MATHS 1012  Mathematics IB
North Terrace Campus  Semester 2  2014

General Course Information
Course Details
Course Code MATHS 1012 Course Mathematics IB 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 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 interrelationships 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: Demonstrate understanding of concepts in linear algebra, relating to vector spaces, linear transformations and symmetric matrices.
 Demonstrate understanding of concepts in calculus, relating to differential equations, limits and continuity, and Taylor series.
 Demonstrate understanding of introductory concepts in twovariable calculus.
 Employ methods related to these concepts in a variety of applications.
 Apply logical thinking to problemsolving in context.
 Demonstrate an understanding of the role of proof in mathematics.
 Use appropriate technology to aid problemsolving.
 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
 Lay: Linear Algebra and its Applications 4th ed. (Addison Wesley Longman)
 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 assessmentopportunities for students to practice 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.
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 55 Mid Semester Test 1 6 Total 156 Learning Activities Summary
In Mathematics IB 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 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, GramSchmidt 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.
 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, onesided 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 maxmin 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 1: Subspaces, linear independence. First order DEs.
Tutorial 2: Row, column and null space. Second order DEs.
Tutorial 3: Rank theorem. Distance, angle and orthogonality. Logistic equation. Orthogonality.
Tutorial 4: GramSchmidt process, projections, linear transformations. Limits, Squeeze Theorem.
Tutorial 5: Linear transformations: kernel, range, standard matrix. Limits, improper integrals.
Tutorial 6: Composition of linear transformations, conic sections.L'Hopital's rule. Discontinuities.
Tutorial 7: Eigenvalues, eigenvectors, diagonalisation. Newton's Method. Intermediate Value Theorem.
Tutorial 8: Standard form for conics and quadrics. Maxmin problems. Mean Value Theorem.
Tutorial 9: Functions of 2 variables, limits and continuity. Mean Value Theorems, graph sketching.
Tutorial 10: Limits, continuity, partial derivatives of functions of 2 variables. Taylor and Maclaurin polynomials.
Tutorial 11: Tangent planes to surfaces. Chain rule. Directional derivatives. Series, convergence.
Tutorial 12: Maximum rate of change. Classification of critical points. Taylor and Maclaurin series.
(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.
 Further Results on R^n (7 lectures)

Assessment
The University's policy on Assessment for Coursework Programs is based on the following four principles:
 Assessment must encourage and reinforce learning.
 Assessment must enable robust and fair judgements about student performance.
 Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
 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 item Distributed Due date Weighting Assignments 1 week 1 week 3 1.4% Assignments 2 week 2 week 4 1.4% Assignments 3 week 3 week 5 1.4% Assignments 4 week 4 week 6 1.4% Assignments 5 week 5 week 7 1.4% Assignments 6 week 6 week 8 1.4% Assignments 7 week 7 week 9 1.4% Assignments 8 week 8 week 10 1.4% Assignments 9 week 9 week 11 1.4% Assignments 10 week 10 week 12 1.4% Assignments 11 week 11 week 13 1.4% Mid Semester Test week 7 15% Assignments 111 are made up of a written component, worth a total of 5%, and an online (Maple TA) component, worth 10%.
Submission
 All written assignments are to be submitted at the designated time and place with a signed cover sheet attached.
 Late assignments will not be accepted without a medical certificate.
 Written assignments will have a one week turnaround time for feedback to students.
 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 149 Fail P 5064 Pass C 6574 Credit D 7584 Distinction HD 85100 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 ongoing 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.

Student Support
 Academic Support with Maths
 Academic Support with writing and speaking skills
 Student Life Counselling Support  Personal counselling for issues affecting study
 International Student Support
 AUU Student Care  Advocacy, confidential counselling, welfare support and advice
 Students with a Disability  Alternative academic arrangements
 Reasonable Adjustments to Teaching & Assessment for Students with a Disability Policy

Policies & Guidelines
This section contains links to relevant assessmentrelated policies and guidelines  all university policies.
 Academic Credit Arrangement Policy
 Academic Honesty Policy
 Academic Progress by Coursework Students Policy
 Assessment for Coursework Programs
 Copyright Compliance Policy
 Coursework Academic Programs Policy
 Elder Conservatorium of Music Noise Management Plan
 Intellectual Property Policy
 IT Acceptable Use and Security Policy
 Modified Arrangements for Coursework Assessment
 Student Experience of Learning and Teaching Policy
 Student Grievance Resolution Process

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