Course Title: Advanced Linear Algebra with Vector Calculus

Part A: Course Overview

Course Title: Advanced Linear Algebra with Vector Calculus

Credit Points: 12.00


Course Code




Learning Mode

Teaching Period(s)


City Campus


145H Mathematical & Geospatial Sciences


Sem 2 2016


City Campus


171H School of Science


Sem 2 2017,
Sem 2 2018,
Sem 2 2019,
Sem 2 2020,
Sem 2 2021,
Sem 2 2022,
Sem 1 2024

Course Coordinator: Dr Graham Clarke

Course Coordinator Phone: +61 3 9925 3225

Course Coordinator Email:

Course Coordinator Location: 15.3.14

Pre-requisite Courses and Assumed Knowledge and Capabilities

Required Prior Study

You should have satisfactorily completed following course/s before you commence this course.



Alternatively, you may be able to demonstrate the required skills and knowledge before you start this course.

Contact your course coordinator if you think you may be eligible for recognition of prior learning.

Assumed Knowledge

Students are assumed to have knowledge of fundamental Calculus (derivatives, integrals, and their applications) and Linear Algebra (vector and matrix properties and operations) when participating in this course.

Course Description

Advanced Linear Algebra with Vector Calculus introduces and studies operations and methods that are the fundamental tools of mathematicians and applied scientists. The course introduces Linear Algebra (vector spaces and subspaces, linear independence, basis, kernel, dimension; inner products, linear transformations, eigenvalues, eigenvectors and diagonalisation) and Calculus of Vector Functions (scalar and vector fields, surfaces and space curves, gradient, divergence and curl, multiple integrals, line integrals and surface integrals; integral Theorems - Green’s, Gauss’ divergence and Stokes’ theorem). The foundation is laid for more specialist mathematical modelling and multivariate statistics subjects undertaken in subsequent years in your program of study. 

Objectives/Learning Outcomes/Capability Development

This course contributes to the following Program Learning Outcomes for BP083 Bachelor of Science (Mathematics), BP245 Bachelor of Science (Statistics) and BH119 Bachelor of Analytics (Hons):

Knowledge and technical competence:

  • use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.


  • synthesise and flexibly apply knowledge to characterise, analyse and solve a wide range of problems
  • balance the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution.

Teamwork and project management:

  • contribute to professional work settings through effective participation in teams and organisation of project tasks
  • constructively engage with other team members and resolve conflict.


  • communicate both technical and non-technical material in a range of forms (written, electronic, graphic, oral) and tailor the style and means of communication to different audiences. Of particular interest is the ability to explain technical material, without unnecessary jargon, to lay persons such as the general public or line managers.

Information literacy:

  • communicate and use data and information and evaluate its quality with respect to its authority and relevance.

Upon successful completion of this course, you will be able to:

  1. Identify the properties of scalar and vector fields and demonstrate your ability to perform operations on them.
  2. Apply basic methods of linear algebra to real vector spaces.
  3. Generalise ideas from real vector spaces to a wider range of linear spaces and explain the significance of these ideas.
  4. Extend concepts from single-variable integration to evaluate multiple integrals, line integrals and surface integrals. 

Overview of Learning Activities

You will be actively engaged in a range of learning activities such as lectorials, tutorials, practicals, laboratories, seminars, project work, class discussion, individual and group activities. Delivery may be face to face, online or a mix of both.

You are encouraged to be proactive and self-directed in your learning, asking questions of your lecturer and/or peers and seeking out information as required, especially from the numerous sources available through the RMIT library, and through links and material specific to this course that is available through myRMIT Studies Course.

Overview of Learning Resources

RMIT will provide you with resources and tools for learning in this course through myRMIT Studies Course

There are services available to support your learning through the University Library. The Library provides guides on academic referencing and subject specialist help as well as a range of study support services. For further information, please visit the Library page on the RMIT University website and the myRMIT student portal.

Overview of Assessment

Assessment Tasks

Assessment Task 1: In-class tests (11) 
Weighting 50% 
This assessment task supports CLOs 1 & 2

Assessment Task 2:Homework assignments (2) 
Weighting 30% 
This assessment task supports CLOs 3 & 4

Assessment Task 3:On-line tests (1)
Weighting 20% 
This assessment task supports CLOs 1, 2, 3 & 4

If you have a long-term medical condition and/or disability it may be possible to negotiate to vary aspects of the learning or assessment methods. You can contact the program coordinator or Equitable Learning Services if you would like to find out more.