7th, Pearson Prentice Hall, USA

Lay, David C. 2014, Linear Algebra and its Applications, 4th, Pearson Higher Ed, USA

Prerequisite(s)

MATH 1054 Calculus 1 or MATH 1063 Mathematical Methods for Engineers 1 (only one of them)

Corequisite(s)

MATH 1064 Mathematical Methods for Engineers 2

Teaching method

Component Duration
INTERNAL, MAWSON LAKES
Lecture 2+2 hours x weekly
Tutorial 1 hour x weekly

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.


Assessment

Assignment, Continuous assessment, Examination

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
To determine the fee for this course as part of a Commonwealth Supported program, go to:
How to determine your Commonwealth Supported course fee. (Opens new window)

Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
Non-award tuition fees are set by the university. To determine the cost of this course, go to:
How to determine the relevant non award tuition fee. (Opens new window)

Not all courses are available on all of the above bases, and students must check to ensure that they are permitted to enrol in a particular course.

* Equivalent Full Time Study Load. Please note: all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation.

Course Coordinators

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