MATHS 1012 - Mathematics IB

North Terrace Campus - Summer - 2014

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: Applications of the derivative; functions of two variables; Taylor series; differential equations. Algebra: The real vector space, eigenvalues and eigenvectors, linear transformations and applications of linear algebra.

  • General Course Information
    Course Details
    Course Code MATHS 1012
    Course Mathematics IB
    Coordinating Unit School of Mathematical Sciences
    Term Summer
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 5.5 hours per week
    Prerequisites MATHS 1011
    Course Description 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: Applications of the derivative; functions of two variables; Taylor series; differential equations. Algebra: The real vector space, eigenvalues and eigenvectors, linear transformations and 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 concepts in linear algebra, relating to vector spaces, linear transformations and symmetric matrices.
    2. Demonstrate understanding of concepts in calculus, relating to differential equations, limits and continuity, and Taylor series.
    3. Demonstrate understanding of introductory concepts in two-variable calculus.
    4. Employ methods related to these concepts in a variety of applications.
    5. Apply logical thinking to problem-solving in context.
    6. Demonstrate an understanding of the role of proof in mathematics.
    7. Use appropriate technology to aid problem-solving.
    8. 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)
    Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all
    The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 4,5,6
    An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 1,2,3,4,5,6
    A proficiency in the appropriate use of contemporary technologies. 7
    A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all
  • Learning Resources
    Required Resources
    Mathematics IB Student Notes.
    Recommended Resources
    1. Lay: Linear Algebra and its Applications 4th ed. (Addison Wesley Longman)
    2. Stewart: Calculus 7th ed. (international ed.) (Brooks/Cole)
    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 6 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, one on algebra and one on calculus.

    Lecture Outline

    Algebra

    • Further Results on R^n (7 lectures)
      • Revision of subspaces, linear independence, basis, dimension.
      • Row and column space, null space of a matrix. Rank and rank theorem.
      • Scalar product, distance. Length and angle. Orthogonality, Gram-Schmidt process.
    • Linear Transformations (4 lectures)
      • Kernel and range, the matrix of a linear transformation.
      • Dimension theorem.
    • Symmetric Matrices (4 lectures)
      • General quadratic equation in 2 variables, conics.
      • Revision of eigenvalues, eigenvectors and diagonalization.
      • Orthogonal diagonalization of real symmetric matrix. Applications.
    Calculus
    • Differential Equations (5 lectures)
      • First order DE's: separable, linear.
      • Linear second order DE's with constant coefficients. Applications.
      • Modelling. The logistic equation.
    • Limits (5 lectures)
      • Definition and uniquess of limit, limit laws.
      • Squeeze Theorem, trigonometric limits, one-sided limits, limits at infinity, unbounded functions.
      • Improper integrals. Linear approximation. L'Hopital's rule.
    • Continuity (2 lectures)
      • Continuity, classification of discontinuities, continuity and differentiation.
      • Intermediate Value Theorem. Newton's Method.
    • Applications of the Derivative (5 lectures)
      • Extrema of continuous functions, applied max-min problems.
      • Rolle's Theorem, Mean Value Theorem and consequences.
      • Graphing: First and second derivative tests, concavity and inflection points.
    • Taylor Series (6 lectures)
      • Taylor and Maclaurin polynomials, Taylor's Theorem, error terms.
      • Power series, geometric series, convergence of power series, interval and radius of convergence.
      • Taylor and Maclaurin series, binomial series, differentiation and integration of power series.
    • Calculus of More than One Variable (8 lectures)
      • Surfaces: planes, cylinders, quadric surfaces.
      • Functions of more than one variable, limits and continuity.
      • Partial derivatives, derivatives of higher order. Chain rules, directional derivative, gradient.
      • Tangent planes, local maxima and minima. Second derivative test for functions of 2 variables.
    Tutorial Outline

    Tutorial 1: Algebra: Subspaces, linear independence. Row, column and null space. Calculus: First order DEs. Second order DEs.

    Tutorial 2: Algebra: Rank theorem. Distance, angle and orthogonality. Orthogonality. Gram-Schmidt process, projections, linear transformations. Calculus: Logistic equation. Limits, Squeeze Theorem.

    Tutorial 3: Algebra: Linear transformations: kernel, range, standard matrix. Composition of linear transformations, conic sections. Calculus: Limits, improper integrals. L'Hopital's rule. Discontinuities.

    Tutorial 4: Algebra: Eigenvalues, eigenvectors, diagonalisation. Standard form for conics and quadrics. Calculus: Newton's Method. Intermediate Value Theorem. Max-min problems. Mean Value Theorem.

    Tutorial 5: Functions of 2 variables, limits and continuity. Limits, continuity, partial derivatives of functions of 2 variables. Mean Value Theorems, graph sketching. Taylor and Maclaurin polynomials.

    Tutorial 6: Tangent planes to surfaces. Chain rule. Directional derivatives. Maximum rate of change. Classification of critical points. Series, convergence. Taylor and Maclaurin series.

    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
    Assessment Task Task Type Weighting Learning Outcomes
    Assignments Formative 15% all
    Mid Semester Test Summative and Formative 15% 1,2,4,5
    Exam Summative 70% 1,2,3,4,5,6,8
    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
    Assessment itemDistributedDue dateWeighting
    Assignments 1 week 1 week 2 2.5%
    Assignments 2 week 2 week 3 2.5%
    Assignments 3 week 3 week 4 2.5%
    Assignments 4 week 4 week 5 2.5%
    Assignments 5 week 5 week 6 2.5%
    Assignments 6 week 6 week 7 2.5%
    Mid Semester Test week 4 15%

    Assignments 1-6 are made up of a written component, worth a total of 5%, 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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  • Policies & Guidelines
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