MATHS 1011 - Mathematics IA
North Terrace Campus - Semester 2 - 2015
General Course Information
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 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 Coordinator: Dr Adrian Koerber
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesOn successful completion of this course students will be able to:
- Demonstrate understanding of basic concepts in linear algebra, relating to matrices, vector spaces and eigenvectors.
- Demonstrate understanding of basic concepts in calculus, relating to functions, differentiation and integration.
- Employ methods related to these concepts in a variety of applications.
- Apply logical thinking to problem-solving in context.
- Use appropriate technology to aid problem-solving.
- 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. 3,4 An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 1,2,3,4,5 A proficiency in the appropriate use of contemporary technologies. 5 A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all
Required ResourcesMathematics IA Student Notes.
- Poole: Linear Algebra a Modern Introduction 4th ed. (Cengage Learning)
- Stewart: Calculus 7th ed. (international ed.) (Brooks/Cole)
Online LearningThis 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 ModesThis 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.
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 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.
- 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.
- 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.
- 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.
- Areas, summation notation. Upper and lower sums, area under a curve.
- Properties of the definite integral. Fundamental Theorem of Calculus.
- Revision of differentiation, derivatives of inverse functions.
- Logarithm as area under a curve. Properties.
- Exponential function as inverse of logarithm, properties. Other exponential and log functions. Hyperbolic functions.
- Substitution, integration by parts, partial fractions.
- Trig integrals, reduction formulae. Use of Matlab in evaluation of integrals.
- Riemann sums, trapezoidal and Simpson's rules.
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.
- Matrices and Linear Equations (8 lectures)
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 Task Task Type Weighting Learning Outcomes Assignments Formative 15% all Mid Semester Test Summative and Formative 15% 1,2,3,4 Exam Summative 70% all
Assessment Related RequirementsAn 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 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 6 15%
Assignments 1-11 are made up of a written component, worth a total of 5%, and an online (Maple TA) component, worth 10%.
- 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 turn-around time for feedback to students.
- Online Maple TA assignments provide instantaneous feedback to students.
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.
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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