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MAT2100 Algebra and Calculus II

Semester 2, 2021 Online
Short Description: Algebra and Calculus II
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
Version produced : 6 August 2021


Examiner: Dmitry Strunin


Pre-requisite: MAT1102 or MAT1502 or ENM1600 or Students must be enrolled in the following program: MSCN or MEPR or BSED

Other requisites

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


This course follows on directly from MAT1102 Algebra and Calculus I in developing the concepts and techniques of calculus and linear algebra for application to problems in engineering and science, or as a basis for higher study in mathematics.


Module 1 is an introduction to ordinary differential equations (ODEs) and series including direction fields, Euler's method, first order separable ODEs, first 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 MAT1102 Algebra and Calculus 1 to cover eigenvalues and eigenvectors, vector space, bases, dimensions, rank, systems of linear equations, symmetric matrices, transformations, diagonalisation with applications.


On successful completion of this course students will be able to:

  1. Develop and apply mathematical techniques and skills to solve problems essential to further study in sciences or engineering
  2. Demonstrate proficiency to interpret and solve basic mathematical problems relevant to this course;
  3. Apply mathematical skills to solve authentic science and engineering problems relevant to this course;
  4. Effectively communicate mathematical concepts and arguments using appropriate notation


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. 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. 30.00
3. Linear Algebra: linearly independent vectors - systems of linear algebraic equations - eigenvalues and eigenvectors - symmetric matrices. 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 2020, Modern Engineering Mathematics, 6th edn, Pearson (Prentice Hall), Harlow.
Study Book (current year), Course MAT2100 3Algebra and Calculus II, USQ Distance and e-Learning Centre, Toowoomba.
(Available on the course StudyDesk.)
Desirable: scientific calculator (non-programmable and non-graphical), 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 2011, Advanced engineering mathematics, 10th edn, Wiley, Hoboken, NJ.

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
Quiz 1 50 5 05 Aug 2021
Assignment 1 100 15 26 Aug 2021 (see note 1)
Quiz 2 50 5 16 Sep 2021
Assignment 2 100 15 14 Oct 2021 (see note 2)
Open Examination - Online 100 60 End S2 (see note 3)

  1. The date may be changed during the Semester (please follow the announcements in the Study Desk).
  2. The date may be changed during the Semester (please follow the announcements in the Study Desk).
  3. This will be an online 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, and to study all materials 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:
    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 a student must obtain at least 50% of the total weighted marks available for the course (i.e. the Primary Hurdle), and have satisfied the Secondary Hurdle (Supervised), i.e. the end of semester examination by achieving at least 40% of the weighted marks available for that assessment item.

    Supplementary assessment may be offered where a student has undertaken all of the required summative assessment items and has passed the Primary Hurdle but failed to satisfy the Secondary Hurdle (Supervised), or has satisfied the Secondary Hurdle (Supervised) but failed to achieve a passing Final Grade by 5% or less of the total weighted Marks.

    To be awarded a passing grade for a supplementary assessment item (if applicable), a student must achieve at least 50% of the available marks for the supplementary assessment item as per the Assessment Procedure (point 4.4.2).

  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:
    An Online 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

Assessment notes

  1. Exam paper presentation: All exam papers should be presented in accurate and clear writing by blue or black pen. Pencil writing is not acceptable. Assignments can be presented using any word processor such as Word or Latex, or can be neatly written by blue or black pen (but not by pencil).

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 6 August 2021