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ENM2600 Advanced Engineering Mathematics

Semester 3, 2021 Online
Short Description: Advanced Engineering Maths
Units : 1
Faculty or Section : Faculty of Health, Engineering and Sciences
School or Department : School of Sciences
Student contribution band : Band 1
ASCED code : 010101 - Mathematics
Grading basis : Graded


Examiner: Benjamin Dexter


Pre-requisite: ENM1600 or Students must be enrolled in one of the following Programs: GCEN or METC or MENS or GDNS or MEPR or MSCN

Other Requisites

This course is substantially equivalent to MAT2100 and MAT2500. Students cannot enrol in ENM2600 if they have successfully completed, or are currently enrolled in MAT2100 or MAT2500.


This course follows ENM1600 Engineering Mathematics in developing the theory and competencies needed for a wide range of engineering applications. In particular, the concepts and techniques of complex numbers, differential equations, multivariable calculus and linear algebra are broadened. These mathematical techniques are explored in the context of engineering applications.


This course further integrates mathematical concepts to provide students with an introduction to the advanced skills required for engineering and surveying. Topics included are: Complex Numbers, Ordinary Differential Equations (ODEs), Series, Multivariable Calculus, and Linear Algebra. The introduction to Ordinary Differential Equations and Series topics include direction fields, Euler's method, first order separable ODEs, first order and second order linear ODEs with constant coefficients, Taylor and Fourier series. Multivariable Calculus includes representation of functions of several variables, surfaces and curves in space, partial differentiation, optimisation, directional derivatives, gradient, divergence and curl, line integrals of the 1-st and 2-nd kinds, iterated integrals, Green's theorem. The topic of Linear Algebra of ENM1600 Engineering Mathematics is extended to cover eigenvalues and eigenvectors, and symmetric and orthogonal matrices. Engineering applications are discussed in each topic.


On completion of this course students will be able to:

  1. Critically examine and apply mathematical techniques and skills to solve problems essential to further study in engineering and surveying;
  2. Proficiently apply mathematical techniques to analyse and solve basic mathematical and authentic engineering and surveying problems relevant to this course.
  3. Effectively communicate mathematical concepts and arguments using appropriate notation;
  4. Use computational aids for graphing, matrix manipulation, concept development and problem solving in algebra and calculus within engineering and surveying contexts.


Description Weighting(%)
1. Differential Equations and Series: direction fields - first order linear ODEs - Taylor series - Fourier series - Euler's method - second order linear ODEs with constant coefficients - engineering applications. 35.00
2. Multivariable Calculus: curves in space - surfaces in space - functions of several variables - partial differentiation - geometric interpretation of partial derivatives - maxima/minima problems - directional derivatives - vector fields - curl and divergence - line and work integrals - independence of path - engineering applications. 35.00
3. Linear Algebra: - eigenvalues and eigenvectors - symmetric and orthogonal matrices - engineering applications. 15.00
4. Complex number applications, Euler form and complex functions. 15.00

Text and Materials

ALL textbooks and materials available to be purchased can be sourced from USQ's Online Bookshop (unless otherwise stated). (

Please contact us for alternative purchase options from USQ Bookshop. (

Glyn James 2019, Modern Engineering Mathematics, 6th edn, Pearson Education Limited.
(4th & 5th edn can also be used.)
Study Book 2014, Course ENM2600 Advanced Engineering Mathematics, USQ, Toowoomba.
(Available on course StudyDesk.)
Scientific calculator (non-graphical and non-programmable) having options for calculation of simple elementary functions: sinx, cosx, ex, lnx, etc. The typical model example is the calculator CASIO fx-100AU.

Reference Materials

Reference materials are materials that, if accessed by students, may improve their knowledge and understanding of the material in the course and enrich their learning experience.
Erwin Kreyszig 2011, Advanced Engineering Mathematics, 10th edn, Wiley, Hoboken, NJ.
Glyn James et al 2009, Solutions Manual, Modern Engineering Mathematics, 4th edn, Pearson (Prentice Hall), Harlow.
Matlab (any recent version). Matlab is freely accessible in the USQ computer laboratories. External students can use Scilab instead. It is a MATLAB clone freely available on the web. Manuals for Matlab and Scilab are available on Study Desk.

Student Workload Expectations

Activity Hours
Assessments 42.00
Online Lectures 52.00
Online Tutorials 13.00
Private Study 65.00

Assessment Details

Description Marks out of Wtg (%) Due Date Notes
Online Quiz 1 50 5 26 Nov 2021
Assignment 1 150 15 14 Dec 2021
Online Quiz 2 50 5 04 Jan 2022
Assignment 2 150 15 24 Jan 2022
Take Home Examination 600 60 End S3 (see note 1)

  1. This will be a Take Home exam. Students will be provided further instruction regarding the exam by their course examiner via StudyDesk. The examination date will be available via UConnect when the Alternate Assessment Schedule has been released.

Important assessment information

  1. Attendance requirements:
    It is the students' responsibility to participate appropriately in all activities scheduled for them, and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.

  2. Requirements for students to complete each assessment item satisfactorily:
    To satisfactorily complete an assessment item a student must achieve at least 50% of the marks or a grade of at least C-. Students do not have to satisfactorily complete each assessment item to be awarded a passing grade in this course. Refer to Statement 4 below for the requirements to receive a passing grade in this course.

  3. Penalties for late submission of required work:
    Students should refer to the Assessment Procedure (point 4.2.4)

  4. Requirements for student to be awarded a passing grade in the course:
    To be assured of receiving a passing grade in a course a student must obtain at least 50% of the total weighted marks for the course.

  5. Method used to combine assessment results to attain final grade:
    The final grades for students will be assigned on the basis of the weighted aggregate of the marks obtained for each of the summative assessment items in the course.

  6. Examination information:
    A Take Home Examination is one in which candidates may have access to any printed, written, or online material as well as a calculator.

  7. Examination period when Deferred/Supplementary examinations will be held:
    Deferred and Supplementary examinations will be held in accordance with the Assessment Procedure

  8. University Student Policies:
    Students should read the USQ policies: Definitions, Assessment and Student Academic Misconduct to avoid actions which might contravene University policies and practices. These policies can be found at

Other Requirements

  1. Computer, e-mail and Internet access:
    Students are required to have access to a personal computer, e-mail capabilities and Internet access to UConnect. Current details of computer requirements can be found at

  2. Students can expect that questions in assessment items in this course may draw upon knowledge and skills that they can reasonably be expected to have acquired before enrolling in this course. This includes knowledge contained in pre-requisite courses and appropriate communication, information literacy, analytical, critical thinking, problem solving or numeracy skills. Students who do not possess such knowledge and skills should not expect the same grades as those students who do possess them.

Date printed 11 February 2022