Advanced Linear Algebra and Infinite Series

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 1)
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Fee-paying program for domestic and international students
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Non-award enrolment
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* 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.