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MAT2500 Engineering Mathematics 3

Semester 2, 2012 On-campus Springfield
Units : 1
Faculty or Section : Faculty of Sciences
School or Department : Maths and Computing
Version produced : 30 December 2013

Contents on this page


Examiner: Yury Stepanyants
Moderator: John Leis


Pre-requisite: MAT1102 or MAT1502 or Students must be enrolled in one of the following Programs: GCEN or GDET or METC or MENS

Other requisites

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


This course follows MAT1502 Engineering Mathematics 2 in developing the theory and competencies needed for a wide range of engineering applications. In particular, the concepts and techniques of differential equations, multivariable calculus and linear algebra are furthered, and some of their engineering applications are explored.


Module 1 is an introduction to ordinary differential equations (ODEs) and series including direction fields, Euler's method, first order separable ODEs, first order and second order linear ODEs with constant coefficients, Taylor and Fourier series. Module 2 covers multivariable calculus including 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. Module 3 extends the linear algebra of MAT1502 Engineering Mathematics 2 to cover eigenvalues and eigenvectors, vector space, bases, dimensions, rank, systems of linear equations, symmetric matrices, transformations, diagonalisation with applications. Engineering applications are discussed in each module.


On completion of this course students will be able to:

  1. demonstrate advances in understanding of mathematical concepts that are essential for tertiary studies in engineering and surveying;
  2. demonstrate proficiency in the skills and competencies covered in this course;,
  3. interpret and solve a range of authentic problems involving mathematical concepts relevant to this course and to engineering;
  4. effectively communicate the mathematical concepts, reasoning and technical skills contained in this course.


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 30.00
3. Linear Algebra: linearly independent vectors - systems of linear algebraic equations - eigenvalues and eigenvectors - symmetric matrices - engineering applications 35.00

Text and materials required to be purchased or accessed

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. (

  • James, G 2008, Modern Engineering Mathematics, 4th edn, Pearson (Prentice Hall), Harlow.
  • USQ Study Book 2012, Course MAT2500 Engineering Mathematics 3, USQ Distance Education Centre, Toowoomba.
  • Desirable: Scientific calculator, Matlab software.

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.
  • James, G 2009, Student's Solutions Manual for James, Modern Engineering Mathematics, 4th edn, Pearson (Prentice Hall), Harlow.
  • Kreysig, E 2006, Advanced engineering mathematics, 9th edn, Wiley, Hoboken, NJ.

Student workload requirements

Activity Hours
Assessments 16.00
Examinations 2.00
Lectures 56.00
Private Study 72.00
Tutorials 28.00

Assessment details

Description Marks out of Wtg (%) Due Date Notes
ASSIGNMENT 1 50 14 17 Jul 2012 (see note 1)
ASSIGNMENT 2 50 14 17 Jul 2012 (see note 2)
WEEKLY HOMEWORK 50 14 17 Jul 2012 (see note 3)
2 HR RESTRICTED EXAMINATION 50 58 End S2 (see note 4)

  1. Exact dates will be specified in the course Introductory Book.
  2. Exact dates will be specified in the course Introductory Book.
  3. Exact dates will be specified in the course Introductory Book.
  4. Examination dates will be available during the Semester. Please refer to Examination timetable when published.

Important assessment information

  1. Attendance requirements:
    It is the students' responsibility to attend and participate appropriately in all activities (such as lectures, tutorials, laboratories and practical work) 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 complete the assignments satisfactorily, students must obtain at least a total of 50% of the marks available for the assignments. To complete the examination satisfactorily, students must obtain at least 50% of the marks available for the examination.

  3. Penalties for late submission of required work:
    If students submit assignments after the due date without (prior) approval of the examiner then a penalty of 5% of the total marks gained by the student for the assignment may apply for each working day late up to ten working days at which time a mark of zero may be recorded. No assignments will be accepted after model answers have been posted.

  4. Requirements for student to be awarded a passing grade in the course:
    To be assured of receiving a passing grade a student must achieve at least 50% of the total weighted marks available 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 aggregate of the weighted marks obtained for each of the summative assessment items in the course.

  6. Examination information:
    The only materials that students may use in the RESTRICTED examination for this course are: non-programmable and non-graphical calculator, one A4 sheet of paper containing basic formulae prepared by examiner and available to students on the Study Desk during the semester. Students whose first language is not English, may take an appropriate unmarked non-electronic translation dictionary (but not technical dictionary) into the examination. Dictionaries with any handwritten notes will not be permitted. Translation dictionaries will be subject to perusal and may be removed from the candidate's possession until appropriate disciplinary action is completed if found to contain material that could give the candidate an unfair advantage.

  7. Examination period when Deferred/Supplementary examinations will be held:
    Any Deferred or Supplementary examinations for this course will be held during the next examination period.

  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

Assessment notes

  1. The due date for an assignment is the date by which a student must despatch the assignment to the USQ. The onus is on the student to provide proof of the despatch date, if requested by the Examiner.

  2. Students must retain a copy of each item submitted for assessment. If requested, students will be required to provide a copy of assignments submitted for assessment purposes. Such copies should be despatched to USQ within 24 hours of receipt of a request being made.

  3. The examiner may grant an extension of the due date of an assignment in extenuating circumstances.

  4. The Faculty will normally only accept assessments that have been written, typed or printed on paper-based media by blue or black pen. Pencil writing is not acceptable.

  5. The Faculty will NOT accept submission of assignments by facsimile.

  6. Students who do not have regular access to postal services or who are otherwise disadvantaged by these regulations may be given special consideration. They should contact the examiner of the course to negotiate such special arrangements.

  7. In the event that a due date for an assignment falls on a local public holiday in their area, such as a Show holiday, the due date for the assignment will be the next day. Students are to note on the assignment cover the date of the public holiday for the Examiner's convenience.

  8. Students who have undertaken all of the required assessments in a course but who have failed to meet some of the specified objectives of a course within the normally prescribed time may be awarded the temporary grade: IM (Incomplete - Make up). An IM grade will only be awarded when, in the opinion of the examiner, a student will be able to achieve the remaining objectives of the course after a period of non directed personal study.

  9. Students who, for medical, family/personal, or employment-related reasons, are unable to complete an assignment or to sit for an examination at the scheduled time may apply to defer an assessment in a course. Such a request must be accompanied by appropriate supporting documentation. One of the following temporary grades may be awarded IDS (Incomplete - Deferred Examination; IDM (Incomplete Deferred Make-up); IDB (Incomplete - Both Deferred Examination and Deferred Make-up).