MATHS 1013 - Mathematics IM
North Terrace Campus - Semester 1 - 2014
General Course Information
Course Code MATHS 1013 Course Mathematics IM Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 5.5 hours per week Prerequisites At least a C- in SACE Stage 2 Mathematical Studies Incompatible Maths 1009, Maths 1010 Restrictions Mathematics IM is not available to students with an A- or better in both Mathematical Studies and Specialist Mathematics. Course Description This course provides the necessary additional mathematics to prepare students for MATHS 1011 Mathematics IA. The course contains an introduction to basic concepts and techniques of calculus and linear algebra, emphasising their inter-relationships and applications to the sciences and financial areas; introduces students to the use of computers in mathematics; and develops problem solving skills with a particular emphasis on applications.
Topics covered are: Calculus: differential calculus with applications; an introduction to differential equations; Algebra: complex numbers; vectors, linear equations and matrices; 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 introductory concepts in algebra, relating to vectors, linear equations, matrices and complex numbers.
- Demonstrate understanding of introductory concepts in calculus, relating to functions, the derivative and differential equations.
- 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 IM Student Notes.
- Lay: Linear Algebra and its Applications, 4th ed. (Addison Wesley Longman)
- 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 practice 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 53 Mid Semester Tests 2 9 Total 156
Learning Activities SummaryIn Mathematics IM 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. (Note that some of the "Algebra" topics are really related to calculus, but taught in the algebra stream.)
- Trigonometric Functions (4 lectures)
- Sine, cosine and tangent functions. Trig identities.
- Further trig functions. Applications to periodic phenomena.
- Vectors (6 lectures)
- Geometric and algebraic approaches to vectors in 3-d.
- Length, dot product, angle between vectors.
- Projections, cross product. Equations of lines and planes.
- Linear Equations and Matrices (6 lectures)
- Algebra of matrices, transpose.
- Systems of linear equations, row operations, reduced row echelon form.
- Geometric interpretation. Vector equations. Linear combinations and the span of a set of vectors.
- Polynomials (3 lectures)
- Real polynomials, graphs of quadratic, cubic and quartic polynomials.
- Factorization of polynomials. The Remainder Theorem.
- Complex Numbers (5 lectures)
- Algebraic and geometric properties. Polar form and De Moivre's Theorem.
- The Fundamental Theorem of Algebra. Zeros of real and complex polynomials.
- Functions (5 lectures)
- Domain, graph and range. Examples and applications of functions, including polynomials, rational functions, modulus function, piecewise defined functions.
- Exponential functions. Growth and decay.
- Combinations of functions, including composition.
- The Derivative (13 lectures)
- Rates of change. Limits and limit laws. Infinite and 2-sided limits.
- The derivative at a point, the derivative function.
- Interpretation and application of the derivative. Rules for differentiation.
- Derivatives of polynomial, exponential, trig functions and their combinations.
- Inverse functions. Logarithmic functions and their derivatives.
- Differential Equations (6 lectures)
- Antiderivatives and the definite integral.
- Introduction to differential equations. Applications.
- Slope fields, Euler's method.
Tutorial 1: Degrees and radians, trig functions. Domain, range, graph of functions.
Tutorial 2: Trig identities. Modulus and exponential functions.
Tutorial 3: Trig graphs, vectors. Composite, rational, piecewise-defined functions.
Tutorial 4: Orthogonal vectors, projections. Limits.
Tutorial 5: Lines and planes. Derivatives.
Tutorial 6: Lines and planes. Matrix products. Differentiation rules.
Tutorial 7: Row operations. Applications of differentiation.
Tutorial 8: Systems of linear equations. Inverse functions.
Tutorial 9: Linear combinations. Polynomials. Antidifferentiation.
Tutorial 10: Polynomials, Remainder theorem. Differential equations.
Tutorial 11: Complex numbers. Euler's method.
Tutorial 12: De Moivre's Theorem, zeros and factors of polynomials. Logistic DE.
(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.
- Trigonometric Functions (4 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 Tests Summative and Formative 15% 1,2,3,4 Exam Summative 70% 1,2,3,4,6
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 Assignment 1 week 1 week 3 1.4% Assignment 2 week 2 week 4 1.4% Assignment 3 week 3 week 5 1.4% Assignment 4 week 4 week 6 1.4% Assignment 5 week 5 week 7 1.4% Assignment 6 week 6 week 8 1.4% Assignment 7 week 7 week 9 1.4% Assignment 8 week 8 week 10 1.4% Assignment 9 week 9 week 11 1.4% Assignment 10 week 10 week 12 1.4% Assignment 11 week 11 week 13 1.4% Mid Semester Test 1 week 7 10% Mid Semester Test 2 week 10 5%
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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