MATHS 1011 - Mathematics IA

North Terrace Campus - Semester 2 - 2016

This course, together with MATHS 1012 Mathematics IB, 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: functions of one variable, differentiation, the definite integral, and techniques of integration. Algebra: Linear equations, matrices, the real vector space determinants, optimisation, eigenvalues and eigenvectors; applications of linear algebra.

  • General Course Information
    Course Details
    Course Code MATHS 1011
    Course Mathematics IA
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 5.5 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites At least a C- in both SACE Stage 2 Mathematical Studies and SACE Stage 2 Specialist Mathematics; or a 3 in International Baccalaureate Mathematics HL; or MATHS 1013
    Incompatible ECON 1005, ECON 1010, MATHS 1009, MATHS 1010
    Assumed Knowledge At least B in both SACE Stage 2 Mathematical Studies and Specialist Mathematics. Students who have not achieved this standard are strongly advised to take MATHS 1013 Mathematics IM before attempting this course.
    Course Description This course, together with MATHS 1012 Mathematics IB, 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: functions of one variable, differentiation, the definite integral, and techniques of integration. Algebra: Linear equations, matrices, the real vector space determinants, optimisation, eigenvalues and eigenvectors; applications of linear algebra.
    Course Staff

    Course Coordinator: Dr Adrian Koerber

    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 basic concepts in linear algebra, relating to matrices, vector spaces and eigenvectors.
    2. Demonstrate understanding of basic concepts in calculus, relating to functions, differentiation and integration.
    3. Employ methods related to these concepts in a variety of applications.
    4. Apply logical thinking to problem-solving in context.
    5. Use appropriate technology to aid problem-solving.
    6. 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)
    Deep discipline knowledge
    • informed and infused by cutting edge research, scaffolded throughout their program of studies
    • acquired from personal interaction with research active educators, from year 1
    • accredited or validated against national or international standards (for relevant programs)
    all
    Critical thinking and problem solving
    • steeped in research methods and rigor
    • based on empirical evidence and the scientific approach to knowledge development
    • demonstrated through appropriate and relevant assessment
    4,5
  • Learning Resources
    Required Resources
    Mathematics IA Student Notes.
    Recommended Resources
    1. Poole: Linear Algebra a Modern Introduction 4th ed. (Cengage Learning)
    2. Stewart: Calculus 8th ed. (metric version) (Cengage Learning)
    Online Learning
    This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, and sample solutions. Students should make appropriate use of these resources. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/

    This course also makes use of online assessment software for mathematics called Maple TA, which we use to provide students with instantaneous formative feedback.

  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on lectures to guide students through the material, tutorial classes to provide students with class/small group/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.
    Workload

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


    Activity Quantity Workload hours
    Lectures 48 72
    Tutorials 11 22
    Assignments 11 62
    Total 156
    Learning Activities Summary

    In Mathematics IA the two topics of algebra and calculus detailed below are taught in parallel, with two lectures a week on each.  The tutorials are a combination of algebra and calculus topics, pertaining to the previous week's lectures.

    Lecture Outline

    Algebra

    • Matrices and Linear Equations (8 lectures)
      • Algebraic properties of matrices.
      • Systems of linear equations, coefficient and augmented matrices. Row operations.
      • Gauss-Jordan reduction. Solution set.
      • Linear combnations of vectors. Inverse matrix, elementary matrices, application to linear systems.
    • Determinants (2 lectures)
      • Definition and properties. Computation. Adjoint.
    • Optimisation and Convex Sets (4 lectures)
      • Convex sets, systems of linear inequalities.
      • Optimization of a linear functional on a convex set: geometric and algebraic methods.
      • Applications.
    • The Vector Space R^n (4 lectures)
      • Definition. Linear independence, subspaces, basis.
    • Eigenvalues and Eigenvectors (5 lectures)
      • Definitions and calculation: characteristic equation, trace, determinant, multiplicity.
      • Similar matrices, diagonalization. Applications.
    Calculus
    • Functions (6 lectures)
      • Real and irrational numbers. Decimal expansions, intervals.
      • Domain, range, graph of a function. Polynomial, rational, modulus, step, trig functions, odd and even functions.
      • Combining functions, 1-1 and monotonic functions, inverse functions including inverse trig functions.
      Integration (5 lectures)
      • Areas, summation notation. Upper and lower sums, area under a curve.
      • Properties of the definite integral. Fundamental Theorem of Calculus.
      Revision of Differentiation (2 lectures)
      • Revision of differentiation, derivatives of inverse functions.
      Logarithmic and Exponential Functions (3 lectures)
      • Logarithm as area under a curve. Properties.
      • Exponential function as inverse of logarithm, properties. Other exponential and log functions. Hyperbolic functions.
      Techniques of Integration (6 lectures)
      • Substitution, integration by parts, partial fractions.
      • Trig integrals, reduction formulae. Use of Matlab in evaluation of integrals.
      Numerical Integration (2 lectures)
      • Riemann sums, trapezoidal and Simpson's rules.
    Tutorial Outline

    Tutorial 1: Matrices and linear equations. Real numbers, domain and range of functions.
    Tutorial 2: Gauss-Jordan elimination. Linear combinations of vectors.Composition of functions, 1-1 functions.
    Tutorial 3: Systems of equations. Inverse functions. Exponential functions.
    Tutorial 4: Inverse matrices. Summation, upper and lower sums.
    Tutorial 5: Determinants. Definite integrals, average value.
    Tutorial 6: Convex sets, optimization. Antiderivatives, Fundamental Theorem of Calculus.
    Tutorial 7: Optimization. Linear dependence and independence. Differentiation of inverse functions.
    Tutorial 8: Linear dependence, span, subspace. Log, exponential and hyperbolic functions.
    Tutorial 9: Basis and dimension. Integration.
    Tutorial 10: Eigenvalues and eigenvectors. Integration by parts, reduction formulae.
    Tutorial 11: Eigenvalues and eigenvectors. Tirigonometric integrals.
    Tutorial 12: Diagonalization, Markov processes. Numerical integration. 
    (Note: This tutorial is not an actual class, but is a set of typical problems with solutions provided.)

    Note: precise tutorial content may vary due to the vagaries of public holidays.

  • 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

    No information currently available.

    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course. Furthermore students must achieve at least 45% on the final examination to pass the course.
    Assessment Detail

    Tutorials 1-11 have a participation mark worth a total of 10%.

    Assignments 1-11 are made up of a written component, worth a total of 10%, and an online (Maple TA) component, worth 10%.

    Submission
    1. All written assignments are to be submitted at the designated time and place with a signed cover sheet attached.
    2. Late assignments will not be accepted without a medical certificate.
    3. Written assignments will have a one week turn-around time for feedback to students.
    4. Online Maple TA assignments provide instantaneous feedback to students.
    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.

  • 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 (http://www.adelaide.edu.au/policies/101/) 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.

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