MATHS 1012 - Mathematics IB

North Terrace Campus - Summer - 2022

This course, together with MATHS 1011 Mathematics IA, provides an introduction to the basic concepts and techniques of calculus and linear algebra, emphasising their inter-relationships and applications to engineering, the sciences and financial areas, introduces students to the use of computers in mathematics, and develops problem solving skills with both theoretical and practical problems. Topics covered are: Calculus: Differential equations, sequences and series, power series, calculus in two variables. Algebra: Subspaces, rank theorem, linear transformations, orthogonality, eigenvalues and eigenvectors, singular value decomposition, applications of linear algebra.

  • General Course Information
    Course Details
    Course Code MATHS 1012
    Course Mathematics IB
    Coordinating Unit Mathematical Sciences
    Term Summer
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 5 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites MATHS 1011
    Incompatible ECON 1005, ECON 1010, MATHS 1004, MATHS 1009, MATHS 1010
    Assessment Ongoing assessment, exam
    Course Staff

    Course Coordinator: Dr Stuart Johnson

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    On successful completion of this course students will be able to:
    1. Demonstrate understanding of concepts in linear algebra, relating to vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors and diagonalisation.
    2. Demonstrate understanding of concepts in calculus, relating to differential equations, sequences, series and convergence and multivariable calculus.
    3. Employ methods related to these concepts in a variety of applications.
    4. Apply logical thinking to problem-solving in context.
    5. Demonstrate an understanding of the role of proof in mathematics.
    6. Use appropriate technology to aid problem-solving.
    7. Demonstrate skills in writing mathematics.
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)

    Attribute 1: Deep discipline knowledge and intellectual breadth

    Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.


    Attribute 2: Creative and critical thinking, and problem solving

    Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.

  • Learning Resources
    Required Resources
    A set of Course Notes are available as a PDF on the MyUni site for this course. (More specific details will be provided on MyUni.)

    Recommended Resources
    1. Poole, D., Linear Algebra: a Modern Introduction 4th edition (Cengage Learning)
    2. Stewart, J., Calculus 9th edition (metric version) (Cengage Learning)
    While it is not compulsory to buy the texts, they are recommended, especially for students who want extra support in this course. Copies of these text books may be purchased from the publisher and electronic versions are also available for purchase from the publisher. Copies of both books are available in the Barr Smith Library for short term borrowing and reference.

    Online Learning

    This course uses MyUni extensively and exclusively for providing electronic resources, such as lecture notes and videos, assignment and tutorial questions, and worked solutions. Students should make appropriate use of these resources. MyUni can be accessed here:

    This course also makes use of online assessment software for mathematics called Mobius, which we use to provide students with instantaneous formative feedback. Further details about using Mobius will be provided on MyUni.

    Students are also reminded that they need to check their University email on a daily basis. Sometimes important and time-critical information might be sent by email and students are expected to have read it. Any problems with accessing or managing student email accounts should be directed to Technology Services.

  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on lecture videos to guide students through the material, tutorial classes to provide students with small group and individual assistance, and a sequence of written and online assignments to provide formative assessment opportunities for students to practise techniques and develop their understanding of the course.

    We provide additional support via discussions on MyUni and via "drop-in" help.

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    Activity Quantity   Workload hours
    Lectures 48 84
    Tutorials 11 11
    Assignments 11 55
    Mid Semester Test 1 6
    Total 156
    Learning Activities Summary

    Mathematics IB Summer is taught double-time compared to Semester 1 or 2. The two topics of algebra and calculus detailed below are taught in parallel, with four lectures a week on each. There are two tutorials per week and two assignments per week, one each on algebra and calculus.

    Lecture Outline


    • Revision: Bases, transpose and dimension (2 lectures)

    • Row space, null space, column space, rank theorem (3 lectures)
    • Linear Transformations (5 lectures)
      • Definition and basic properties.
      • Kernel and range.
      • Standard matrix.
      • Dimension theorem.
    • Orthogonality, Gram-Schmidt (4 lectures)
      • Inner product and orthogonality.
      • Gram-Schmidt process.
      • Orthogonal projection.
      • Ortogonal transformations and matrices.
    • Eigenvalues, eigenvectors and diagonalisation (6 lectures)
      • Application: Google PageRank.
      • Eigenvalues and eigenvectors.
      • Properties of eigenvalues.
      • Diagonalisation.
      • Symmetric matrices.
      • Orthogonal diagonalisation.
    • Singular value decomposition and applications (3 lectures)


    • Differential Equations (5 lectures)
      • First order separable equations.
      • Phase lines.
      • First order linear equations.
      • Euler and Runge-Kutta methods.
      • Second order constant coefficient homogenous equations.
      • Second order constant coefficient non-homogenous equations.
    • Sequences, Series and Convergence (10 lectures)
      • Sequences and applications.
      • Series and applications.
      • Power series, Taylor series.
      • Radius of convergence.
    • Multivariable Calculus (7 lectures)
      • Surfaces in three dimensions.
      • Functions of several variables including polar coordinates.
      • Limits and continuity in two variables.
      • Partial derivatives.
      • Directional derivatives and the gradient.
      • Extrema of functions of two variables.
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Assessment for this course will consist of regular assignments, one mid-semester test and a final exam.

    All assessment will be conducted online, including the mid-semester test and final exam.

    Assessment Task Task Type Weighting Learning Outcomes
    Written Assignments Formative and Summative 12.5% all
    Mobius Assignments Formative and Summative 12.5% all
    Mid Semester Test Summative and Formative 15% 1,2,3,4
    Final Exam Summative 60% 1,2,3,4,5,6
    Assessment Detail
    Precise details of the nature and timing of all assessment components will be provided on the MyUni site for this course.
    See MyUni for comprehensive details regarding online assignment submission, our late policy etc.
    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    FNS   Fail No Submission
    F 1-49 Fail
    P 50-64 Pass
    C 65-74 Credit
    D 75-84 Distinction
    HD 85-100 High Distinction
    CN   Continuing
    NFE   No Formal Examination
    RP   Result Pending

    Further details of the grades/results can be obtained from Examinations.

    Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

    Final results for this course will be made available through Access Adelaide.

    Replacement and Additional Assessment Examinations (R/AA Exams)

    Students are encouraged to read the University's R/AA exam information on the University’s Examinations webpage here:
  • Student Feedback

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy ( course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

  • Student Support
  • Policies & Guidelines
  • Fraud Awareness

    Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student’s disciplinary procedures.

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