# Course Title: Linear Algebra and Vector Calculus

## Part A: Course Overview

Course Title: Linear Algebra and Vector Calculus

Credit Points: 12.00

### Teaching Period(s)

MATH2140

City Campus

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 1 2006,
Sem 1 2007,
Sem 1 2008,
Sem 1 2009,
Sem 1 2010,
Sem 1 2011,
Sem 1 2012,
Sem 1 2013,
Sem 1 2014,
Sem 1 2015,
Sem 1 2016

MATH2140

City Campus

171H School of Science

Face-to-Face

Sem 1 2017

Course Coordinator: Assoc Prof John Shepherd

Course Coordinator Phone: +61 3 9925 2587

Course Coordinator Email: john.shepherd@rmit.edu.au

Course Coordinator Location: 8.9.22

Pre-requisite Courses and Assumed Knowledge and Capabilities

To successfully complete this course, you are expected to have capabilities consistent with the completion of MATH1142 and MATH1144. That is, you are expected to be able to correctly recognise and apply the concepts of vectors; perform basic vector algebraic operations, including finding sum, scalar multiple, dot product and cross product of vectors; solve simultaneous linear equations; recognise and apply the concepts of matrices; perform basic algebraic operations on matrices, including finding sum, scalar multiple, transpose, matrix product and inverses; set up parametric equations for straight lines and equations for planes in space; perform elementary row operations on matrices; recognise and apply the concepts of differentiation and integration; find the derivative and anti-derivative of functions; determine definite integrals.

Course Description

Linear Algebra and 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. The MATLAB mathematics package will be used to support the learning in this course.

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 (Honours):

Knowledge and technical competence:

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

Problem-solving:

• 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.

On completion of this course you should be able to:

1. Describe and manipulate vector spaces, subspaces and their bases.
2. Determine the kernel, image space and matrix representation of a linear transformation.
3. Construct an orthonormal basis from a given basis and obtain a basis for the orthogonal complement.
4. Determine, and apply, the important quantities associated with scalar fields, such as partial derivatives of all orders, the gradient vector and directional derivative.
5. Determine, and apply, the important quantities associated with vector fields such as the divergence, curl, and scalar potential.
6. Evaluate line, surface, double and triple integrals and use these integrals to verify the seminal integral theorems (Green’s theorem in the plane, Gauss’ divergence theorem and Stokes’ theorem).

Overview of Learning Activities

You will attend lectures where syllabus material will be presented and explained, and the subject will be illustrated with demonstrations and examples. You will complete fortnightly practice classes which will consolidate your basic skills and your basic knowledge of the topics presented in class. Fortnightly closed book tests will alternate with the practice classes and will give you feedback on your progress and understanding. You are expected to undertake private study where you will work through the course material presented in class in addition to any homework problems.

Overview of Learning Resources

You will be able to access course information and learning materials through myRMIT Studies (Blackboard). myRMIT Studies will give access to important announcements, a discussion forum, staff contact details, the teaching schedule, online notes, assessment timelines, review exercises and past exam papers. You are advised to read your e-mail daily for important announcements. You should also visit myRMIT Studies at least once a day for  important course announcements and course-related documents.

A Library guide is available at  http://rmit.libguides.com/mathstats

Overview of Assessment

☒This course has no hurdle requirements.

Early Assessment Task 1:  Practice Class 1

Weighting 2% (approx – best 5/6 are taken.)

Note: Held in Week 2

This assessment task supports CLOs  1, 4

Early Assessment Task 2:  Closed-Book Test 1

Weighting 8%

Note: Held in Week 3

This assessment task supports CLOs  1, 4

Assessment Task 3 :  Practice Classes 2 - 6

Weighting 8% (approx. – best 5/6 are taken.)

Note: Held in weeks 4, 6, 8, 10 and 12

This assessment task supports CLOs  1 - 6

Assessment Task 4 :  Closed-Book Tests 2 - 5

Weighting 32%

Note: Held in weeks 5, 7, 9 and 11

This assessment task supports CLOs 1 - 6